--

•

ASPECTS OF INSTITUTIONAL MOBILITY PATTERNS

OF CHEMISTS IN HIGHER EDUCATION

by

Ii:un Su1 Lee

Institute of StatisticsMimeograph Series No. 616li'ebruary 1910

I

"

)e.ABSTRACT

LEE, EON Sut. Aspects of Institutional Mobility Patterns of Chemists

in Higher Education. (Under the direction of CHARLES HORACE HAMILTON

and CHARLES HARRY PROCTOR).

This study is concerned with mobility of scholars among colleges

and universities in the academic training phase as well as in the

postdoctoral phase of professional careers. Patterns of mobility are

examined in terms of horizontal and vertical dimensions of academic

stratification system: geographic location and prestige structure of

institutions. The necessary data for the study are obtained from the

American Chemical Society's Directory of Graduate Research.

Mobility patterns of chemists among the 86 major institutions of

higher education is analized based on a random sample of 1,128 scholars

from seven successive directories covering the 1955-1967 period. Three

types of mobility are identified by linking such points of career

development as baccalaureate graduation, doctorate graduation, and

employment status. Inferences about patterns of these types of mobil­

ity are made by examining the departures of the observed from the

expected frequencies of movements. The expected frequencies are de-

rived from the f1 quasi-perfect mobilityfl model presented by Goodman.

This model assigns zero frequencies along the main diagonal of the

mobility matrix and, subject to this constraint, calculates expected

values on the assam.Ption of no assooia.tion between the institution of

origin and the institution of destination.

The mobility from the bacoalaureate to the doctorate training is

oharacterized by stronger tendenoies toward regionalism than toward

prestige level homoge~eity. The regionalistio tendenoies appear to be

stronger for the institutions at the lower prestige level. The mobil­

ity from the doctoral institution to the institution of employment is

also oriented toward stronger regionalistic tendencies than selective

prestige level tendencies. Thus, the academic stratification system

can be said to be a set of regional hierarchies rather than a rigid

prestige hierarchy. It is noted that downward mobility is more common,

especially at earlier stages of postdoctoral careers. Institutions at

the lower prestige level appear to have a relatively higher rate of

inbreeding and a stronger regionalistic orientation. Although patterns

are less distinctive than the tio'O previous types of mobility due in

part to insufficient number of cases, the postdoctoral job mobility

patterns are characterized by about equally strong tendencies toward

regionalism and prestige level homogeneity. The regionalistic tenden­

cies are relatively stronger for institutions at the lower prestige

level and the tendencies toward homogeneous prestige were more operative

for institutions at the higher prestige level.

Implications of these mobility patterns for regional inequalities

in the quality of higher education and interregional cultural differ­

ences are suggested. Regional tendencies would impose restrictions on

the development of institutions at the lower spectrum of quality and

newly emerging universities. Regions where higher education is compar­

atively less effective are likely to remain so if mobility is allowed

to remain the primary equilibrium force.

A regression analysis using pair variables (mobility indicator and

distance between institutions) and point variables (institutional

characteristics) is performed to study the implied relationships and to

examine implications for mathematicaJ. model building. An examination

•-.

~.

of the residuals reveals a need for modifying extreme outliers or for

disaggregating the mobility into logical components for separate

analyses.

It is found that there is a high positive intraclass co=elation

among the residuals, which appears to be the reflection of structural

effects of the mobility system. Therefore models such as gravity models

~Ihich assume the independence among the pairwise interchanges of mobil­

ity seems to.be inappropriate. An applica~ion of the systems theory

approach seems to offer some help in this line of further investiga­

tion.

•

~.

ASPECTS OF INSTITUTIONAL MOBILITY PATTERNS OF CHEMISTS

IN HIGHER EDUCATION

by

EUN SUL LEE

".

A thesis submitted to the Graduate Faculty ofNorth Carolina State University at Raleigh

in partial fulfillment of therequirements for the Degree of

Doctor of Philosophy

DEPARTMENT OF SOCIOLOGY AND ANTHROPOLOGY

and

DEPARTMENT OF EXPERIMENTAL STATISTICS

RALEIGH

1 9 1 0

)

APPROVED BY:

Co-chairman of Advisory Committee Co-chairman of Advisory Committee

ii

:BIOGRAPHY·

The author was born September 19, 1934, in Kongju, South Choong-

chong, Korea. He reoeived his elementary and middle sohool eduoation

in Kongju and graduated from Chongju High Sohool, Chongju, Korea. In

1957, he reoeived the :Bachelor of Arts degree in Sooiologyfrom Seoul

National University, Korea. He was employed by the Christian Children's

Fund, Ino. until he oame to the United States for graduate study in

1962.

While studying at the University of Kentuoky, the author was

granted a graduate research assistantship. He reoeived the Master of

Arts degree in Sooiology from the University of Kentuoky in 1964. He,

transferred to North Carolina State University at Raleigh for further

graduate stUdy in the oo-major program in Sociology (Demography) and

Experimental Statistics. He was employed by the North Oarolina :Board

of Higher Eduoation as Research Assooiate and Direotor of Statistioal

Services from June 1966 to August 1969. He aocepted a position as

Researoh Demographer with The University of Texas, School of Publio

Health at Houston effeotive September 1, 1969.

The author married Chong :Mahn Lee in 1964, and they have one

daughter, Margaret Juhae, who was born April 26, 1966 in Raleigh,

North Oarolina.

iii

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation to

Professors C. Horace Hamilton and Charles H. Proctor for their skillful

guidance throughout the period of the graduate study, espeoia.lly in the

preparation of this dissertation. Appreoiation is also extended to the

other members ot the advisory' oommittee, Drs. Glenn C. McCann and F. E.

McVay, for reading the manuscript and making helpful suggestions.

Speoial gratitude is expressed to Dr. B. Ro Stanerson, exeoutive

seoretary, American Chemical Sooiety, for making available the old

direotories of the Society and to Professor O. D. Dunoan and J. Michael

Coble of Population Studies Center, University ot Miohigan, for prOVid­

ing computer programs used in this study.

The author is grateful to the members of North Carolina Board of

Higher Eduoation staff (former Director, Dr. Howard R. Boozer, and

present Director, Dr. Cameron P. West) who inspired the present study

and gave him oontinued enoouragement in the completion ot this study.

Finally, the author expresses his thanks to his wite and daughter

tor their patience and sacrifice during the oourse ot this study.

iv

TABLE OF CONTENTS

Page

LIST OF TABLES. • • • • • • • • • • • • • • • • • • • • • • • • vi

LIST OF FIGURES • • • • • • • • • • • • 0 • • • • 0 • • • • • • viii

INTRODUCTION •• • • • • • • • • • • • • • • • • • • • • • • .. .. 1

The Problem • • • • • • • • • • • • • • • • • • • • • • •The Purpose .Signifioanoe of the Study ............... ••••The Data • • • .. • .. • • .. • • • • • • • • • .. • • • • ....Organization of the Thesis • • • .. .. .. • • .. .. .. • .. .. .. •

• •.. ... .· ..· ..

12345

REVIEW' OF LITERATURE .... • • • • • • • • • • • • • 0 • • • 7

Migration Theory • .. .. .. .. .. .. .. .. • • • .. .. • • .. • .. .. • .. .. 7Migration Models .. • .. .. .. .. .. • • .. .. .. .. .. .. .. • .. .. .. .. .. • 10Studies ot College Faoulty Mobility .. .. .. .. .. • • • .. • .. • .. 17

STu.DY PERSPECTIVE • 0 • • • • • • • • • • • • • • • • • • • • • 23

Frame of Referenoe • .. • .. .. • • .. .. .. • .. .. .. • .. .. • .. • • ..Hypotheses .. .. .. • .. .. .. • • .. .. .. • .. • .. .. .. • .. .. .. .. .. .. ..Definition of Mobility .. .. .. • • .. .. • .. .. • .. .. .. • • .. .. .. ..Sampling Prooedures • .. .. .. .. .. .. .. • .. .. ..Methods of Analysis • .. • • .. .. .. • • .. .. .. .. .. .. ..

2326272830

General Desoription of Data .. .. .. .. .. • .. • .. .. • .. .. • .. • ..Baooalaureate to Dootorate MObility .. • .. .. • , .. .. .. .. .. .. ..Dootorate to Employment Mobility.. • .. • • .. .. .. .. .. .. • • .. •Postdootoral Job Mobility .. .. .. .. .. .. • .. , .. • .. .. .. • .. .. ..

ANALYSIS OF MOBILITY' PATTERNS • • • • • • • • • • • •• • • • • • 35

35384755

REGRESSION ANALYSIS .. .. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 61

Effeots of Distanoe 62Effeots of Prestige and Compensation .. .. .. .. .. .. .. • .. .. .. .. .. 66Examination of Residuals .. .. .. • .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 69Implioations for MathematiQal Model Building .. .. .. .. .. • • • .. 77

.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .sm-1MARY AND CONCLUSIONS

• • • • •

• • • • •

79

85

91.. ... .. .

.. .. ..

. ..

.. ..

.. ..... ... ..

. .. .. .... .... ..

.. .... .. .. ..

LIST OF B.EFERENCES •

APPENDICES • .. • •

v

TABLE OF CONTENTS (continued)

Page

APPENDIX A. Institutions Included in the Study • • • • • • • 91APPENDIX B. Regiona.l and Prestige Groupings of Institutions. 94APPENDIX C. A Note on the Method Used in Ca.lculating

Expected Frequencies in MObility Matrix • • • • 96APPENDIX D. Statistioal Tables ••••••••••••••• 100

vi

LIST OF TABLES

Page

Study population and selection of sample • • • • • • • • • 29

2. General characteristics of chemists sampled from doctoraldegree granting institutions, 1955-1967 • • • • • • • • • 36

3. Baccalaureate to doc'torate mobility patterns of chemistsamong the 86 major institutions of higher education. • • 39

4. Analysis of regional differences in baccalaureate todoctorate mobility patterns among the 86 majorinstitutions of higher education ••••••••• • • 0 42

5. Analysis of prestige level differences in bacoalaureate todoctorate mobility patterns of chemists among the 86major institutions· of higher eduoation •• • • • • • • • 44

6. Analysis of trends in baocalaureate to dootorate mobilitypatterns of ohemists among the 86 major institutions ofhigher education • • • • • • • • • • • • • • • • • • • • 46

7. Dootorate to employment mobility patterns of chemists amongthe 86 major institutions of higher eduoation • • • • • • 48

8. Analysis of regional differences in dootorate to employmentmobility patterns of chemists among the 86 major .institutions of higher eduoation • • • • • 0 • • • • • • 50

9. Analysis of prestige level differenoes in dootorate toemployment mobility patterns of ohemists among the 86major institutions of higher education • • • • • • • • • 52

100 Analysis of trends in doctorate to employment mobilitypatterns of chemists among the 86 major institutionsof higher education • • • • • • • • • • • • 0 • • • • • • 54

11. Postdoctoral job mobility patterns of chemists among the86 major institutions of higher education • • • • • • • • 56

12. Analysis of regional differenoes in postdoctoral jobmobility patterns of chemists among the 86 majorinstitutions of higher education ••••••••••

Analysis of prestige level differences in postdoctoraljob mobility patterns of chemists among the 86 majorinstitutions of higher education • • 0 • • • • • • •

• •

• •

58

59

vii

LIST OF TABLES (continued)

Page

14. Analysis of trends in postdootoral job mobility patternsof ohemists among the 86 major institutions of highereduoation .. • • • • It • • • .. • • • • .. .. • • • • • .. ... 59

15. Regression analysis for baooalaureate to dootoratemobility of chemists among the 86 major institutions ofhigher eduoation .. .. .. .. .. .. It • .. • It • • • .. • • • .... 6;

16. Regression analysis for dootorate to employment mobilityof chemists among the 86 major institutions of highereduoation .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. • • .. • • • .. • 64

18.

Regression analysis for postdootoral job mobility ofchemists among the 86 major institutions of highereduoation .. .. .. .. .. .. .. .. .. .. .. .. • .. .. • • • • .. .. ..

Differenoes of residuals and estimation of oorrelationfor the unordered pair regression .. .. • .. .. • • • .. ..

Differenoes of residuals and estimation of correlationfor the ordered pair regression .. .. .. .. .. • • .. • .. ..

.. ..

.. ..

• •

65

75

76

viii

LIST OF FIGURES

1. A typology of interinstitutional mobility components • . ., .Page

37

2. Distributions of residuals based on the standard errorof estimate for two types of regression analyses •••• 70

_e

Scatter diagrams of residuals against the fitted valuesfor regression analyses of baccalaureate to doctoratemobility • • • • • • • • • • • • • 0 • • 0 • • • • • • • 72

INTRODUCTION

The Problem

Institutional mobility of college and university professors is

rather high. Some eleven percent of teaching faculties in degree-grant­

ing institutions were newly arrived from another educational institu­

tion in the 1962-63 academic year (Dunham.ll~., 1966). There was

another ten percent newly employed in these institutions in that year.

This high rate of mobility is undoubtedly related to the well-documented

faculty shortage (McGrath, 1961; Porter, 1965; Brown, 1967, Pl'. 10-22;

Rogers, J. F., 1967). The increasing demand for faculty results from

rapidly increasing college enrollments which are a response to the

greatly increased demand for higher education and the increasing

societal requirement for research. Increasing faculty mobility has be­

come a serious problem for educational planners and administrators in

assessing the supply of the faculty work force. Enrollment projections

placing the total at nine million in 1975, an increase of nearly four

million from 1965 (American Council on Education, 1968) lead us to

expect the demand, and hence faculty mobility, to continue at a high

rate in the foreseeable future.

Information about the supply of the faculty work force, as in any

demographic studies, could be reduced to three basic processes: births,

deaths, and migration. Although a reasonable amount of information

about ~aculty births," such as new degrees conferred, and about "faculty

deaths," such as retirement and actual mortality, is usually aVailable,

information about mobility is grossly inadequate. To describe, and

more importantly, to project the supply and location of the faculty work

2

force, information about its mobility is essential, increasingly so in

an increasingly mobile aoademic oommunity.

The Purpose

The movement of scholars from one institution to another can be

seen as the outcome of a complex individual deoision making prooess

under social constraints. Attraction and retention of an individual

in an institution beoomes a funotion of the oompatibility between indi­

vidual conditioning and expeotations on the one hand and the charaoter­

istios of the sooial system of the institution on the other. Inter­

institutional mobility oan be studied from several different perspeo­

tives. The foous of study oan be plaoed on the individual in a

oolleotivity. The problem may be formulated to understand motivations

for a move. The mobility oan also be studied in terms of institutional

attraotiveness~ The problem may be posed to understand how institutions·

of higher eduoation are attraoting scholars and how they are retaining

them. The institutional mobility oan also be studied from the stand­

point of the total eduoational system.

The foous of the present study is on the total educational system.

There is a need to understand how institutions of higher education are

interaoting with one another in the exchange of scholars. The purpose

of this study is to desoribe and analyze patterns of migratory movements

of soholars among oolleges and universities with the ultimate aim of

developing a mathematioal model whioh oan satisfaotorily prediot inter­

institutional mobility.

3

Significance of the Study

Mobility of professionals among colleges and universities is of

special interest and significance not only to students of population but

also to college administrators, educational planners and policy makers.

Development of all aspects of a modern society is intimately bound up

with the education of adequately trained manpower and the efficient and

effective use of their talents. College administrators are always con­

cerned with the effectiveness of the institution. Does faculty mobility

improve the effectiveness of the educational institution in performing

its function of preserving, disseminating, and increasing knowledge?

Educational planners and policy makers are concerned with the effective­

ness of the total educational system. Does interinstitutional mobility

improve the effectiveness of the total higher educational system in

fulfilling its mission? While maximizing institutional effectiveness

will tend to maximize the effectiveness of the total system, there may

be larger considerations which require examination from the standpoint

of the totality alone. While the present study is not addressed to such

broad questions, knowledge of significant trends and patterns in the

distribution of professionals among colleges and universities can be of

assistance to educational planners and policy makers in allocating

functions among institutions and in determining the strategy of geo­

graphic realignment with respect to educational and socioeconomic

development of regions ..

Comparatively little is known, of a quantitative nature, regarding

the mobility of professionals among colleges and universities. Even in

general population research the migration component remains a source of

great uncertainty, especially in population estimates and forecasts.

4

This uncertainty is founded in part on conceptual difficulties. The

events of migration are difficult to cast in the same frame of reference

as vital events. While thepopulation-at-risk in vital events is rela­

tively easy to define, migration as an event involves at least two

populations, one at the o:I,'igin and one at the destination of movement.

It is not at all clear which population is at risk, or how the migration

rate should be calculated. l These conceptual difficulties are coupled

with the lack of satisfactory data in the United States, although the

decennial census, supplemented by sample surveys, permits reasonable

estimates of migration. These circumstances challenge students of

population to search for new perspectives in migration research,.

The Data

Because as a rule it takes less research funds and time, secondary

analysis, as contrasted to interviewing a newly drawn sample, has become

increasingly prevalent in contemporary social science research. Of

course, the secondary analyst has no control over the questions which

were asked or not asked, and he must sometimes be frustrated by the

absence of a question or the classification of data in ways which in­

hibit their usefulness to him. However, the advantages of secondary

analysis often far outweigh its limitation. For this reason an attempt

was made to utilize existing data which would allow the analysis of

institutional mobility.

The massive data collected by the National Science Foundation for

the National Register of Scientific and Technical Personnel looked

~ut practical suggestions were made by Hamilton (1965).

5

promising for the present study. The data have been collected every two

years for the past fourteen years and some recent data. have been formed

into a longitudinal file covering such subjects as geographic mobility,

mobility among types of employers, and career patterns in terms of train­

ing and employment. Unfortunately, it was discovered that the identifi­

cation of college or university with which a scientist was affiliated

was not included in the longitudinal file, although such information

was collected on the original questionnaire.

Since no other satisfactory data were available, it was decided to

obtain a random sample from the directories of professional societies.

TWo criteria were used in selecting professional societies: (l) the

availability of old directories covering at leas·t the past te~n years

and (2) the inclusion of a sufficient number of d,ata items in ·the

directory. One of the-key data items ""Tas this institutional affilia­

tion of scientists. Most directories examin€.~d simply list the mailing

address for which the residential address is frequently given. Only

the American Chemical SocietJrt s Directory of Graduate Research met

these two criteria. The directory has been published every two years

since 1955. All the directories were availabll~ at the Society's

national office in Washington. A 25 percent remdom sample was obtained

from these directories. The sampling and recording of the data required

about 20 man-days. The detailed sampling proced~ures will be described

later.

Organization of the Thesis

This thesis is prese~ted under six major headings. The present

introduction is followed b:!y an extensive review o£. ~elated literature

6

in "three areas of interest: major migration researches, migration models

and methodology, and studies of oollege faoulty mobility. The study

perspective is presented to describe a frame of referenoe, hypotheses,

definition of mobility, sampling prooedures, and methods of analyses.

The next seotion describes analyses of mobility patterns by utilyzing

regional and prestige groupings of institutions. Three different types

of mobility are discussed: baccalaureate to doctorate, doctorate to

employment, and postdoctorate job mobility. A regression analysis is

performed to detect any relationships between interinstitutional

mobility and some independent variables, and to see whether suoh

relationships could be used in developing a model to forecast future

mobility. This is followed by a section oontaining the summary and

conclusions.

7

REVIEW OF LITERATURE

Migration Theory

Migration is oonsidered to be one of three major population

prooesses, but it differs fundamentally from the other two: mortality

and fertility. Lacking a biological basis, migration is neither in­

evitable like death nor essential for the survival of a society like

reproduction. It is a more distinctively human activity occuring in

a social and cultural context. "The motives for which men migrate are

far more heterogeneous than their attitudes toward death or childbear­

ing" (Wrong, 1962, p. 82). Due to its oomplexity, migration remains to

be least understood of the three major population processes, and it is

often the major unknown component of population estimates and forecasts.

The field of migration study is divided into two branches: inter­

national migration and internal migration - movements of people within

national boundaries. Internal migration poses more of a theoretical

problem than international migration due to the fact that the latter

has been inspired by political and religious conflicts, while the former

takes place freely within national boundaries.

The first systematic study of migration was made by Ravenstein in

England in the late 19th oentury. He was concerned with producing

counter-evidence to a remark that migration appeared to go on without

any definite law. His two celebrated papers on "the laws of migration"

(Ravenstein, 1885 and 1889) can be summarized under the following head­

ings: (1) migration and distance; (2) migration by stages; (3) migra­

tion stream and counterstream; (4) urban-rural differences in propensity

to migrate; (5) predominance of females among short-distance migrants;

..

8

(6) technology m1d migration; and (7) dominance of economic motive. He

noted that the title of papers "ras ambitiously headed and warned that

"laws of population, and economic laws generally, have not the rigidity

of physical lavlS."

Ravensteinfs laws of migration provided the starting point for

work in migration theory. "In the three-quarters of a century "1hich

have passed, Ravenstein has been much quoted and occasionally challeng­

ed. Eut, while there have been literally thousands of migration studies

in the meantime, few additional generalizations have been advance~'(Lee,

1966, p. 48).

A review of classic research literature since Ravenstein seems to

lead to the following three points: (1) there is a marked difference

in the various characteristics of migration streah1S between diffe~ent

types of areas or groups - migration differentials or selectivity;

(2) the volume of migration between pairs of areas is positively re­

lated to the populations of the t\vO areas and negatively to the distance

between them; and (3) mi[,Tation can be interpreted as an effort to

maximize socioeconomic opportunities. These three classical points are

ordinarily presented by summary descriptions of migration data with

little attempts to generalize and relate the findings to a larger body of

social theory.

Most studies on differential migration focused upon the character­

istics of migrants with little reference to the volume of migration,

and few studies have considered the reasons for migration. The tradi­

tion of differential migration research reached its zenith in the study

by Eogue and Hagood (1953). I~y studies, however ended with a plea

for more data and more statistical ingenuity applied to existing data.

9

Most articles in migration theory have dealt with migration ro1d

distance and developed mathematioal formulations of the relationship.

The basic formulation was that the volume of migration between pairs of

cities stands .insome direct relation to the populations of the two

cities and in some inverse relation to the distance between the cities.

Perhaps the best known of recent theories of migration is Stouffer's

theory of intervening opportunities (1940 and 1960)0

Migration has been most frequently related to job-related variables.

Job opportunities were considered to be the driving mechanism ofmigra­

tiona A simple theory is that economic opportunities are ca.used by

differences in the marginal produotivity of labor force that, in turn,

are caused by differential fertility and technical development of some

areas. Non-economic opportunities were also considered in some studies.

But measurement of opportunities hampered studies in this line. The

measurement has been complicated especially by its social-psychological

details.

At least two recent essays made effo~ts to provide a theoretical

frame of reference for migration ~tudies. Lee (1966) attempted to

develop a general schema of migration and to formulate certain hypo­

theses in regard to the volume of migration, the establishment of stream

and counterstream, and the characteristics of migrants. :Beshera (1967)

attempted to interpret the past migration research literature from a

theoretical framework: household decision-making process within socio­

cultural oonstraints. :But, neither Lee's conceptual schema nor :Beshers'

theoretical perspective seems to suggest a new direction of migration

researoh.

10

Perhaps migration "is hardly a subject of rapid advance in popula­

tion study," as Davis (1959, p. 314) pu't it, due to the complexity of

migration phenomena and the heterogeneity of migration statistics.

This problem in migration study seems to be met by the following practi­

cal suggestions; (1) the limitation of research projects to a small

number of important hypotheses, or to selected types of areas and

streams of migration; (2) limitation of studies to specific population

categories; and (3) concentrating research on specific factors (Hamilton,

1961, p. 300).

Migration Models

A variety of mathematical models have been developed to describe

and analyze patterns of internal migration. In most models of migration,

one or more of the following general principles were considered: (1)

distance between the origin and destination is an obstacle to migration;

(2) the volume of migration depends on the size of populations involved;

(3) the differential attractiveness of the origin and alternative des­

tinations determine the volume of migration. The substance of these

principles finds its expression in the so-oalled gravity model, various

forms of which have been widely used to study social as well as physi­

oal prooesses (See Carrouthers, 1956).

Perhaps the first of all migration models was Zipf's well known

P1P2/D hypothesis (1946a and 1946b; Dodd, 1950). It is based on the

first two principles above and states that gross migration is directly

proportional to the product of the populations of the two regions

involved, and inversely proportional to the distance between the

regions. This model reads in formula:

M..... kP.P .(Do .)-a~J ~ J ~J

(1)

11

where M.. indicates gross migration between regions i and j, P stands~J

for the size of population, Dij is the distance between i and j, and k

and a are positive variables. This gravity formulation does not specify

the directional flows of migration and defines distance in a purely

geographic sense.

In his "intervening opportunities" model, Stouffer (1940) consid-

ered the directional flow of migration and redefined distance in terms

of the cumulated "sizes" of intervening destinations. In other words,

his model states that the number of persons going to a given distance

is directly proportional to the number of opportunities at that distance

and inversely proportional to the number of intervening opportunities.

StoufferOs model can be represented:

(2)

•

where Mi~j total migration from i to j.

Mi. total out-migration from i to all other places.

M.j

total in':'migration to.j from all other places.

MI total in-migration to places located inside the circle

whose diameter connects i and j.

Later, Stouffer (1960) took the logical step of recognizing inter-

vening "competing migrants." In other words, the attractiveness of

place j for migrants from place i depends on how many potential migrants

are closed to j than are the potential migrants in i. For this effect

a new term is introduced in the denominator of equation (2):

,:

"

12

where MO represents total migration from all places in the circle

centered on j with radius Dij~

Stouffer's model has been tested with generally supportive results

by a number of people (Bright and Thomas, 1941; Isbell, 1944;

Strodtbeck. 1949; Folger. 1953; Galle and Taeuber. 1966). But the main

difficulty with this model is the appearance of l!non~competitive oppor-

tunities." That is to say. different types of opporlunites are relevant

for different migrants and they can not be represented by one indicator.

Besides, the usefullness of Stouffer's model seems to be limited in

explaining migration. since it does not include any variables other

than concurrent migration flows.

A model which takes into consideration the attractiveness of each

place is developed in the Netherlands by Somermeijer (ter Heide. 1963).

He takes advantage of the Zipf's hypothesis and introduces the relative

attractiveness of places i and j. Attractiveness indices were formu-

lated from such variables as per capita income, percent unemployed,

degree of urbanization, recreational resources, and quality of dwell-

ings. The following two formulas describe migration streams in opposite

directions:

M. . = [!k + c(F. - F.)] P.P .(D. ')-a~-J J ~ ~ J ~J

M. . = r!k + c(F. - F.) ] P. P . (D .. )-aJ~~ L ~ J ~ J ~J

where F represents average combined value of attractiveness factors.

The sum of these two formulas gives gross migration which takes the

same form as Zipf's model in equation (1). Somermeijer tested his

model with good results on migration between Dutch provinces and

13

obtained correlation coefficients for the effeots of the attractiveness

factors on net migratio~ in the neighborhood of 0.9 by fitting the con-

stants by iteration.

In an effort to explain migratory flows in the United States,

Lowry (1966, pp. 11-22) introduces a model that incorporates economic

as well as "gravity" variables. As Lowry (1966, p. 11) stated, her

model is "closest in spirit to Somermeijer's." Lowry's model takes the

following form:

(6)

•

\'J'here Li,Lj • =number of persons in the nonagricultural labor force at

i and j, respectively.

Ui ' Uj = unemployment as a percentage of the civilian nonagri­

cultural labor force in i and j respectively.

Wi'Wj = hourly manufacturing wage, in dollars, in i and j

respectively•

.Lowry*s model is exceedingly convenient because it becomes linear

Ul1der logarithmic transformation as follows:

and this e:l>.']?ression is easy to use in a multiple linear regresElion. In

this model, attractiveness is proportional to the relative influences

of employment and of wages. Thus, it offers a very neat format for

data analysis and accessible interpretation as well. This model has

been tested bYLO\~ for national data and retested by Rogers (1968,

pp. 74-82) in California with minor modification, using "proxy" variables.

(8)

•

14

In her monograph, Lowry (i966, pp. 35-59) introduces another model

that is more useful as a tool for forecasting the migration component of

population change but less useful for scientific explanation. While the

first model considers the directional flows among various pairs of

metropolitan areas, the second model is addressed to the net effect of

migration upon metropolitan population growth. Lowry's second model is

patterned directly after the basic model developed by Blanco (1964).

The Lo~~'s version of Blanco model reads:

d11i = aO + aldPi + a2dQi + a3dAi

+ a4dEi + a5dI i + u

where dPi = net ohange in the number of residents 15-64 years of age in

the absence of migration ("natural inorease").

dQi = net ohange in oivilian nonagricultural employment.

dAi = net ohange in the number of Armed Foroes Personnel.

dEi = net ohange in the number of school enrollment 14-29 years

of age.

dIi = ohange (in percentage) in median inoome for "families and

unrelated indivieJ.uals."

By fitting this regression model, Lowry obtained an impressive value of

R2 = .9744, indicating that 97 peroent of the variance in migration

rates among Standard Metropolitan Statistical Areas could be accounted

for by regression on these independent variables.

Lowry's first model assumes that the interchange within eaoh pair

of places is independent of that within each other pair. This assump­

tion greatly simplifies calculation and helps to achieve certain practi­

cal objectives. But, the point of criticism stems from this assumption.

•

15

In this model, system effeots are disoarded so that any pair of oities

may be viewed as a oomplete system without regard to the migration flows

to and from the oities disoarded. In other words, a family of models

whioh use gravity prinoiples assumes a standard formula for pairwise

interaotions and the formula remains the same regardless of the struo­

ture of the partioular system, or even of the nature of the phenomenon

itself. Certainly one formula does not work for everything and inter­

aotion really is not invariant with structure and nature of the phenome­

non. The systems theory approaoh seems to offer a new direction in

model-building efforts in migration researoh. A model based on a

connected graph with network concepts will remedy the weakness of

gravity formulas. The systems theory models prove to be promising in

various fields (Ellis and Van Doren, 1966).

Some other models have also been developed in migration studies.

Additive models suoh as those of Price (1959) and Tarver (1961) calcu­

late migration probabilities by adding various attraotiveness factors

to form an attraotiveness index for eaoh region. In these models, the

"opportunities" faotors are introduoed only at the expense of losing

the distance and communication faotor. Thomlinson's model (1961)

provides a technique to control seven spatial variables including

distance, somewhat similar to standardization techniques in fertility

and mortality analyses. Thomlinson's model explains very little about

opportunities and its practical usefulness seems to be limited.

Paralleling the growing interest in quantitative analysis of migra­

tion phenomena has been the emergence of Markov chain theory as a

methodological tool for investigating social, industrial, and geographic

mobility. Mobility in this conception is represented by quantities

•

16

governing the time until movement and by others governing the choice of

a destination, the transition probabilities. With its great variety

and flexibility as uncovered by extensive mathematical development,

Markov chains seem to have a great potential in studying various tempor-

al changes of social phenomena. Markov chain models have been used to

examine intergenerational social mobility (Prais, 1955; Kemeny and

Snell, 1960, pp. 191-200), to study the movement of workers between

industries (Blumen, ~~., 1955) and to project future population

totals for Census Divisions in the United States (Tarver and Gurley,

1965). The mover-stayer model, a generalization of the Markov chain

model, was elaborated by Goodman (1961) to present consistent estimators

and some statistical methods of testing hypotheses concerning the model.

Although not fully tested, some further modification has been attempted

to use the Markov chain model in sociological and demographic research

(Coleman, 1964; MYers,~~., 1967; McGinnis, 1968).

By and large, Markov chain models are more useful in analyses of

past migration flows and of less practical use in efforts to forecast

future place-to-place movements. This may be because the .transition

__~ probabilities themselves are changing in time in ways that need to be,_~ji~'

better understood. However, Markovian concepts do provide a useful

description of the observed differential behavior of migrant cohorts at

a given point in time (See Rogers, 1968, pp. 86-104).

The flcl''' of any kind of quantifiable transactions, including migra-

tion, usually requ1rel'l some preliminary gross analysis to eliminate the

primary effects of the "size variable" before introducing other possible

explanatory variables. For this purpose a statistical "null model" was

17

developed by Savage and Deutsch (1960). The method develops a matrix

of expected or baseline data from assumptions of complete indifference

among the actors and measures the plus or minus differences between

this baseline value and the actual amount of transactions in each direc­

tion for every pair of actors. It thus removes gross size effects and

permits tentative inferences about the distribution of preferences

among pairs of larger groups of actors; about degree of clustering or

integration among actors; and about changes over time, if several

matrices are used. It thus locates interesting pairs or groups for

further study. This method was called a "null model" in the sense that

the departures from it are of primary interest. Savage and Deutsch

developed this model to analyze import-export data among North Atlantic

nations.

Subsequently Goodman (1963, 1964 and 1965) found that the methods

given by Savage and Deutsch require certain modifications and suggested

alternative methods that are preferable in some respects to the Savage­

Deutsch method. Goodman further presented a generalization of the model

appropriate when transactions between certain actors may be restricted.

This model appears to be the most appropriate method for the preliminary

analysis of migratory flow data.

Studies of College Faculty Mobilit~

Sociologists have studied various aspects of the academic community

from a sociological perspective (Wilson, 1942; Lazarsfeld and Thielens,

1958; Caplow and McGee, 1958; Donovan, 1964; Hagstrom, 1965). A recent

study adds the perspective of an economist (Brown, 1965 and 1967). In

addition to these major studies, many studies on college faculty have

•

18

been conducted by institutions of higher education (Stecklein and

Lathrop, 1960), by states (Wilson, !i~., 1961)~ and by national organ­

izations (Harmon, 1965; National Academy of Sciences, 1968), in order to

meet specific information needs. Some studies have dealt intensively

with faculty mobility, while others have provided insightful informa-

tion about problems related to mobility.

An earlier study made by Sorokin (1947, pp. 417-420) dealt with

patterns of faculty recruitment in four major universities. Another

earlier study by Hollingshead (1940) was concerned with progression

through faculty ranks and other aspects of the mobility patterns.

WilsonQs classical study, The Academic Man, can not be omitted from any

review of literature in this field. Though not systematic research,

his book provides a sensitive and insightful description of the careers

and problems of college faculty.

An intensive study of faculty mobility within and between ten major

universities was conducted more than ten years ago by Caplow and McGee

(1958). This study carried out the most extensive investigation of

faculty mobility in the academic stratification system. It was observed

that the possession of appropriate "contacts" in the discipline was an

important factor in recruitment to positions in academic institutions.

Caplow and McGee state:

A distinction must be made between the two kinds ofrecruitment in general use, "open" or competitive hiringand "closed," or preferential hiring. In theory, academicrecruitment is mostly open. In practice, it is mostlyclosed (Caplow and McGee, 1958, p. 109).

Deviations from the universalistic-achievement pattern in the

academic community are also observed in other studies. Marshall (1964,

pp. 85-90) reports some evidence of this in the academic market for

•

19

economists. Hargens and Hagstrom (1967) show that the prestige of the

institution where a scientist received his doctorate is related to the

prestige of his present affiliation even when the effects of his

productivity are controlled.

Hargens and Hagstrom related their findings to Turner's (1960) con-

cept of "contest" and "sponsored" mobility. Turneros two ideal-type

modes of social mobility might serve fruitfully as sensitizing concepts

in further research in this line. These two ideal-types of mobility

were designed to clarify observed differences in the predominantly

similar English and American systems of stratification and education.

Turner distinguishes these two types as follows:

Contest mobility is like a sporting event in which manycompete for a few recognized prizes. The contest isjudged to be fair only if all the players compete on ane~ual footing. Victory must be won solely by one's ovmefforts. The most satisfactory outcome is not necessarilya victory of the most able, but of the most deserving. • •Sponsored mobility, in contrast, rejects the pattern ofthe contest and favors a controlled selection process. Inthis process the elite or their agents, deemed to be best~ualified to judge merit, choose individuals for elitestatus who have the appropriate ~ualities. Individuals donot win or seize elite status; mobility is rather a processof sponsored induction into the elite (Turner, 1960, p.855).

In their investigations of academio stratification system, socio-

logists have emphasized the importanoe of a prestige faotor that leads

to deviations from the contest mobility. From an eoonomist's viev~oint,

Brown (1967, p. 62) desoribes the academic market place as a series of

submarkets partially isolated from each other by geography, subject

matter, research interest, demographic characteristios, purpose, and

stature. BrOi~ observes:

When viewed against olassical wage theories conoerningmobility in an economic utopia, the academic labor

20

market appears to be a maverick. Entry into and exit fromthe market are not unrestricted. Because of such practicesas inbreeding, promotion from within~ anti-pirating pacts,tenure, and fringe benefits, along with adherence to thecode of ethics, movement within the market is not free.Nor is movement costless; it involves both monetary andemotional costs. Decisions to relocate are seldom madewithin the confines of economic rationality or profit maxi­mization (Brown, 1961, p. 61).

Some studies have been directed toward the causes of faculty flow

to and from a particular institution. These studies have direct impli~

cations for college and university administrators who are interested in

maximizing their institution's power to attract and retain staff.

Caplow and MoGee (1958) studied the job vacancy, the factors that had

led to the vacancy, and procedures followed in filling it. Their study

provided the following generalizations:

In summary, these findings lend support to the view thatthe "push" of academic migration is stronger than the"pull." The majority of vacancies cannot be attributed tothe lure of opportunities elsewhere but to dissatisfaction ­either the failure of the incumbent to please his associatesor their failure to please him, or both (Caplow and McGee,1958, p. 80).

and

In general we may say that an institution!s attractivenessto a candidate is determined by what it can offer him inthe way of prestige, security, or authorit~. The specificattraction is a function of the candidate 9s OylIl situation,so that, for example, prestige is usually the strongerlure for men on the way up, whereas security and authoritybecome more attractive to men on the way down (Caplow andMoGee, 1958, p. 147).

The University of Minnesota conducted the most intensive ,stUdy to

determine factors that were affecting faculty mobility at that institu­

tion (Stecklein and Lathrop, 1960). The factors found to be influential

in this study mayor may not be typical of oonditions at other large

institutions. In fact, such faotors may change continuously at the same

21

institution. This study had led Stecklein to make the following remarks:

It should be clear by now that the factors that influ=ence faculty members to change jobs ~'e many and varied.They are different for individuals teaching in the sameand in different disciplines; they differ for differentage groups; they are different for single and marriedfaculty members and for married faculty members withand without children; they are determined by where aperson was born, went to school, or lived, they changefrom year to year or even from week to week and theyare influenced by sets of circumstances that no one eWl

predict or control (Stecklein, 1961, p. 31).

Despite the complexity and unpredictability of individual cases,

Ferriss (1966) maintains that faculty mobility ~ masse may present a

more predictable profile. After reviewing some fragmented mobility

studies, Ferriss hypothesizes that faculty mobility follows more "the

endogamous pattern" than flIthe stepladder pattern." He cites six factors

which influence faculty to move more readily between institutions of

similar character than between institutions of different type. The six

factors are (1) kinship among "sister" institutions, (2) informal

communication, (3) role performance and role rewards, (4) teaching or

research specialtyp (5) faculty-institutional organization, and (6) re-

muneration. In his discussion Ferriss implied that various colleges

and universities can be ranked in a hierarchical fashion.

The basis of this stratification of institutions has been usually

expressed in terms of institutional prestige. Veblen (1957, pp. 98-107)

suggested that academic prestige might be viewed as a type of institu-

tiona1 "good will" which attracted money from potential benefactors and

which could be unrelated to scholarly quality or achievement. He saw

American institutions of higher education as business enterprises which

acquired prestige by improving and expanding their physical facilities.

e

e

~e

•22

More recent discussions have portrayed academic prestige in terms of

the quality of scholars employed and trained at various institutions

(Caplow and McGee, 1958; Reisman, 1957; Berelson, 1960). It is clear

that the hierarchy of institutions consists of more than existing social

evaluations. Caplow and McGee (1958, p. 193) employ a "major league ­

minor league- bush league" metaphor in their discussion of the hierarchy,

and suggest that scholars are often enabled or condemned to spend their

entire careers in the "league" in which they obtain their doctorates.

Thus, the academic community is portrayed as a set of vertically

arranged strata, with little mobility between strata and hence the

dominance of horizontal mobility within the stratum. However, few

studies have attempted to summarize systematically the implications of

such inquiries for more general theories of stratification and to

examine these phenomena in the light of other pertinent factors that

are usually considered in migration researches, such as distance between

institutions, 1. £,., ,the dimension of regionalism.

•23

STUDY PERSPECTIVE

Frame of Reference

Institutional mobility of scientists is to be viewed as the result

of their individual decisions in the context of the social structure

and interpersonal relationships in the educational system. The recog­

nition of individual decisions has been insufficient in traditional

demographic studies. In recent years, the possibilities of micro­

demography, of building up demographic trends from individual decisions,

has become stronger as more individual control can be exerted over the

demographic events (Baok, 1967). T'ne most insightful discussion of the

effects of individual decisions upon demographic consequenoes was given

by Beshers (1967).

A move by an individual from one institution to another is a result

of the selection of alternatives by him. The individual selects alter­

natives in terms of the consequences that he ascribes to them. Thus,

the occurrence of mobility in a given time period is viewed as the out­

come of a process of decision making under sooial constraints.

Classic decision theory assumes that a complete set of his action

alternatives is known to the decision maker along with the set of

possible states of the world facing him, and that he is able to assign

a pair of numbers to each outcome. An outcome is a particular action

applied to a particular state of affairs. One number is the probability

of the occurrence of the state of affairs and the other number indexes

the desirability of the outcome, the utility of the result of aoting in

a certain way when the world is in a certain state. The individual

deoision maker takes the product of the pair of numbers associated with

•.

24

each outcome and adds these over all states of affairs, compares the

resulting expected utilities for all alternatives, and then selects

that alternative that will maximize his expected utility (Chernoff and

Moses, 1959). However, the actual deoision making is a process of

continuous reassessment of the probabilities and utilities using con-

stantly received new information, and accommodating to shifting values.

Characteristic patterns of decision making may differ between

traditional and modern society and among various groups of people in

modern society. :By slightly modifying Max Weber's concepts, :Beshers

(1961, p. 85) distinguishes three modes of orientation: traditional,

short-run hedonistic, and purposive-rational. In the traditional mode,

a decision is made according to custom with no recourse to new informa-

tion. The shorl-run hedonistic mode is oriented to a very brief future

time perspective. The individual acting in the purposive-rational mode

has an elaborate time perspective with sensitive recourse to new infor-

mation.

The events of institutional mobility of scientists could be

represented as the outcome of decision processes that are constrained

by the modes of orientation, social variables, and social psyohological

decision making prooesses. The job-ohange decision usually takes the

form of joint deoision in the family. The main constraints stem from

oharacteristics of the husband's job and from characteristics of the

household. When the mobility does not involve change of residence, the

job characteristios alone constitute the constraint.

The factors which enter into the deoision to move from one institu-

tion to another may be summarized under the following four controls of

mobility process:

•25

(1) The geographic extension of the academic job opportunities.

(2) The dispersion of knowledge about possible destinations.

(3) The differential attractiveness of the origin and possible

destinations.

(4) Personal and household characteristics a

The first and second variables are olosely interrelated and cannot be

studied separately. The fact that information itself may become less

available as distance increases makes it difficult to separate these

two. The third factor is most often expressed in terms of notions of

institutional "quality" or "prestige." It has been known that there is

a high positive correlation between institutional quality and other

indicants of attractiveness, such as average salary (Carter, 1966, pp.

111-112), formal honorary awards and recognitions (Crane, 1965; Cole

and Cole, 1967), and other social-cultural benefits. The fourth factor

includes the nuniber and spacing of children, the life cycle, the hous­

ing requirements, and personal preferences. It is also known that

additional personal characteristics may offset the other factors cited

a.bove. For instance, the influence of distance is contingent upon the

skills of individuals. In general, the higher the skills of the indi­

vidual, the more geographically extended the job market. High quality

scientists tend to be exposed to a national market and lower quality

scientists tend to form a local or regional market. Brown (1965, p.

132) has observed that top-quality institutions comprise a separate

labor market.

•,

26

Hnotheses

The foregoing observations se~m to suggest that the geographio

distrib~tion of institutions and the quality or prestige struoture of

institutions oomprise the major oonstraints on movement of persons

amongoolleges and universities. Studies (Marshall, 1964, pp. 71-90;

Brown, 1965, pp. 86-125) have shown that informal oontacts are a

primary means by which scholars obtain new positions. NeWly trained

doctorates are especially dependent upon their teaohers who already

have some sort of established communication ohannel. In such oiroum-

stanoes, geographic proximity provides an opportunity for the develop-

ment of regionalistio tendenoies in oommunioation and henoe mobility.

On the other hand, sooial-cultural proximity provides an opportunity

for the development of a stratification system within the academio

community. Thus, previous investigations (Caplow and McGee, 1957, p.

193; Hargens and Hagstrom, 1967, pp. 31-32) have asserted that posses-

sion of a degree from a top university is almost a necessary oondition

for recruitment to a position in a top university regardless of one's

competenoe.

From this line of notions the following hypotheses are derived:

(1) Institutions in the sa.Jlle region tend to exohange professionals

more among themselves than with institutions in other regions•

. MOre speoifically, ins~itutional mobility is negatively

assooiated with the distance involved between institutions

when the effect of institutional size is controlled.

(2) Institutions in the same prestige level tend to exchange

•r

27

mobility is negatively associated with the difference in the

prestige rankings of institutions when the effect of institu-

tional size is controlled.

(3) The tendencies and relationships specified in (1) and (2) are

• more distinctive for young scholars than for their elders.

Definition of Mobility

}~bility is defined in this study as a change of institutional

affiliation. No restriction is placed upon the distance of the move or

upon the voluntary or involuntary nature of the act. Thus, a move from

one institution to another in the same city constitutes mobility, re-

gardless of the involvement of geographic migration. .Any move from one

school or department to another within the same institution is not con-

sidered as mobility. In most cases there is no problem in choosing the

boundaries of institutions, but in a few cases of recently merged insti-

tutions it was decided to treat the merger as retroactive for the entire

period of the study.

Three types of mobility emerge ').'I.pon linking such points of career

development as baccalaureate graduatton, doctorate graduation, and

employment. The following three types of mobility are treated in this

study:

(1) Baccalaureate-to-doctorate mobility refers to the change of

educational institution between baccalaureate graduation and doctorate

graduation.

(2) Doctorate-to-ernwloyme~tmobility is the change of educational

institution between doctorate graduation and employment in institutions

of higher education.

e"

•

28

(3) Postdoctoral job mobility is the job change from one institu-

tion to another following the doctorate.

SamPling Procedures

The population to be studied consists of all faoulty members

affiliated with chemistry departments offering graduate degree programs

in institutions of higher education in the United States. The American

Chemioal Society (ACS) publishes directories of graduate programs every

two years, which contain such Wormation as degree origins and dates

and listing of pUblications for each scholar. The ACS Directory of

Graduate Research also inoludes as a separate seotion the departments

of biochemistry, medioal-phE;l.rlllaceutical ohemistry and chemical engineer­

ing, but these related fields are excluded from the present. stUdy.

Canadian institutions are also-excluded from the stUdy.

The study sample was selected from seven successive editions of

direotories (1955, 1957, 1959, 1961, 1963, 1965 and 1967), using a

single-stage cluster sampling procedure. The main portion of the

directory is arranged by institution, with an alphabetical listing of

individual names at the end. The alphabetical listing of the latest

directory (1967) was first subdivided into 80 clusters of adjacent

listed names and a random sample of 20 clusters were selected. The

starting point of eaoh oluster in the alphabetical sequenoe plays an

important role in identifying the selected sample olusters in each cf

previous editions of the direotory. For example, suppose oluster 3 was

seleoted from the 1967 directory, then the corresponding cluster in the

1965 directory can be identified by taking a block of names in the

alphabetical listing inoluding the starting point of cluster 3 and not

29

including the starting point of cluster 4. The sample, then, consists

of all chemists included in these 20 clusters in at least one edition

of the directory. Thus, included in the sample are those who left the

profession as well as those who newly joined the profession during the

1955-1967 period.

A total of 1,128 unduplicated individual names were selected from

the 20 selected clusters following through the seven successive edi-

tions of the directory. The recording of names and necessary informa-

tion was done starting from the latest directory and working back to

earlier directories. From each of the earlier directories new names

were added. The recording of data from earlier editions of the direc-

tory was less time-consuming than the initial recording, since the main

task was to record the institutional affiliation to the names already

in the record. The sizes of the study population and sample are shown

in Table 1. Of the 1,128 names 244 appear in all seven successive

directories and 215 appear only one time.

Table 1. Study Population and Selection of Sample

Number of Estimated Number of Number ofYear institutions number of names new names

listed total names selected added

1967 165 3,572 881 881

1965 153 3,127 801 81

1963 140 2,686 653 461961 125 2,190 555 41

1959 122 2,087 504 31

1957 110 1,731 450 28

- 1955 98 1,556 376 20

Total • • • • • 1,128

.,

30

For eaoh listed name the following information was recorded; full

name, sex, year of birth, speoialty in chemistry, year and institution

of baohelor's degree, year and institution of master#s degree, year and

institution of doctorts degree, and institutions of employment with

academic rank for the seven directories. All the records were coded

and punched for IBM machine-processing - one card for each name. In

addition to careful checking of codes and verification of punched cards,

cheoking by machine was performed to detect and eliminate certain resi-

dual errors, such as impossible codes.

Methods of Analysis

The first task in the analysis of the data was to select a manage-

able number of institutions among whioh the flow of scholars could be

analyzed. The criteria employed in selecting institutions were (1) the

institution is included in the Directory since 1955 and (2) it employed

at least 15 faculty members and produced 5 or more doctorates in 1966­

1967 in the chemistry department. After the screening process 86 insti­

tutions were selected (See Appendix A).

In order to record the information about the flow of scholars

among these 86 institutions, sociometric-type matrices of the order of

86 x 86 were formed for various types of mobility. These matrices show-

ing observed numbers of movements were analyzed by using a method

presented by Goodman (1963 and 1964) in order to obtain expected fre-

quencies of movements. As reviewed earlier, this method assigns zero

frequencies along the main diagonal of the mobility matrix and, subject

to this constraint, calCUlates expected values on the assumption of no

association between the institution of origin and the institution of

,>

•

31

destination (See Appendix C). Then, a comparison of the observed and

expected frequenoies of movement would indicate the exoess or deficit

of mobility between institutions.

Inferences about patterns of mobility were made by utilizing a

combination of regional and prestige level groupings of institutions.

Regional groupings were formed basically on the census regions of the

United States (See Appendix B). The following five regions were used:

New England, Middle Atlantic, Midwest (East North Central and West

North Central), South (South Atlantic, East South Central, and West

South Central), and West (Mountain a.'1d Pacific). Any regional classi...

fication, including the one used here, is more or less arbitrary and

might be interpreted best as a crude method of measuring distance.

Prestige groupings were based on the American Council on Education

(ACE) study on quality rating of graduate faoulty as reported by Carter

(1966). Four levels of prestige groupings are used in this study (See

Appendix B). Although there is folklore in abundance regarding pres-

tige d..ifferentials among colleges and universities, there are no common-

ly acoepted indexes available analogous to the occupational and other

prestige scales routinely used in stratification research. While many

sociological studies of prestige have emphasized persons and categories

of persons as the unit of analysis, systematioally conducted research

of prestige as it relates to complex orgarli~ations is relatively rare.

The ACE study reported by Carter represents one of the rare pieces of re-

search in assessing quality or prestige of academic institutions.

The Carter study is essentially a subjective assessment of institu-

tional prestige based on responses from departmental chairmen, senior

scholars, and junior scholars. In order to avoid the shortcomings of

, ,

32

earlier studies (Keniston, 1959; Hughes, 1928), Carter made an attempt

to obtain well-balanced representation of judges. He provided separate

ratings for 29 different fields of study. Ninety six chemistry depart-

menta that awarded one or more q.octorates from July 1952 through June

1962 were rated by 218 chairmen, senior scholars and junior scholars.

These judges were asked to rate each institution on a six-point scale

concerning two quality aspects of graduate programs in chemistry: the

quality of graduate faculty and the effectiveness of doctoral program.

Results of the two sets of ratings are similar. The rating based on

the quality of graduate faculty was used in this study.

The analysis by the use of regional and prestige level groupings

was followed by a regression analysis. An index of mobility for each

ordered pair of institutions was oomputed from the signed difference

between the observed and expected frequencies of movements desoribed

earlier. The index of mobility is thus not symmetric. In other words,

the index from institution A to institution B is different from the

index from institution B to institution A. There are 7,310 (86 x 85)

ordered pairs to be analyzed in the 86 x 86 mobility matrix.

While the index of mobility is a "pair" variable, derived for each

of the 7,310 ordered pairs of institutions, some independent variables

such as prestige and average compensation are "point" variables which

are scored for each of t4e 86 institutions. As a third kind of vari-

able, another "pair" but symmetrical variable, the distance between

institutions, is measured for each of the 3,655 unordered pairs. ~le

"point" variables need to be converted into "pair" variables on ordered

pairs in order to carry out regre~sion analyses of the index of mobility.

..

33

Also, the index of mobility needs to be "symmetrical" in order to in-

elude distance as an independent variable. It was thus decided to

perform two types of regression analyses, one using the 3,655 unordered

pairs and the other using the 7,310 ordered pairs as the units of

analysis.

The regression analysis of unordered pairs was done using the

average of the two directional indices of mobility between each pair of

institutions as the symmetrical variable and the distance, absolute

differences of prestige scores and average compensation and average of

prestige scores and average compensation for each pair as the indepen-

dent variables. The distance was measured by highway mileage between

the locations of institutions. Prestige scores were taken from the 1964

American Council on Educ~tion study reported by Carter. The average

compensation (salary plus other benefits) figures were the mean of 1962-

63, 1963-64, and 1964-65 figures reported in the American Association

of University Professors (AAUP) Eulletin (1963, 1964 and 1965).

In the regression analysis of ordered pairs, the index of mobility

does not need any adjustment. The adjustment of prestige scores and

average compensation was done by taking the signed difference for each

ordered pair of institutions. Since the distance is symmetric, it was

necessary to consider the ~irection of distance. The adjustment of

distance was accomplished by designating as positive the south-to-north

direction and as negative the north-to-south direction; similarly,

west-to-east was designated positive and east-to-west negative. Thus

two sets of distance figures were entered in the regression analysis.

The computations of regression analyses were performed by using

the multiple regression comput~r program written by Goodnight (1967).

.'

•

34

This program provides more options to obtain various statistios associ-

ated with the regression analysis than other available oomputer programs.

These options, among other things, include simple statistios for eaoh

variable, bi-variate statistios, all statistics in the Doolittle prooe-

dure, and expected values. The input subroutine of the program also

allows transformations and other data manipulation before entering into

the main regression program.

•

35

ANALYSIS OF NOBILITY PATTERNS

General Description of Data

Some general characteristics of the data sampled for this study

are summarized in Table 2. It is to be noted that 97 percent of all

chemists in this study are men and only 3 percent are women. Due to

the small number of women in the sample, no attempt can be made to

analyze mobility patterns by sex. Of the total sample, 97 percent hold

the doctorate and the small number of non-doctorate chemists does not

allow any separate analyses.

The academic rank held in 1967 were divided as follows: professor,

42 percent; associate professor, 24 percent; assistant professor, 32

percent; and instructor and research associate, 2 percent. Since the

sample was obtained from the graduate school faculty in the institu­

tions offering doctorate programs, the percentage of professors in the

sample is somewhat higher than it is in the total faculty in colleges

and universities.

The regional distribution of doctorate origins indicates that more

than one-third of the chemists in the sample obtained their doctorate

from the Midwest, whose doctorate-producing institutions constitute

principally the "Big Ten." iJ;'his J;'egion seems to provide dootorate

graduates in large numbers for other regions. This is apparent when

one compares the distribution of doctorate origins with the distribu­

tion of postdoctoral employment. Whi~e producing 37 percent of the

doctorate in the sample, the Midwest employed only 24 percent of the

total in 1967. On the other hand, the South employed 22 percent of the

total doctorate in 1967 but produced only 10 percent. Many research and

-.Table 2. General Charaoteristios of Chemists Sampled from

Doctoral Deb~ee Granting Institutions, 1955-1967

36

Characteristios Number Percent

~

:Hale 1,094 97 .Ol~Female 34 Z·O

Total 1,128 100.0

Highest DeSFee Held

Dootor 1,099 97.4I'Taster 24 2.1Baohelor 5 0.5

Total 1,128 100.0

Speoialty

Analytioal chemistry 120 10.6Orgffi1io chemistry 308 27.3Inorganio chemistry 150 13.3Physioal oh~mistry 387 34.3Bioohemistry 71 6.3Other specialties 92 8.2

Total 1,128 100.0Regional Distributiop of Doctorate Orie;in

Nevi England 166 15.1I'riddle Atlantio 189 17.2NidVlest 401 36.5South 104 9.5"i'lest 165 15.0Foreign oountries 74 6.7

Total 1,099 100.0

Academio Rank in 1967

Professor 368 41.8Assooiate professor 210 23.8Assistant professor 286 32.5Instruotor &researoh assooiate 17 1.9

Total 881 100.0

Regional Distribution of Employrrlent in 1961New England 105 11.9Middle Atlantio 182 20.7Mid"lest 215 24.4South 196 22.2\I/est 183 20.8

- Tota~ 881 100.0

..

•

37

policy concerns have been fooused on suoh an imbalanoe in the quantita-

tive distribution and redistributj.on of doctoral manpovler. However, the

sheer quantitative consideration seems to be insufficient in assessing

regional equality. An understanding of the qualitative aspect and the

exchange mechanisms of scholars among institutions would add a new

perspective in studying the distribution and redistribution of educated

manpower.

The analysis of mobility patterns will be divided into three

general sections. The first section will focus upon patterns of the

baccalaureate-to-doctorate mooility among the 86 institutions; the

second section upon patterns of the doctorate-to-employment mobility;

and the final section upon patterns of po~tdoctoral job mobility. For

each section an origin-destination matrix describing the flow of

scholB.;l:.'s among the 86 institutions is analyzed to reveal mobility

patterns. As described earlier, the expected mobility is computed by

using Goodman's method (See Appendix C). These observed and expeoted

mobility matrices are condensed by using regional and prestige group-

ings of institutions. The following oomponents of mobility will be "

used in presenting the data:

Prestige groupingRegionalgrouping Same level Different level

Same region (I) Intraregional, (II) Intraregional,horizo~tal mobility vertical mobility

Different region (III) Interregional, (IV) Interregional,horizontal mobility vertical mobility

Figure 1. A Typology of Interinstitutional Mobility Components

e.

38

In addition to the above four components, there is another compo-

nent to be considered, namely, the non-movers or those who stayed at the

same institution. In the first two sections the stayer component w~ll

be considered as the fifth component g but it should be separated from

the other four, as far as the computation of expected values is con-

cerned. While the stayer component is calculated on the basis of the

total cases (movers plUS stayers), the other four components are calcu­

lated on the basis of the total movers (total cases minus stayers).

The expected frequency for the stayer component is computed from the

observed frequencies along the main diagonal of the institutional

mobility matrix (diagonal cells not blocked) in the manner used in

ordinary contingency table analysis testing for independence (See Appen­

dix C). For example, in the doctorate-to-employment mObility matrix,

if a given institution produced one-fifth of all the doctorates (total

including diagonal cells) during the study· period and employed one-

te~th of the total doctorates, one would expect that institution to

employ 2 percent (.20 x .10) of Us own doctorates. Summing expected

probabilities for all diagonal cells, one obtains the expected percent-

age for the stayer component. On the other hand, the other four compo-

nents are calculated from non-diagonal cells of the institutional

mobility matrix (diagonal cells blocked) according to a method presented

by Goodman (See Appendix C).

Bacca1aureate-to-Doctorate Mobility

Table 3 presents data on the baccalaureate-to-doctorate mobility

among the 86 major institutions of higher education. The table is

divided into five components and each component is further divided into

39

Table 3. Baccalaureate to Doctorate Mobility Patterns of ChemistsAmong the 86 Major Institutions of Higher Education

Component of Observed Expeoted DifferenceMobility Percentage Percentage (Ob-Ex:P)

(I) Intraregional, horizontal 21.1% 11.1% +10.6%

At top prestige level ~19.2~ ~10.5~ ~+8.1~At lower prestige levels 2.5 0.6 +1.9

(II) Intraregional, vertical 13.0 8.3 +4.1

Upvlard mobility ~ 8.6~ ~ 5.8~ ~+2.8~Downward mobility 4.4 2.5 +1.9

(III) Interregional, horizontal 38.0 43.3 -5.3

At top prestige level ~36.1~ ~4l.1~ ~-5.0~At lower prestige levels 1.3 1.6 -0.3

(IV) Interregional, vertical 21.3 31.2 -9.9

Upward mobility F1.1~ ~27.8~ ~-6.1~Downward mobility 5.6 9.4 -3.8

(V) Stayersa

At top prestige levelAt lower prestige levels

Number of movers

Number of stayers

Total

(22.8)( 1.6)

360

157

511

+21.3

~ose who stayed at the same institution where they received thebaccalaureate to get the doctorate. The stayer component is computedon the base of the total (movers plus stayers) and the other componentsare computed on the base of the movers only.

40

sub-components. The figure at the first column corresponding to each

component represents the proportion of scholars who received both their

baccalaureate and doctorate in a homogeneous manner with respeot to that

oomponent. The second column consists of the peroentage of soholars

whioh would be expected for each oomponent if there were no statistioal

assooiation between the institution where a soholar receives his baooa­

laureate and the institution where he obtains his dootorate. As men­

tioned earlier, the first four components are computed on the same base

and these four add up to 100 percent. The fifth component is based on

a different base, namely, the total including movers and stayers. The

third oolumn in the table presents a crude measure of the extent to

whioh the observed values for each component deviate from those which

would be expected on the basis of a random distribution model.

It is shown in Table 3 that 35 percent (22% + 13%) of movers who

reoeived their two degrees from different institutions moved within the

same region. This percentage is higher than would be expeoted (11% +

8% a 19%). It is also shown that 60 percent (22% + 38%) of movers moved

to the institutions of the same prestige level as their baooalaureate

institutions, and this figure is slightly higher than the expected

peroentage (11% + 43% = 54%). Within the same region, the horizontal

mobility with respeot to prestige level far exoeeds the expeoted mobil­

ity, while the vertical mobility is slightly higher than the expeoted

mobility. The fifth component shows that more than 30 peroent of the

total soholars (movers plus sta.yers) stayed at the same institution

where they received the baocalaureate to get the dootorate, and this

figure is muoh higher than would be expeoted (3%). Thus, it appears

41

that the effects of two factors hYJ?othesized are substantiated in Table

3. The selective tendencies displayed here also suggest that the aca­

demic stratification system in the baccalaureate to doctorate mobility

is better represented as a set of regional hierarchies rather than a

strict prestige hierarchy.

The results of chi-square tests to reinforce these conclusions can

be found in Appendix D. In the mobility matrix there are 7,310 cells,

and the difference between the observed and expected frequencies in each

cell can be considered as a Poisson distributed quantity. It is known

that grouping these 7,310 quantities in four categories and calculating

chi-square values will give a chi-square distribution with th~ee degrees

of freedom. The results of chi-square tests show large statistically

significant differences between the observed and expected frequencies.

The partition of the chi-square value into three factors (region, pres­

tige level and interaction) reveals that the regional factor aocounts

for the most of the total chi-square value and the chil-square value for

the prestige factor tails to produce statistically significant differ-

ences.

Since Table 3 is an aggregated presentation of the data, the possi­

bility exists that the general patterns revealed above may not Charac­

terize each region and each prestige level considered separately. In

order to investigate this possibility, eaoh region is separately con­

sidered in Table 4 and data for each prestige level are shown in Table 5.

The data in Table 4 reveal that the general tendencies observed

above exist in every region, although the sizes of the differences

between observed and expected percentages vary from one region to an­

other. For example, the first row shows that the intraregiona1,

·e.,~ .:...

e

Table 4. Analysis of Regional Differences in Baccalaureate to Doctorate MobilityPatterns Among the 86 Major Institutions of Higher Education

"e

G R 0 UP I N GaREGIONALComponent ofMobility

Intraregional

New EnglandOb Exp Ob-Exp

1-Tidd1e AtlanticOb Exp Ob-Exp

MidwestOb Exp Ob-Ex]?

SouthOb Ex:P Ob-Exp

WestOb Exp Ob-Exp

2.0 2.0 0.0 11.8 6.8 +5.0 19.3 14.3 +5.0 10.4 5.1 +5.3 14.7 8.7 +6.0

(I) Horizontal

(II) Vertical

Int'erregional

24.5 12.5 +12.0 10.5 5.0 +5.5 32.1 19.4 +12.7 3.4 1.4 +2.0 30.9 11.8+19.1

(III) Horizontal..

(IV) Vertical

(v) Stayers

63.3 63.9 -0.6 40.8 43.8 -3.0 32.1 40.1 -8.0 22.4 21.4 +1.0 39.7 51.9 -12.2

10.2 21.6 -11.4 36.9 44.4 -7.5 16.5 26.2 -9.7 63.8 72.1 -8.3 14.7 27.6 -12.9

33.8 7.8 +26.0 31.5 1.8 +29.7 34.3 2.8 +31.5 8.7 0.2 +8.5 26.9 4.3 +22.6

Number of movers 49Number of stayers --l2.

Total 74

76

--2.2.111

109

--2.166

58

--l:.2.73

68

--1.2.93

aSince regional classification is based on the location of baccalaureate institutions, thedata in this table refer to sending patterns .from each region.

..f::>­I\)

43

horizontal mobility tendency is weakest in the South and the Middle

Atlantic, but t4ey still have mOr~ mobility than the expected in this

respect. The intraregional, vertical mobility shown in the second row

also exceeds the expected mobi~itr with the exception of New England

where it isbal~ced. Pn the other hand, the percentage differences

for the interregiona.l mobility are all negative in sign, with the lone

exception of the South. But the plus sign appears only in horizontal

mobility. In other words, the South is sending its baccalaureate grad­

uates to institutions of the same prestige level in other regions for

their doctorate slightly more ott~n than would be expeoted, while the

interregional, vertical mobilitr is still far less than the expected

mobility. It is also interesting to note that 86 percent of the movers

from the South went to other reS'ione and only 14 percent remained in

the South to get their doctorate. The tendency to remain at the same

institut.i,on is strongest ~ the ~dwest where the "Big Ten" are looated,

and it is weakest in the South which has few prestigious dootorate­

producing institutions. In general, the results shown in Table 4 are

consistent with those ~ Table 3.

The data presente4 ~ Table 5 indicate that at each ~restige level

of baccalaureate institut;l.on&;l, the movement to doctoral institutions

tends to be oriented toward both the same region and the same prestige

level. ~ese tendencies are consistent with the ones observed above.

The patterns ot mobility at the lowest prestige level are similar to

those obse~ed for the South ;l.n Table 4. Examining the third row, it

appears that institutions in the lower prestige levels tend to send

their baccalaureate gra.duates to t~e f,1ame prestige level but in

.e e l,e

(v) Stayers 34.2 4.3 +29.9 29.3 0.8 +28.5 21.0 0.3 +20.7 11.4 0.8 +10.6

Number of movers 227 53 49 31Number of stayers ...l!§. ~ -.ll ---!

Total 345 75 62 35;./

aSince prestige classification is based on the prestige score of baccalaureate institution,the data in this table refer to sending patterns from each prestige level. ~

~

•

•.

45

different regions. This interregional, horizontal mobility at the low-

est level is, in fact, slightly more than would be expected on the

basis of a random model, but this is not the case at higher prestige

levels. Two other features of the data in Table 5 are noted. First,

rates of remaining in the same region~ prestige level are lowest at

lower prestige levels. Table 4 showed that these rates are lowest in

the South, for this region is charaoterized by having institutions

which are predominantly in the lower prestige levels. Second, rates of

remaining at the same institution as onets baccalaureate institution

beoome also lower as the prestige level decreases. Thus, in general

the selective tendencies shown in Table 5 for each prestige level are

consistent with those observed in Table 3.

In order to investigate possible trends in the baocalaureate-to-

doctorate mobility patterns, the young and old scholars are analyzed

separately. The re8ults of this investigation are presented in Table 6.

The young cohort in the table oonsists of those who received their

baocalaureate since 1950 and the old cohort includes those who received

their baccala~eate before 1950. The data reveal that both the young

and the old cohort do not deviate from the general mobility patterns

oriented toward the same region and the same prestige level. There is

some indioation that the regionalistic orientation is gradually decreas-

ing. The young cohort shows a slightly lower rate of intraregional,

horizontal mobility and the percentage remaining at the same institution

is much lower for the young oohort than for the old cohort. Eut the

differences between the oorresponding values for the young an.d old on

each component are quite s:mall, wit:p. the possible exception of the

.e e

Table 6. Analysis of Trends in Baooalaureate to Dootorate Mobility Patterns ofChemists Among the 86 Major Institutions of Higher Eduoation

"e

a bComponents of Old Cohort Young Cohort

Observed Expeoted Dif£erenoe Observed Expeoted DifferenoeMobility Percentage Peroentaf,.re (Ob-Exp) Percentage Peroentage (Ob-Exp)

Intraxegiona.l

(I) Horizontal 24.4 12.2 +12.2 19.6 10.3 +9.3At top level ~23.7~ ~11.51 ~+12.2~ ~15.7~ ~ 9.8~ ~ +5.9~At low'er levels 0.7 0.7 0.0 3.9 0.5 +3.4

(II) Vertioal 12.8 9.0 +3.8 13.2 7.8 +5.4Upward ~10.3~ ~ 7.l~ ~ +3.2~ ~ 7.4~ ~ 4.9~ ~ +2.5~Downward 2.5 1.9 +O.ti 5.8 2.9 +2.9

Interre~ional

(III) Horizontal 34.6 43.6 -9.0 40.7 43.1 -2.4At top level p2.7~ ~42.3~ .~ -9.6~ p9.7~ ~4l.2~ ~ -1.5~At lower levels 1.9 1.3 +0.6 1.0 1.9 -0.9

(IV) Vertioal 28.2 35.2 -7.0 26.5 38.8 -12.3Upward F2.4~ ~28.2~ ~ -5.8~ ~21.1~ ~27.5~ ~ -6.4~Downward 5.8 7.0 -1.2 5.4 11.3 -5.9

(V) Stayers 39.3 3.1 +36.2 21.5 3.0 +18.5At top level pO.4~ ~ 2.9~ ~+27.5~ ~15.4~ ~ 2.8~ ~+12.6~At lower levels 8.9 0.2 +8.7 6.1 0.2 +5.9

Number of movers 156 204Number of stayers ..1Q!

2~~Total 257

~ose who reoeived the bachelor's degree before 1950 ~0'\

Those who reoeived the baohelor's degree sinoe 1950

47

fifth component. Thus no great exceptions to the general patterns of

mobility so far presented occur when the sample is analyzed in terms of

these two broad cohorts.

Doctorate-to-Employment Mobility

The distribution of newly trained doctorates to positions in the

academic community is examined in this section. In order to obtain the

distribution patterns, the institution from which on individual received

his doctorate is related to the institution 'Vlhere he held a position.

Since the sample is longitudinal, there is more than one institution of

employment for those i'lho changed their job during the 1955-1967 period

covered in the study. In such oases, the institution of earliest employ­

ment reoorded in the sample was used.

An analysis of mobility patterns from the institution of doctorate

training to the institution of employment is presented in ~able 7. Of

those who were not inbred into their dootoral institutions, 14 percent

obtained positions in the same region~ the same prestige level as

their dootoral institutions. This observed peroentage is somewhat

higher than the expeoted percentage. Twenty one percent of them moved

to institutions of different prestige levels in the same region, and it

is also higher than the expeoted percentage. Here again the tendenoy

toward intraregional mobility is apparent and it is oOIlsistent with the

tendenoy obs~rved in the mobility from the institution of baocalaureate

training to the institution of dootorate training. Examining the first

and the third oomponents together, it is found that the horizontal

mobility with respect to the prestige level accounts for 39 peroent

(14% + 25%) of the total movers. This observed peroentage is only

48

Table 7. Doctorate to Employment Nobility Patterns of ChemistsAmong the 86 Major Institutions of Higher Education

Components of Observed Expected Dif'ferenceNobility Percentage Percentage (Ob-Exp)

(I) Intraregional, horizontal 13.6 8.8 +4.8

At top prestige level ~12.8~ ~ 8.0~ ~+4.8~At lower prestige levels 0.8 0.8 0.0

(II) Intraregional, vertical 20.8 12.3 +8.5

Upward mobility ~ lo5~ ~ 1.9~ ~-0.4~Downward mobility 19.3 10.4 +8.9

(III) Interregional, horizontal 25.1 27.2 '-2.1

At top prestige level ~23.0~ ~24.8~ ~-1.8~At lower prestige levels 2.1 2.4 -0.3

(IV) Interregional, vertical 40.5 51.7 -11.2

Upward mobility ~ 3.2~ ~ 6.2~ ~-3.0~Downward mobility 37.3 45.5 -8.2

(v) Stayersa

At top prestige levelAt lower prestige levels

10.3 +9.0

Number of movers

Number of stayers

Total

617

_7)."

688

~ose who obtained the job at the same institution where theyreceived the doctorate. The stayer component is computed on the base ofthe total (movers plus stayers) and the other compcnents are computed onthe base of the movers only.

49

slightly higher than the expected percentage (9% + 27% = 36%). Thus it

would appear that the mobility is oriented toward horizontal patterns

but the deviation from the random model is quite small. Thus, regior.­

alistic tendencies appear to be stronger than the selective prestige

level tendencies. The results of chi-square tests to support this con­

clusion are presented in Appendix D.

Another feature of the data presented in Table 7 appears in the

second and the fourth components. Although the intraregional, vertical

mobility as a whole exceeds the expected mobility, the upward mobility

(decomposition of the intraregional, vertical mobility) shows the nega­

tive deviation from the expected mobility. This tendency toward down­

ward mobility may be considered as normal, since new doctorates tend to

move down from the prestige level of their doctoral institutions during

their early careers (Berelson, 1960, pp. 113-114; Caplow and MoGee,

1958, p. 181). In fact, 57 percent, examining the first column, of the

movement was downward mobility, while 39 percent remained at the same

prestige level and only four percent moved upward.

The fifth component in Table 7 shows percentages of stayers in the

doctorate to employment mobility, whioh indicate institutional inbreed­

ing patterns. One out of ten soholars held position at the same insti­

tution where he reoeived his dootorate. This rate of institutional

inbreeding is muoh higher than would be expected on the basis of the

random distribution model.

An analysis of regional differences in the doctorate to employment

mobility is presented in Table 8. First of a.ll, a. comparison of the

second and the third components ot ea.oh region indicates that seleotive

,e e

Table 8. Analysis o:f Regional Di:f:ferences in Doctorate to Emplo;yment Nobility patternso:f Chemists Among the 86 Major Institutions o:f Higher Education

..e

G R 0 U PIN GaREGIONALComponents o:fMobility

Intraregional

NeYT EnglandOb Exp Ob-Exp

Middle AtlanticOb E:xp Ob-Exp

Mid'"estOb Exp Ob-Exp

SouthOb Exp Ob-Exp

WestOb Exp Ob-Exp

(I) Horizontal

(II) Vertical

Interregional

(III) Horizontal

(IV) Vertical

(V) Stayers

13.3 5.6 +7.7 6.5 4.6 +1.9 18.1 14.2 +3.9 10.9 4.4 +6.5 10.9 5.0 +5.9

7.5 4.1 +3.4 16.3 9.9 +6.4 23.3 16.9 +6.4 56.5 20.4 +36.1 18.2 9.5 +8.7

35.8 33.4 +2.4 27.2 30.1 -2.9 18.5 21.9 -3.4 8.7 23.5 -14.8 33.6 31.8 +1.8

43.4 56.9 -13.5 50.0 55.4 -5.4 40.1 47.0 -6.9 23.9 51.7 -27.8 37.3 53.7 -16.4

5.5 1.0 +4.5 16.4 1.0 +15.4 8.1 1.4 +6.7 17.8 0.9 +16.9 11.3 1.5 +9.8

Number o:f movers 120

Number o:f stayers ---1.Total ·127

9218-

110

249....,gg

271

46

--19.56

110

-M124

aSince regional c1assi:fication is based on the location o:f doctoral institutions, thedata in this table re:fer to sending patterns :from each region.

\J1o

• 51

regional tendencies are stronger than selective prestige level tenden­

ci.es for each region. In all five regions, the observed percentage of

movers "lho remained in that region but moved to a different prestige

level exceeds the expected percentage in this component" On the other

hand, the observed percentage of movers who moved to a different region

but remained in the same prestige level is lower than the expected per­

centage in all regions with two exceptions of the New England and the

West" ,A.lthough the general patterns are similar in each region, there

emerge some regional peculiarities. For example, the South retained 67

percent of its doctorate graduates who are not inbred into their doctor­

al institutions, while New England retained only 21 percent in this

respect. The South also had the highest rate of inbreeding (10%) and

the lowest rate of inbreeding is found in New England" Thus, the data

suggest that the regions with predominantly lower prestige institutions

tend to have higher inbreeding rates and stronger intraregional tenden­

cies. This point will be further elaborated later.

Prestige level differences in mobility patterns of dootorates who

obtained positions in another institution of higher eduoation are exam­

ined in Table 9. Due to the insufficient number of cases, the third

and fourth prestige levels are combined in this table. Stronger intra­

regional than intraprestige level tendencies are consistently displayed

in each prestige level. Apart from these general tendencies, the data

show that institutions in the lower prestige levels tend to retain

their graduates more in their own institutions and send more to insti­

tutions in the same region than institutions in the higher prestige

levels. The rate of inbreeding is eight percent at the highest prestige

,e e >,e

Table 9. Analysis of Prestige Level Differences in Doctorate to Employment MobilityPatterns of Chemists Among the 86 Major Institutions of Higher Education

Components of PRESTIGE GROUPINGSa

Mobility Level 1 (Hi@) Level 2 Level 3 & 4 (Low)Ob Exp Ob-Exp Ob Exp Ob-Exp Ob Exp Ob-Exp

Intraregional

(I) Horizontal 15.3 9.5 +5.8 1.5 4.6 -3.1 11.4 5.1 +6.3

(II) Vertical 18.5 11.2 +7.3 27.7 18.5 +9.2 40.0 20.0 +20.0

Interregional

(III) Horizontal 27.5 29.6 -2.1 16.9 15.4 +1.5 5.7 12.0 -6.3

(IV) Vertical 38.7 49.7 -11.0 53.9 61.5 -7.6 42.9 62.9 -20.0

(v) Stayers 7.7 1.4 +6.3 17.7 0.6 +17.1 28.8· 0.6 +28.2

Number of movers 517 65 35Number of stayers ---M. --M --M

Total 560 79 49

aSince prestige classification is based on the prestige score of doctoral institutions,the data in this table refer to sending patterns from each prestige level. \J1

(\)

•53

level, while the rate is more than three times higher (29%) at the low­

est level. These tendenoies of higher inbreeding and intraregional

mobility at lower prestige levels oan be interpreted in the light of

the formation of aoademio labor market. Those who attend more presti­

gious institutions and, presumably, reoeive a better eduoation, tend to

form a national market, while those attending less prestigious institu­

tions more generally form a looal or regional market. The oonsequenoes

of the operation of these two kinds of labor markets seem to be refleot­

ed in the data presented in Table 9. However, the most important obser­

vations in Table 9 are tendenoies toward intraregional mobility whioh

are somewhat stronger 1;;han seleotive prestige level tendenoies.

Another deoomposition of the data in Table 7 may be oarried out by

a.na.lyzing the patterns of mobility for the young and old oohorts. This

analysis is given in Table 10. The two broad oategories are formed by

diohotomizing the sam~le aooording to the year of dootoral degree. The

young oohort oonsists of those who reoeived their dootorate sinoe 1955.

The analysis of the young oohort would reveal the mobility patterns of

neW dootorates to their first jobs, sinoe the sample of this study

oovers the Period beginning 1955. The results show that the general

tendenoies toward intraregional and intraprestige level mobility are

oonsistent in both oohorts. Although the differenoes between the oor­

responding peroentages for the two oohorts on eaoh oomponent are quite

small, there is some indioation that the tendenoy toward intraregional

mobility is more prominent for the old oohort than for the young. The

rate of inbreeding is much higher for the old oohort (15%) than for the

young (5%). While there is more downward mobility than upward mobility

·e e

Table 10. Analysis of Trends in Doctorate to Employment Mobility Patterns ofChemists .Among the 86 Major Institutions of Higher Education

J,e

a bComponents of Old Cohort Young Cohort

Observed Expected Difference Observed Expected DifferenceMobility Percentage Percentage (Ob-Exp) Percentage Percentage (Ob-Exp)

Intraregional

(I) Horizontal 16.1 10.0 +6.1 11.1 7.5 +3.6At top level ~15.5~ ~ 9.0~ ~ +6.5~ ~10.1~ ~ 6.8~ ~ +3.3~At lower level 0.6 1.0 -0.4 1.0 0.7 +0.3

(II) Vertical 22.3 12.9 +9.4 19.2 11.7 +7.5Upward ~ 4.2~ ~'l 9~ ~ +2.3~ ~ 1.6~ ~ 1.9~ ~ -0.3)Downward. 18.1 11:0 +7.1 17.6 9.8 +7.8)

Interregional

(III) Horizontal 22.9 28.1 -5.2 27.4 26.4 +1.0At top level ~21.6~ ~26.1~ ~ -4.5~ (24.4~ ~23.4~ ~ +1.0~At lower levels 1.3 2.0 -0.7 ( 3.0 3.0 0.0

(IV) Vertical 38.7 49.0 -10.3 42.3 54.4 -12.1Upward ~ 3.5~ ~ 5.1~ ~ -~.6~ ( n 9~ ~ 7.2~ ~ -4.3~Downward 35.2 43.9 -0.7 C39:4 47.2 -7.8.• I.

(V) Stayers 15.3 1.9 +13.4 4.7 0.6 +4.1----~__ At top level ~10.1~ ~ 1.8~ ~ +8.3~ ~ 1.9~ ~ 0.3~ ~ +1.6)-----------.0 _,

+5.1 +2.5)!t ..LUwer levels 5.2 0.1 2.8 0.3

Number of movers 310 307Number of stayers ....2§. ---12

Total 366 322_. II

~ose who received the doctorate before 1955v"..j:::.

Those who received the doctorate since 1955

55

in both cohorts, the old cohort shows more upward mobility than the

young cohort. These slight differences between the young and old co-

horts may reflect the development of postdoctoral careers of scholars.

At earlier stages of their careers, scholars are more willing to accept

jobs at lower prestige institutions than their doctoral institutions

and more willing to move to other regions. As their professional ex-

periences increase, they tend to move upward to more presigious insti-

tutions and many of them return to their Alma Mater.

Postdoctoral Job Mobility

In order to obtain information about postdoctoral job mobility,

six origin-destination matrices were formulated for the follOWing six

biennial periods: 1955-1957, 1957-1959, 1959-1961, 1961-1963, 1963-1965

and 1965-1967. Although it is possible to analyze each of these

matrices separately, all six matrices were combined due to insufficient

number of cases in each matrix. The total number of moves identified

among the 86 institutions during the entire 12 year period adds up to

only 83. Thus, the fifth component is not considered in this section.

Analysis of job mobility patterns during the 1955-1967 period is

presented in Table 11. The positive differences in the first two com-

ponents indicate excess intraregiona1 mobility and the positive signs

in the first and third component reflect excess horizontal mobility

with respect to prestige level. About the same magnitude of differences

between the observed and expected percentage in the second and the third

components suggest that seleotive prestige level tendenoies are as

strong as selective regional tendencies in the job mobility. Further

evidence for this point is shown in the chi-square statistios presented

e"

56

in Appendix D. An examination of sub-components in the first and third

rows indicate that less prestigious institutions tend to exchange fac-

ulties with institutions in the same prestige in the same region, while

more prestigious institutions tend to exchange with institutions in the

same prestige level in other regions.

Table 11. Postdoctoral Job Mobility Patterns of Chemists Amongthe 86 Major Institutions of Higher Education

Components of Observed Expected DifferenceMobility Percentage Percentage (Ob-Exp)

(I) Intraregional, horizontal 8.4% 7.5% +0.9%

At top prestige level ~ 4.8~ ~ 5.5~ ~ -0.7~At lower prestige level 3.6 2.0 +1.6

(II) Intraregional, vertical 21.7 13.9 +7.8

Upward mobility ~ 4.8~ ~ 4.5~ ~ +O.3~Downward mobility 16.9 9.4 +7.5

(III) Interregional, horizontal 33.7 26.1 +7.6

At 'top prestige level ~28.9~ ~20.7~ ~ +8.2~At lower prestige levels 4.8 5.4 -0.6

(IV) Interregional, vertical 36.2 52.5 -16.3

Upward mobility ~ 9.6~ ~18.3~ ~ -8.7~DOvlll,,'ard mobility 26.6 34.2 -7.6

Number of moves 83

•57

Regional differenoes in the job mobility patterns are analyzed in

Table 12. Although the small number of oases in eaoh region do not

allow any detailed observations, seleotive prestige level tendenoies

seems to be stronger than regionalistio tendenoies in all regions

exoept for the :Middle Atlantio. Those who were employed in the :Middle

Atlantio seem to prefer to move to a different prestige level in that

region rather than moving to the same prestige level in other regions.

Prestige level differenoes are oonsidered in Table 13. Institu­

tions in lower prestige levels are more strongly oriented toward intra­

regional mobility than institutions at the highest level. Soholars in

higher prestige level institutions tend to move to institutions in the

same prestige level in other regions.

An attempt is made in Table 14 to investigate any possible trends

in job mobility by oarrying out separate analyses for the 1955-1961 and

1961-1967 periods. The oorresponding peroentages for the two periods

are quite similar. Thus, there seems to be no marked ohange in the job

mobility patterns.

In summary, the results reported in Tables 3 through 14 suggest

the following oonolusions about interinstitutional mobility patterns of

ohemists at various stages of their oareers. The oono1usions oan be

further baoked up by the ohi-square tests presented in Appendix D.

First, the mobility from the baooalaureate to the dootorate training is

charaoterized by stronger tendenoies toward regionalism than toward

prestige level homogeneity. The largest deviations from a model of

random mobility patterns are found for the stayers and the intraregiona1,

horizontal movements. These regiona1istio tendenoies seems to be more

·e e

Table 12. Analysis of Regional Differences in Postdoctoral Job Mobility Patternsof Chemists Among the 86 Major Institutions of Higher Education

·e

New Eng1oo~d Middle Atlantic ~lidwest South WestOb Exp Ob-Exp Ob Exp Ob-Exp Ob Exp Ob-E.."'q) Ob Exp Ob-Exp Ob Exp Ob-Exp

Components of:t-10bi1ity

Intraregiona1

REGIONAL G R 0 U PIN Ga

(I) Horizontal

(II) Vertical

Interregional

(III) Horizontal

(IV) Vertical

9.1 7.3 +1.8 5.6 3.9 +1.7 14.8 11.9 +2.9 0.0 4.3 -4.3 7.7 9.2 -1.5

18.2 0.9 +17.3 33.3 10.6 +22.7 14.8 22.2 -7.4 21.4 14.3 +7.1 23.1 11.5 +11.6

54.5 33.6 +20.9 16.7 38.3 -21.6 33.3 21.1 +12.2 28.6 20.0 +8.6 4G.l 30.8 +15.3

18.2 58.2 -40.0 44.4 47.2 -2.8 37.1 44.8 -7.7 50.0 61.4 -11.4 23.1 48.5 ~25.4

Number of moves 11 18 27 14 13

aSince regional classification is based on the location of institutions of origin, thedata in this table refer to sending patterns from each region.

\J1Q)

•59

Table 13. Analysis of Presti~e Level Differences in Post­doctoral Job Mobility Patterns of Chemists Amongthe 86 Major Institutions of Higher Education

Components ofMobility

Intraregional

(I) Horizontal

(II) Vertical

Interregional

(III) Horizontal

(IV) Vertical

Number of moves

PRESTIGE

Level 1 (High)Ob Exp Ob-Exp

7.8 9.0 -1.817.6 12.0 +5.6

47.1 33.9 +13.227.5 45.1 -17.6

51

Levels 2. 3 &4 (Low)Ob Exp Ob-Exp

9.4 5.0 +4.428.1 16.5 +11.6

12.5 13.8 -1.350.0 64.7 -14.7

32

aSince prestige classification is based on prestige scores ofinstitutions of origin, the data in this table refer to sending :patternsfrom each prestige level.

Table 14. Analysis of Trends in Postdoctoral Job Mobility Patterns ofChemists Among the 86 Major Institutions of Higher Eduoation

Components of 1955-1961 Period 1961-1967 PeriodMobility Ob Exp Ob-Exp Ob EX]? Ob-Exp

Intraregional

(I) Horizontal 9.5 6.6 +2.9 7.7 7.0 +0.7(II) Vertical 27.6 18.9 +8.7 19.2 13.0 +6.2

Interregional

(III) Horizontal 23.8 21.4 +2.4 39.5 32.8 +6.7(IV) Vertical 39.1 53.1 -14.0 33.6 47.2 -13.6

e Number of moves 29 54

60

prominent for the lower prestige level institutions. Second, in the

distribution of new doctorates to positions in academic institutions,

as in the baccalaureate-to-doctorate move, regionalistic tendencies

appear to be stronger than selective prestige level tendencies. Thus,

the academic stratification system in the doctorate to employment

mobility is one of a set of regional hierarchies rather than a rigid

prestige hierarchy. It is also noted that downward mobility is more

common at earlier stages of postdoctoral careers. The lower prestige

institutions seem to have relatively higher rate of inbreeding and a

stronger regionalistic orientation. Third, postdoctoral job mobility

patterns are characterized by about equally strong tendencies toward

homogeneity in region and in institutional prestige level. The region-

alistic tendencies appear to be relatively stronger for lower prestige

levels and tendencies toward prestige homogeneity are more operative

for higher prestige levels. Thus, chemists in high prestige level

institutions tend to move to the same prestige level in other regions,

while those in lower presti~ level institutions tend to move within

that region. Finally, it should be pointed out that these results are

based on a limited number of cases and the small number of cases might

impose limitations, more so in the job mobility analysis.

•

61

REGRESSION ANALYSIS

The purpose of regression analysis is twofold: (1) to extract the

main features of the relationships hidden or implied in the data and

(2) to examine possibilities of using such functional relationships for

forecasting institutional mobility from knowledge of other variables.

From the 86 institutions to be studied, there are 3,655 unordered

pairs and 7,310 ordered pairs that can be formed. As mentioned earlier,

the dependent variable is the signed departure of observed frequency

from the expected frequency for each of the ordered pairs in the 86 x 86

mobility matrix. Thus, the dependent variable matrix is asymmetric.

Among the independent variables, the distance between institutions is

symmetric. Other independent variables are formed from the "pair"

variables: prestige score and average faculty compensation of 86 insti-

tutions. The absolute difference and average of the pair are symmetric,

but the signed difference is asymmetric (they change sign when the order

of the pair is reversed). There are basically two kinds of variables:

symmetric and asymmetric •... In the study of analyzing pair data and point

data on sociometric relationships, Proctor (1969) suggested that these

tvlO kinds of variables ought not be mixed in the same regression ana1y-

sis. Thus, two kinds of regression analyses are performed; one for

the unordered pairs to analyze symmetric variables and one for ordered

pairs to analyze asymmetric variables. For the former, the dependent

variable is transformed to a symmetric variable by taking the average

of corresponding ordered pairs. In more familiar terminology in migra-

tion research, the dependent variable in the unordered pair regression

corresponds to gross migration, though the average rather than the sum

•

•

62

of two directional flows is used. The depenqent variable in the ordered

regression congerns the directional flows.

In both regression analys~s all the variables are transformed by

taking basically the logarithm of the original values. Since the loga-

rithmic transformation cannot be used directly for zero values and when

some of the values are negative, it is necessary to adjust all the

values before taking logarithms. When a variable contains some zero

values and negative values, not smaller than minus one, the adjustment

is made by adding one to each number prior to taking logarithms. This

transformation acts like the square root for small values and like the

logarithm for large values. When a variable contains some negative

values smaller than minus one, each number is divided by a positive

constant which is slightly larger than the absolute value of the small-

est negative value prior to adding one and taking logarithms.

The results of regression analyses are presented in Table 15 for

the baccalaureate to doctorate mobility, in Table 16 for the-doctorate

to employment mobility, and in Table 17 for the postdoctoral job mobil-

ity. These tables show the fitted regression coefficients obtained from

least-squares regression, their t-statistics, and the coefficient of

determination (R2). Although the coefficients of determination are not

impressive at all, the regression coefficients and the accompanying t-

values can be used to screen relationships.

Effects of Distance

The hypothesized inverse relationship is substantiated in every

case of unordered pair analyses presented in Table 15 through 17. The

accompanying t-value indicates that the regression coefficient is

,e e ..

\

,e ,

Table 15. Regression Analysis for Baccalaureate to Doctorate Mobility of ChemistsAmong the 86 Major Institutions of Higher Education

Young cohortRegression tcoefficient value

-0.0089*** -5.4810

-0.0179

-0.0059

-0.0343

-0.0005

-1.6163

-1.1776

-1.2883

-0.2895

2R = 0.0162

-0.0008 -0.1899

-0.0019

-0.0029

0.0191

-0.4731

-0.3571

1.7378

2R = 0.0016

* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence

*** Significantly different from zero at .001 level of confidence

Ch\..N

.e e ~Je

Table 16. Regression Analysis for Doctorate to Employment MObility of ChemistsAmong the 86 Major Institutions of Higher Education

Young cohort

-0.0156** -2.6844

2R = 0.0023

Regression tcoefficient value

0.8496

-0.0732

-1.9413

-0.9404

-1.1337

0.0265

-0.0010

-0.0227

-0.0048

2R = 0.0110

-0.0007 -0.1422

-0.0023

-0.0058** -3.0618

-0.0302* ~2.3290

Total sample Old cohortRegression Independent Regression t Regression t

run variable coefficient value coefficient value

(I) Unordered Distance -0.0212*** -7.3691 -0.0166*** -8.9867pair

regression Average of -0.0558** -2.8487 -0.0099 -0.7864prestige scores

Absolute difference -0.0293* -2.3099 -0.0065 -1.1520in prestige scores

Average of 0.0174 0.3697 -0.0234 -0.7742compensation

Absolute difference -0.0065* -2.0901 -0.0040* -2.0147in compensation

2 2R = 0.0292 R = 0.0285

(II) Ordered North-South -0.0004 -0.1161 -0.0092 -1.5727pair distance

regression East-West -0.0029 -0.7871 -0.0090 -1.5589distance

Signed difference -0.0160* -2.3081 -0.0250 -1.9231in prestige scores

Signed differences -0.0062 -0.6174 0.0015 0.0934in compensation

2 2R = 0.0028 R = 0.0038

~

* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence

*** Significantly different from zero at .001 level of confidence

0'\~

,e e 'e

Table 17. Regression Analysis for Postdoctoral Job ¥~bility of Chemists Amongthe 86 Yajor Institutions of Higher Education

-0.0010 -1.3201

-0.0012 -0.4928

0.0062 0.3862

2R = 0.0037

-0.0011 -0.6758

-0.9582

-0.7871

0.0031 0.7584

2R = 0.0003

-0.0013

-0.0021

-0.0029* -2.1547

-0.0060 -0.8523

1261-1967 periodRegression tcoefficient value

1955-1967 period 1955-1961 periodRegression Independent Regression t Regression t

run variable coefficient value coefficient value

(I) Unordered Distance -0.0028** -2.8991 -0.0031*** -3.8513pair

reb'Tession Average of -0.0059 -0.8834 -0.0052 -0.9320prestige scores

Absolute difference -0.0014 -0.4650 -0.0015 -0.3856in prestige scores

Average of 0.0057 0.3574 0.0054 0.2988compensation

Absolute difference -0.0012 -1.1696 -0.0011 -1.2728in compensa'tion

2 2R = 0.0038 R = 0.0051

(II) Ordered North-South -0.0011 -0.7699 -0.0021 -0.9823pair distance

regression East-West -0.0012 -0.8222 -0.0011 -1.0231distance

Signed difference -0.0026 -0.9299 -0.0031 -0.9825in prestige scores

Signed difference 0.0033 0.8051 0.0023 0.9253in compensation 2 2

R = 0.0004 R = 0.0008

* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence

*** Significantly different from zero at .001 level of confidence,

0'\VI

•

•

66

significantly different from zero in every analysis. The distance vari­

able appears to be the most important one among the independent vari­

ables considered. The standard partial regression coefficients which

indicate the relative importance of the independent variables in rela­

tion to the dependent variable can be found in Appendix D. These find­

ings are consistent with the strong regionalistic tendencies described

in the previous section.

In the ordered pair regression analysis two distance variables were

included: north-south directional distance and east-west directional

distance. While the distance variable contributes significantly to the

explanation in the unordered pair regression analysis, these two direc­

tional distances in the ordered pair analysis contribute very little to

the explanation. The consistent negative signs of coefficients in the

three types of institutional mobility suggest that there is more mobil­

ity from the north to the south and from the east to the west rather

than the reverse directions. The only coefficient which is significant­

ly different from zero appears in the east-west directional distance in

the old cohort of baccalaureate-to-doctorate mobility, but the coef­

ficient of east-w3st directional distance for the young cohort is not

significant.

Effects of Prestige and Compensation

Two sets of prestige variables are used in the unordered pair re­

gression analysis: the absolute difference and the average of prestige

scores. As far as interpretations of the results are concerned, the

absolute difference makes more sense than the average of prestige scores•

The negative coefficients of the absolute prestige difference indicate

•

67

that, when the differenoe in prestige scores increased~ institutional

mobility decreased. This relationship is oonsistent with the tenden-

oies toward horizontal mobility with respeot to prestige as observed

earlier. Although the hypothesized relationship between mobility and

llrestige is upheld in its anticipated direction, the strength of the

relationship and hence the contribution to the regression is somewhat

discouraging. The coeffioient is significantly different from zero

only in the dootorate-to-employment mobility analysis.

The average of prestige scores appears to be somewhat better in its

contribution to the unordered pair regression than the absolute prestige

differenoe (See Appendix D). The relationship between the average of .

prestige soores and the average mobility turned out to be negative.

This seems to suggest that there was more mobility in lower prestige

levels than in higher prestige levels. :But this statement oan not be

taken in a sheer quantitative sense, sinoe the mobility variable indi-

cates the extent to which the observed mobility deviates .from the ex-

pected mobility. The averaging of prestige soores of the top and bottom

institutions would produce a fairly high score~ but the mobility between

these two institutions would be the lowest in the light of the inverse

relationship observed between the absolute prestige differential and the

mobility. Therefore the results in this regard make less sense when any

interpretations are attempted.

The signed difference in prestige scores in the ordered pairanaly-

sis consistently yielded a negative relationship with mobility. This

relationship can best be interpreted as a propensity for mobility be-

tween institutions of similar prestige characteristics. Its regression

coefficient is significantly different from zero in the baccalaureate

•

68

to doctorate mobility and the doctorate to employment mobility.

Another set of independent variables concern faculty compensation.

Although this factor may be J.rrelevant for the baccalaureate to doctor-

ate mobility, compensation should be an important variable in the doc-

torate to employment mobility and especially for postdoctoral job mobil-

ity. The absolute difference in compensation in the unordered pair

analysis consistently produced negative signs and the regression

coefficient for the doctorate to employment mobility is significantly

different from zero. This negative relationship is expected consider-

ing the inverse relationship between prestige differential and mobility.

In fact, the prestige score is highly correlated with faculty compensa­

tion (r-.77). On the other hand, average compensation of the pair

institutions contributes virtually nothing to the explanation and its

coefficient is not significantly different from zero in each unordered

pair analysis. The signs of coefficients are not consistent from one

analysis to another.

The compensation factor in the ordered pair analysis does not

significantly contribute to the regression. While the signed difference

in prestige scores consistently yielded negative relationships, the

signed difference in compensation produced positive relationships in

the baccalaureate to doctorate mobility and postdoctoral job mobility.

Surprisingly, the coefficient is positive and significantly different

from zero in the baccalaureate to doctorate mobility. But it is hard

to see any direct connection between the movement of students from the

baccalaureate to doctorate institution and faculty compensation. The

faculty compensation must be related to other factors which are

69

relevant to the student movement.

Examination of Residuals

In performing the regression analyses, particularly in using the

t-values, certain assumptions have been made about the errors. The

usual assumptions are that the errors are independent, have a constant

variance, and follow the normal distribution. The last assumption is

required for making F-tests and using t-tables. Thus it is always

helpful to examine whether the residuals tend to conform to these

assumptions. The problem of examining how closely the ideal conditions

are satisfied is a very broad one. The error distribution can be

checked by measuring its skewness and kurtosis. The dependence of the

residuals on the fitted values can be examined by computing the statis-

tics concerning heteroscedasticity and nonadditivity as suggested by

Anscombe (1961 and 1963). For the present study the error distribution

is first examined by a graphic method and then an aspect of suspected

dependence among the residuals is considered.

Since the 3,655 observations in the unordered pair regression and

7,310 observations in the ordered pair regression were so numerous, a

random sample of 73 observations (2% of the unordered pairs and 1% of

the ordered pairs) was drawn from eaCh analysis to plot the error dis-

tribution. The distributions of errors for unordered and ordered pair.~~~,

analyses are shown in Figure 2. The distributions are plotted in terms

of the standard error of estimate. These distributions should resemble

a normal distribution with zero mean if the regression model is correct

for each analysis. As the plots exhibit, the distributions are somewhat

irregular. The distributions of unordered analyses exhibit a positive

e,

Baccalaureate to DootorateMobility

e

UNORDERED PAIR REGRESSION

-S 4 3 2eDoctorate to Employment

Mobility

+Se

..e

2S 2 1 0 1 2 3 4 5 6+S7e e

Postdoctoral Job Mobility

-S ~ ~ ~ ~ I V I 2 3 ~S

e Baccalaureate to Doctorate eMobility

~S 7 6 5 4 3 2 1 0 1 2 3 ~S

e Doctoreate to Employment Mobility egs 1 0 1 2 3 4 5 b 7+S

8

epostdoctoral Job Mobility e

Figure 2. Distributions of Residuals Based on the Standard Error ofEstimate for Two Types of Regression Analyses

-Jo

•

•

71

ske,~ess. All distributions appear to be leptokurtic, hence positive

fourth cumulants are suspected.

Another good way to examine the residuals may be to prepare scatter

diagrams showing the dependence of residuals on the fitted values. In

Figure 3 every sampled observation for unordered and ordered analyses

of the baccalaureate to doctorate mobility is represented by a point

whose ordinate is the residual and whose abscissa is the fitted values.

Outliers can be seen rather readily as isolated points with extreme

ordinates. It has been suggested that it may be wise to reject or pre­

ferably modify observations whose residuals are very large in magnitude.

A procedure of modification has been described as Winsorization (Tukey,

1962). Since most of outliers in Figure 3 represent most prestigious

institutions, a simple rejection or modification may not be wise.

Rather it may be preferable to perform a separate regression analysis

for different components of mobility such as the ones identified by

using regional and prestige groupings.

The diagram for the unordered pair analysis in Figure 3 exhibits a

somewhat greater dispersion of the residuals for smaller fitted values

than for larger values, apart from outliers. This indicates a depend­

ence of variability on level or a non-homogeneous variance. Weighted

least squares or another type of transformation might be needed in

order to stabilize the variance.

In a general regression situation, when p parameters are estimated

from n observations, the n residuals are associated with only n-p de­

grees of freedom. Thus the residuals cannot be independent and correla­

tions exist among them. Eut it is suggested that the effect of

72

• +40 ,--• .. ""

+30

+20 ..

+10

• " .. 0

0 6 • •• • . ..... ......'... . •.. •• 0 ...'11 .-.... • •.. • .. ••• • • 'O •• ... ..;"10 ..

•

-20 -• Unordered Pair• Regression

-30 -

Fitted Values-40 5 6 7 8 9 10 11 12 13 14+404

• • -,

•+30 . -

+20

+10

0 ..... ~.

• - ~•• o"i~ o••

0 •• •.. • • •·~1O

•

-20Ordered PairRegression

-30

-40 I - I •

• F'igure 3. Scatter Diagrams of Residuals against Fitted Values forRegress:ion Analyses of Baccalaureate to Doctorate Mobility

•

•

73

correlation need not be considered when plots are made, except when the

ratio (n-p)!n is quite small (Draper and Smith, 1966, p. 94).

In the present study, however, there is a need to check an usual

aspect of dependence among the residuals. Since the observations were

taken from the 86 x 86 matrix, the residuals can be represented as eij

which is associated with institutions i and j (i'j). In the unordered

pair analysis, the subscripts i, j are taken with i) j. In this situa.-

tion the major departure from the ideal condition of independent errors

could be expeoted as a oorrelation between a certain e. . and theJ.J

associated errors of eij • or eitj where i~i' and j,cjt. The estimation

of a correlation matrix between eijts whose size reaches 3,655 x 3,655

for the unordered pair regression and 7,310 x 7,310 for the ordered pair

regression would be an impossible undertaking, and so some simplifica.-

tion is needed.

utiliZing an approach suggested by Proctor (1969), such a correla-

tion is estimated for unordered and ordered pair regressions of the

baccalaureate to doctorate mobility. Of the 6,677,685 pairs of errors

for the unordered pair regression, 307,020 or 4.6 percent would have a

subscript in common. It may be supposed that the eijt of overlapped

pairs were correlated, while the mutually exclusive pairs were not. A

random sample of 20 residuals was obta.1ned to estimate the correlation.

These 20 residuals formed 190 pairs of residuals among which 183

mutually exclusive and 7 (3.7%) overlapped pairs were found. The dif-

ference of the two residuals was reoorded for each pair and the

variance of these differences was calculated for the exolusive and

overlapped pairs separately: the results of the calculation were

• == 237.25 and S2 == 20.39, respectively.lap.

74

These computations are

•

shown in Table 18. From these data an estimate of correlation is de-

rived as follows:

If the subsoripts of eij and eitjt are mutually exolusive, it is

supposed that

but if they are not mutually exolusive, then

V(e .. - eitjt ) == Vee .. - e. t.) • 20"'2 (1 - tJ).~J ~J ~ J e \

Therefore, s12 /82 can be used as an estimate of (1 _P).ape exe. \

Thus, ~== 1 - ( s12 /s2 ) == 1 - (20.39/237.25) == .91\ ape exc.

Simila.:r;ly, the correlation is estimated for the ordered pair re­

gression. There are 26,714,395 pairs of residuals of which 614,040 or

2.3 percent have a subscript in common (the order of subscripts con­

sidered). From the sample of 20 residuals, 190 pairs were formed which

resulted in 6 overlapped and 184 exolusive pairs. Using the same compu-

tational prooedure used above, the oorrelation was estimated to be .998

(See Table 19). Although the estimation was based on a small sarr~le of

residuals, there appears to be a sizeable positive intraclass correla-

tion in this type of analysis of pair data.

Having examined the three assumptions of regression theory and

found all three to be somewhat unrealistic, one should be more cautious

in interpreting the t and F values. On the other hand, it should be

noted that the leptokurtosis has a conservative effect on F ratios, the

variance heterogeneity does not seem to be too extreme, and the non­

zero correlations of errors affects only 4.6 peroent of the cases of

,e e •Table 18. Differences of Residuals and Estimation of Correlation for the Unordered Pair Regression

Resi- D iff ere n c e sin A b sol ute Val u e~

No. I. D. duals (1) (2) (3) (4) (5) (6) (1) (8) (9) (10) (11) (12) (13) (14) (15) (16) (11) (18) (19)

1.5

237.25

1e3

43416.77

Exclusive pairs

7

20.39

142.79

Overlapping pairs

f= 1 - (20.39/237.25) =.914

Sum of Sqs.

Avg. Sq. Dif.

No. of pairs

(1) (4,47) -2.6(2) (11,36) -0.5 2.1(3) (2,67) +1.7 4.3 2.2(4) (3,35) -6.9 4.3 6.4 8.6(5) (4,45) -0.4 12.21. 0.1 2.1 6.5(6) (20,58) -1.1 1.5 0.6 2.8 5.8 0.7(7) (23,81) +0.6 3.2 1.1 1.1 7.5 1.0 1.7(8) (25,64) -0.5 2.1 0.0 2.2 6.4 0.1 O.~ 1.1(9) (13,56) +3.4 6.0 3.9 1.7 10.3 3.8 4.5 2.8 3.9

(10) (26,40) -27.4 24.8 26.9 29.1 20.5 27.0 26.3 28.0 26.9 30.8(11) (46,74) +0.5 3.1 1.0 1.2 7.4 0.9 1.6 0.1 1.0 2.9 27.9(12) (20,83) +3.3 5.9 3.8 1.6 10.2 3.7 14.41 2.7 3.8 0.1 30.7 2.8(13) (6,73) -0.2 2.4 0.3 1.9 6.7 0.2 0.9 0.8 0.3 3.6 27.2 0.7 3.5(14) (11,83) -4,,4 10 8 ]3.91 6.1 2.5 4.0 3.3 5.0 3.9 7.8 23.0 4.9 17.71 4.2(15) (13,68) -0.6 2.0 0.1 2.3 6.3 0.2 0.5 1.2 0.1 14.0[26.8 1.1 3.9 0.4 3.8(16) (59,71) -0.3 2.3 0.2 2.0 6.6 0.1 0.8 0.9 0.2 3.7 27.1 0.8 3.6 0.1 4.1 0.3(17) (25,84) -0.5 2.1 0.0 2.2 6.4 0.1 0.6 1.1 10.01 3.9 26.9 1.0 3.8 0.3 3.9 0.1 0.2(18) (28,34) +36.4 39.0 35.9 34.7 43.3 36.8 37.5 35.8 36.9 33.0 63.8 35.9 33.1 36.6 40.8 37.0 36.7 36.9(19) (21,30) -0.4 2.2 0.1 2.1 6.5 0.0 0.7 1.0 0.1 3.8 27.0 0.9 3.7 0.2 4.0 0.2 0.1 0.1 36.8(20) (24,56) -1.9 0.7 1.4 3.6 5.0 1.5 0.8 2.5 1.4 15.3r25.5 2.4 5.2 1.7 2.5 1.3 1.6 1.4 38.3

Boxed figures represent differences for overlapping pairs.-.J\J1

e e ~

Table 19. Differences of Residuals and Estimation of Correlation for Ordered Pair Regression

586.07

184

107837.01

Exclusive pairs

6

1.26

7.54

Overlapping pairs

f = 1 - (1.26/586.07) = .998

Sum of Sqs.

Avg. Sq. Dif.

No. of pairs

Resi- D iff ere n c e sin A b sol ute Val u e sNo. I. D. duals ~1.Li.2) (3) ~4) (5) (6) (1) (8) (9) (10) (11) (12) (13) (14) (12) (16") (11) (18) (19)(1) (67,28) -6.3(2) (42,66) -0.4 5.9(3) (33,83) +2.0 8.3 2.4(4) (1,24) +0.3 6.6 0.7 1.7

, (5) (78,59) -2.9 3.4 2.5 4.9 3.2(6) (78,59) ...3.0 3.3 2.6 5.0 3.3 jO.l]

(7) (41,84) -0.6 5.7 0.2 2.6 0.9 2.3 2.4(8) (28,29) -9.1 2.8 8.7 11.1 9.4 6.2 6.1 8.5(9) (52,33) +0.4 6.7 0.8 1.6 0.1 3.3 3.4 1.0 9.5

(10) (30,18) -0.9 5.4 0.5 2.9 1.2 2.0 2.1 0.3 8.2 1.3(11) (22, 2) +1.0 7.3 1.4 1.0 0.7 3.9 4.0 1.6 10.1 0.6 1.9(i2) (41,36) -1,,8 4.5 1.4 3.8 2.1 1.1 1.2 11..21 7.3 2.2 0.9 2.8(13) (36,39) +0.3 6.6 0.1 1.7 0.0 3.2 3.3 0.9 9.4 0.1 1.2 0.7 2.1(14) (47,39) -1.4 4.9 1.0 3.4 1.7 1.5 1.6 0.8 7.7 1.8 0.5 2.4 0.4 J1.71(15) (55,42) +0.2 6.5 0.6 1.8 0.1 3.1 3.2 0.8 9.3 0.2 1.1 0.8 2.0 0.1 1.6(16) (52,21) +1.2 7.5 1.6 0.8 0.9 4.1 4.2 1.8 10.3 lO.8J 2.1 0.2 3.0 0.9 2.,6 1.0(17) (79,39) +0.2 60 5 0.6 1.8 0.1 3.1 3.2 0.8 9.3 0.2 1.1 0.8 2.0 10.11. 11.61 0.0 1..0(18) (40,77) +73.2 79.5 73.6 71.2 72.9 76.1 76.2 73.8 82.3 72.8 14.1 72.2 75.0 72.9 74.6 73.0 72.0 73.0(19) (62,26) +2.0 8.3 2.4 0.0 1.7 4.9 5.0 2.6 11.1 1.6 2.9 1.0 3.8 1.7 3.4 1.8 0.8 1.8 71.2(20) (5,15) -3.0 3.3 2.6 5.0 3.3 0.1 0.0 1.4 6.1 3.4 2.1 4.0 1.2 3.3 1.6 3.2 4.2 3.2 76.2 5,,0

~0'\

Boxed figures represent differences for overlapping pairs.

•77

unordered pairs and 2.3 percent of the cases of ordered pairs.

Implications for Mathematical MOdel Building

The regression analysis was undertaken specifically for analytical

purposes, but the possibility of using analytical information for build­

ing a forecasting model may be worth examining. Although the analysis

gO far reported provide substantial information concerning tendencies

and patterns of mobility, the usefulness of regression equations for

quantitative solutions of forecasting seems to be limited, considering

the amount of variation accounted for by the equations. In order to be

useful the regression equations need to be improved by introducing

additional independent variables, disaggregating the mobility into

meaningful components, and applying some more suitable transformation

to the mobility rates.

Since the response variable in the regression equations represents

the extent to which the observed mobility deviates from the expected

mobility, additional consideration is necessary to develop a practical

model which would foreoast the volume of mobility. The full strategy

of building a forecasting mode:i may be first to perform this type of'

functional analysis at eaCh level of geographic and structural detail

and then to synthesize all components and linkages. This type of

strategy is often described as the systems approach. This approach can

be compared with the gravity models of migration. Although these two

types of models have similarities in many aspects, the main difference

lies in their conceptual formulation. While the gravity model is

essentially a formula with component parameters built in, the sytems

approach is a procedure for oonstructing a system analog. The relative

•T

78

superiority of the systems theory model to the gravity model was demon­

strated in a study of recreational traffio flows in 11ichigan (Ellis and

Van Doran, 1966). It is not intended here to review the sY9tems model

formulation techniques which have been developed in physical sciences

especially in electrical engineering, but the findings in this study

seem to indicate that further investigation in this line of approach is

worth pursuing.

The high positive intraclass oorrelation among the residuals found

in this study is worthy of special attention in building any forecasting

models. This suggests that there exist system effects stemming from

the peouliar struoture of the system. Gravity models assume that the

interchange between each pair of institutions is independent of that

between each other pair. But it appeared that they are highly dependent.

•79

S~~y AND CONCLUSIONS

This study has been concerned with analyzing patterns of migratory

movements of scholars among colleges and universities in the academic

training phase as well as in the postdoctoral phase of professional

careers. The focus of the study was on the total higher educational

system in which institutions of higher education are interacting with

one another in the exchange of scholars. It also was hoped that this

analysis would suggest some strategies of developing a mathematical

model which can satisfactorily predict institutional mobility.

Review of migration research literature, mathematical models of

migration and sociological studies of institutions of higher education

provided a conceptual frame of reference for the present study. The

academic community was conceptualized as a two-dimensional system: the

geographic distribution of institutions and the prestige structure of

institutions. It was hypothesized that institutional mobility would

increase as the proximity increases along these two dimensions.

Realizing the advantageous saving of research funds and time in

secondary analysis, an attempt was made to utilize existing data such

as the data collected by the National Science Foundation for the Nation­

al Register of Scientific and Technical Personnel. Since the data did

not allow the proposed analyses, it was decided to obtain a random

sample from the directories of professional societies. The American

Chemical Society's Directory of Graduate Research provided the neces­

sary data for the present study.

The analysis of institutional mobility patterns of chemists was

based on a random sample of 1,128 scholars from directories of graduate

•..

80

faculties covering the 1955-1967 period. Although the size of sample

was small, these longitudinal data supported on analysis of three types

of mobility: (1) from the institution of baccalaureate training to the

institution of doctorate training, (2) from institution of doctorate

training to the institution of postdoctoral employment, and (3) the job

change from one institution to another. MObility patterns were analyzed

by examining the departures of the observed from the expected frequen­

cies of movers. The results of the analysis can be summarized as

follows:

The mobility from the baccalaureate to the doctorate training was.

characterized by stronger tendencies toward regionalism than toward

prestige level homogeneity. It appeared that for their doctoral study,

students tended to stay at the same institution or move to institutions

of the same prestige level in the same region. Consequently, inter­

regional and interprestige level mobilities were less than would be

expected on the random distribution model. The regionalistic tendencies

seem to be stronger for the institutions at the lower prestige level.

The mobility from the doctoral institution to the institution of

employment was also oriented toward stronger regionalistic tendencies

than selective prestige level tendencies. Thus, the academic stratifi­

cation system in doctorate-to-employmentmobility can be said to be a

set of regional hierarchies rather than a rigid prestige hierarchy. It

was noted that downwaxd mobility was more common, espeoially at earlier

stages of postdoctoral careers. Institutions at the lower prestige

level had a relatively higher rate of inbreeding and a stronger region­

alistic orientation.

•81

82

the persistence of regional inequalities in the quality of higher

education, ·the intelleotual style and perspective, a.."1d the setting of

cultural patterns. These kinds of inequalities serve both as possible

sources of unnecessary disputes in academic community and as possible

bases for the structural cleavages within American society. Regional

tendencies would impose restrictions on the development of institutions

at the lower spectrum of quality and newly emerging universities.

Regions '\'lhere higher education is comparatively less effective are

likely to remain so if migration is allowed to remain the primary equi­

librium force and major adjustm~nt in regional differenoes in education­

al quality are not undertaken.

As to the question whether the regionalistic tendency might be

decreasing, this study did not provide any substantial eveidence. The

indication was that the young cohorts were slightly less oriented to­

ward regionalistic tendencies ~hat the old cohorts in the baccalaureate

to doctorate mobility and the doctorate to employment mobility. Fur­

ther efforts to investigate trends in these pattems over time would be

J:.·elevant.

Two kinds of regression analyses were performed to investigate the

association among the pair variables such as flows of mobility from the

origin to the destination and the distance between them, and the point

variables such as various characteristics of the origin or the desti­

nation point. The first regression analysis dealt with the unordered

pairs of institutions. In more familiar teminology in migration re­

search, the indices of mobility (dependent variable) in the unordered

pair regression oorresponds to gross migration, though the average

83

rather than the sum of two directional flows is usede The second re­

gression analysis was concerned with ordered pairs of institutionse In

this case, the dependent vaz-iable is directional flows of scholars from

one institution to anothere The results of both regression analyses

were not impressive in terms of the amount of variance accounted for,

but was useful in screening the implied relationships and provided

guidelines for further experimentatione

The distance variable consistantly yielded an inverse relationship

with the mcbilitYe The prestige and faculty compensation had some

effects on the mobility, that is, the greater the difference in pres­

tige scores and compensation between two institutions, the smaller the

mobility between them. Considering the amount of variance accounted

for by the regression, there was a need for introducing additional rele­

vant independent variables.

An examination of the residuals revealed a need for modifying

extreme outliers or for disaggregating the mobility into logical compo­

nents for separate analyses. It was found that there was a high posi­

tive intraclass correlation among the residuals\) wr.J.oh appeared to be

the refleotion of structural effects of the mobility system. Therefore

any models which assume independence among the pai:rwise interchanges of

mobility seems to be inappropriate. Any descriptive or forecasting

model would need to take into oonsideration the system effects by

building a separate functional relationship for each component of

mobility. An application of the system theory approach seems to offer

some help in this line of further investigation.

84

Finally, it should be pointed out that the small number of cases

has imposed certain limitations to the findings in this study. It is

hoped that the results of this study will lead to a larger study along

these lines.

85

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•Abbreviated Name

AlabamaArizonaArkansasBostonBrandeisBrooklyn Polytech.BrownBuffalo

California(Berkeley)

Ca.lifornia(Davis)

Cal. Tech.

Carnegie-MellonCase ReserveChicagoCincinnatiColoradoColumbiaConnecticutCornellDelawareDukeEmoryFloridaFlorida StateGeorgetownGeorgia Tech.HarvardHoustonIllinoisIllinois·Tech.IndianaIowaIowa StateJohns HopkinsKansasKansas StateKentuckyLouisiana State:M. I. T.

Maryland

91

APPENIlIX A

Institutions Included in the Study

Full Name and Location

University of Alabama (University, Ala.)University of Arizona (Tucson, Arizona)University of Arkansas (Fayetteville, Arkansas)Boston University (Boston, Mass.)Brandeis University (Waltham, ~Iass.)Polytechnio Institute of Brooklyn (Brooklyn, N. y.)Brown University (Providenoe, R. I.)state University of New York at Buffalo

(:Buffalo, N. y.)University of California (:Berkeley, Calif.)

University of California (Davis, Calif.)

California Institute of Technology(Pasadena, Calif.)

Carnegie-Mellon University (Pittsburgh, Pa.)Case Western Reserve University (Cleveland, Ohio)University of Chioago (Chicago, Ill.)University of Cincinnati (Cincinnati, Ohio)University of Colorado (Boulder, Colorado)Columbia. University (New York, N. y.)University of Connecticut (Storrs t Conn.)Cornell University (Ithaoa, Nc Y.)University of Delaware (NeWark

lDelaware)

Duke Uni:versity (Durham, J)T. C.Emory University (A-Uanta, Ga.University of Florid.a (Gainesville, Fla.)Florida State University (Tallahassee, Fla.)Georgetown University (Washington, D. C.) .Georgia. Institute of Technology (Atlanta, Ga.)Harvard Univeraity (Cambridge, Mass.)University of Houston (Houston, Texas)University of Illinois (Urbana, Ill.)Illinois Institute of Technology (Chicago, Ill.)Indiana University (Bloomington, Ind.)University of Iowa (Iowa City, Iowa)Iowa State University (Ames, Iowa)Johns Hopkins University (Baltimore, Md.)University of Kansas (Lawrence, Kansas)Kansas State University (Manhattan, Kansas)University of Kentucky (Lexington, Ky.)Louisiana Sta.te University (Baton Rouge, La.)Massachusetts Institute of Technology

(Cambridge, Mass.) .University of Maryland (College Park, Maryland)

•92

APPENDIX A (continued)

Abbreviated Name

MassachusettsMichiganMichigan StateMinnesotaMissouriN. Y. U.NebraskaNorth Carolina

N. C. State

NorthwestemNotre DameOhio StateOklahomaOklahoma StateOregonOregon StatePennsylvaniaPenn. StatePittsburghPrincetonPurdueRensselaerRiceRochesterRutgersSt. John'sSouthern Cal.

StanfordTempleTennesseeTexasTexas A & MTuftsTulaneU. C. L. A.utahVanderbiltVirginiaV. P. I.Washington

(St. Louis)

FIlII Name and Location

University of Massachusetts (Amherst, Mass.) .University of Michigan (Ann Arbor, Mich.)Michigan State University (East Lansing, Mich.)University of Minnesota (Minneapolis, Minn.)University of Missouri (Columbia, Mo.)New York University (New York, N. Y.)University of Nebraska (Lincoln, Nebraska)University of North Carolina at Chapel Hill

(Chapel Hill, N. C.)North Carolina State University at Raleigh

(Raleigh, N. C.)Northwestem University (Evanston, Ill.)University of Notre Dame (Notre Dame, Indiana)Ohio State University (Columbus, Ohio)University of Oklahoma (Norman, Oklahoma)Oklahoma State University (Stillwater, Oklahoma)University of Oregon (~ene, Oregon)Oregon State University (Corvallis, Oregon)University of Pennsylvania (Philadelphia, Pa.)Pennsylvania State University (University Park, Pa.)University of Pittsburgh (Pittsburgh, Pa.)Prinoeton University (Princeton, N. J.)Purdue University (Lafayette, Ind.)Rensselaer Polyteohnic Institute (Troy, N. Y.)Rioe University (Houston, Texas)

*University of Rochester (New York, N. Y.)Rutgers - The Sta.te University (Brunswick, N. J.)Saint John's University (Jamaioa, N. Y.)University of Southem California

(Los Angeles, Calif.)Stanford University (Stanford, Calif.)Temple University (Philadelphia, Pa.)University of Tennessee (KnOXVille( Tenn.)University of Texas (Austin, Texas)Texas A &MUniversity (College Station, Texas)Tufts University (Medford, Mass.)Tulane University (New Orleans, La.)University of Califomia (Los Angeles, Calif.)University of utah (Salt Lake City, utah)Vanderbilt University (Nashville, Tenn.)University of Virginia (Charlottesville, Va.)Virginia. Polytechnic Institute (Blacksburg, Va.)Washington University (St. Louis, Mo.)

*Name now changed to Rookefeller University.

• APPENDIX A (oontinued)

Abbreviated Hame Full Name and Looation

93

\vashington(Seattle)

Washington StateWayne StateWest VirginiaWisoonsinYale

University of Washington (Seattle, Washington)

Washington State University (Pullman, Washington)Wayne State University (Detroit, IvIioh.)West Virginia University (Morganton, W. V.)University of Wisoonsin (Madison, Wisoonsin)Yale University (New Haven, Conn.)

94• APPElIDIX 13

Regiona.l and Prestige Groupings of Institutions

Region PrestiGe Level Institution

New England 1 (High) Brandeis M. I. T.Brown YaleHarvard

4 (Low) Boston MassachusettsConnecticut Tufts

Middle Atlantic 1 (High) Brooklyn Polytech. Penn. stateColumbia PrincetonCornell

2 Carnegie-Mellon PittsburghPennsylvania Rochester

3 N. Y. U. RutgersRensselaer

4 (Low) Buffalo TempleSt. John's

Midwest 1 (High) Chicago MinnesotaIllinois NorthwesternIndiana Ohio StateIowa State PurdueMichigan Wisconsin

2 Ir,wa WashingtonKansas (St. Louis)Michigan State Wayne StateNotre Dame

3 Case Reserve Kansas StateCincinnati NebraskaIllinois Tech.

4 (Low) Missouri

South 1 (High) Johns Hopkins TexasRice

- 2 Duke North CarolinaFlorida

• APPENDIX B (continued)

95

Prestige Level Institution

South (conttd)

West

3

1 (High)

2

3

DelawareGeorgia Tech.Louisiana State

AlabamaArkansasEmoryFlorida Sta-teGeorgetownHoustonKentuckyN. C. State

California(Berkeley)

Cal. Tech.Stanford

California(Davis)

Colorado

ArizonaOregon State

MarylandVanderbiltVirginia

OklahomaOklahoma StateTennesseeTexas A & MTulaneV. P. I.West Virginia

U. C. L. A.Washington

(Seattle)

OregonSouthern Cal.Utah

Washington State

• 96

APPENJ)IX C

A Note on the Method Used in Calculating ExpectedFrequencies in Mobility ~~trix

In earlier studies of social mobility, the concept of "perfect

mobility" was introduced to describe the idealized situation where an

actor's social status at a given time is independent of his status at

an earlier time or his father's status (Glass, 1954, pp. 218-265).

This concept corresponds to the concept of independence in a contin-

gency table in elementary statistics textbooks.

The contingency analysis in testing for independence in a k x k

matrix involves computation of estimates of the 2k non-negative para-

meters, PI ••• Pk, Rl • • • ~, which determine the probability qij

associated with a given cell (i,j) according to the formula:

k ksuch that L P. = 1 and L R. '" 1-

i=l ~ j=l J

Then, the expected value of the frequency f ij in the cell (i,j) can be

written as:

where n is the total frequency for the table. Denoting the observed

totals in the i-th row and j ..th column by r i and cj ' the maximum likeli­

hood estimators of P. and R. are:~ J

Pi = ri/n and Rj = cj/n

We can thus see that the maximum likelihood estimator of E(f.. ).. ~J

Fij = nP1.Rj = ricj/n

is:

•97

>Iodification of this statistical method is necessary in certain

circumstances when dealing with incomplete contingency tables. An in­

complete table is one containing at least one cell for which no frequency

(zero or otherwise) is provided. Such a cell occurs (1) if for any

reason the appropriate value cannot be determined, (2) if one wishes

deliberately to eliminate one or more cells from consideration, though

their frequencies are known, and (3) if the cell has no meaning in a

particular problem.

An example is the transaction flow tabl" in which one is usually

concerned exclusively with flows between areas or institutions. In the

mobility analysis of industrial workers, it \vas suggested t.hat the stay­

ers should be separated from the movers (Elumen, ~~., 1955). For

this p~rpose, the conoept of '.l quasi-perfect mobility'l was introduced

(Goodman, 1965) to desoribe the situation in which an actor's status is

independent of his father's status oonsidering only those individuals

who have moved out of their father's status strata. This model treats

mobility as a separate phenomenon from the statuB inheritance or tend­

enoy of remaining in a social or geographi~ looation.

·vlhen the stayers at the main diagonal in a mobility matrix are to

be excluded from the analysis, the expected pattern of mobility for the

movers can be derived from the "quasi-perfect mobility" model and these

expectations can be estimated from the observed marginal distributions

of movers exoluding the stayers. This model oorresponds to the concept

of independence in a restricted or incomplete contingenoy table.

The analysis of restricted oontingency table where main diagonal

oells are to be excluded from oonsideration will be treated here. Since

•98

the expected frequencies for diagonal cells must effectively be restrict-

ed to zero, the parameters P. and R. defined above will no longer apply.J. J

Denoting by P.. the modified probability associated with the cell (i,j),J.J

in order to make the probability of falling in nondiagonal cells add up

to unity, we should define:

{

O,

Pij = P.R./[l - t P R l,J. J 1Il=1 m ill,;

We can rewrite the above formula as:

for i=j

for i=j

where Ui and Vj are positive constants which are such that

k k k k kL.: L. Pi' = [L L U.v·1 -L: U Vm III 1.i=l j=l J i=l j=l J. J mel m

The formula for the expected frequency in each nondiagonal cell bij is

where h is the total frequency in nondiagonal cells.

The maximum likelihood estimator of E(b .. ) isJ.J

Bij = hUIVj, for i~j

where U! and V~ are the maximum likelihood estimatore of Ui and VJ.,

J. J

respectively•

.An iterative method for determining the U! and V~ is given byJ. J

Goodman (1964). The iterative procedure given by Goodman not only leads

to the desired estimates but also reduces the number of arithmetic opera-

tions, compared with the corresponding procedure introduced earlier by

Savage and Deutsch (1960). Briefly, the procedure given by Goodman is

•99

as follows.

Let xi and Yj denote the totals in the i-th row and j-th column not

including the diagonal oell. The iterative procedure is initiated

taking

oW. = x.~ ~

The 2m-th step (m~l) is executed taking

Zi2m- l = yi /(w. 2m- 2 _ Wi2m- 2J

kwhere W. = 2: Wi. As the (2m+l)th step, take

i=l

W. 2m = x./(z.2m-l _ Z. 2m-lJ~ ~ ~

kwhere Z. = L. Z .•

j=l JThe iterative steps are continued for mal, 2, . . ,

until the desired accuracy is obtained. Then the expected value Bij for

a given nondiagonal cell can be obtained by

B. . = w. 2m Z. 2m-l for i'&j.~J ~ J

A generalized computer program to analyze contingency tables with

restrictions at the diagonal as well as nondiagonal is given by Coble

(1969). This program handles up to a 50 x 50 matrix with 50(50-2) or

less restricted cells. For the present study, this computer program was

expanded to handle up to 90 x 90 matrix and adapted for the IBM 360/75

at the Triangle University Computing Center.

•APPENDIX D

statistical Tables

Table D. 1 Chi-Square Statistics for Analysis of theBaccalaureate to Doctorate Mobility Patterns

Table D. 2 Chi-Square Statistics for Analysis of theDoctorate to Employment 110bility Patterns

Table D. 3 Chi-Square Statistics for Analysis of thePostdoctoral Job Mobility Patterns

Table D. 4 Zero-Order Correlation Matrix for UnorderedPair Regression

Table D. 5 Zero-Order Correlation Matrix for Ordered PairRegression

Table D. 6 Standard Partial Regression Coefficients

Table D. 7 Analysis of Variance Tables for Unordered Pairand Ordered Pair Regression

100

Table D. 1 Chi-Square Statistics for Analysis of theBaccalaureate to Doctorate MObility Patterns

101 --Factor and Component Observed Expected Chi-square

of Nobility Frequency Frequency Value

Re«ion and Prestige Level

(I) Intra-regional, 78 40horizontal

(II) Intra-regional, 47 30 ,; ... 57.72"*vertical

(III) Inter-regional, 137 156 d.f.... 3horizontal

(IV) Inter-regional, -2§. ..Jl.4.vertical

Total 360 360

Region e2(I) Intra-regional mobility 125 70 X = 53.64"*

(II) Inter-regional mobility ~ ..l2.Q. d•. f .... 1

Total 360 360

Prestis,e Level,

2(I) Horizontal mobility 215 196 it "" 4.04*

(II) Vertical mobility ..ill. ~ d.f. "" 1

Total 360 360

Interaction

By subtraction 2X. ... 0.03

d.f.... 1..

* Significant at .05 level** Significant at .01 level

"* SignU'icant at .001 level •

•102

Table D. 2 Chi-Square Statistics for Analysis of theDoctorate to Emp10ymant Mobility Patterns

Factor and Componentof Mobility

ObservedFrequency

ExpectedFrequency

Chi-squareValue

Region and Prestige Level

(I) Intra-regional,horizontal

(II) Intra-regional,vertical

(III) Inter-regional,horizontal

(IV) Inter-regional,vertical

Total

84 54

128 76 2 68.17***~ ...

155 168 d.f.... 3

..£2Q. ....ll2.

617 617

Region

(I) Intra-regional mobility

(II) Inter-regional mobility

Total

Prestige Level

212

....4.Q2

617

130

.Ml617

2X ... 65.53***

d.f.... 1

(I) Horizontal mobility

(II) Vertical mobility

Total

Interaotion

239 222 2X ... 2.03

.....ll§. ~ d.f.... 1

617 617

By subtraction

* Significant at .05 level** Signifioant at .01 level

*** Significant at .001 level

2X ... 0.61

d.f.... 1

•103

Table D. 3 Chi-Square Statistics for Analysis of thePost-doctoral Job Mobility Patterns

Factor and Componentof 1"'10hility

ObservedFrequency

ExpectedFrequency

Chi-squareValue

Region and Prestige Level

(I) Intra-regional,horizon~ual

(II) Intra-rf)gional,vertical

(III) Inter-~egional,horili.wntal

(IV) Inte~-regional,vertical

Total

Region

7 6.2

18 11.5 7.-2 = 9.85*

28 21. 7 d.f. = 3

-lQ. 43.6

83 83.0

(I) 1ntra-regional mobility

(II)! Inter-regional mobility

Total

,Eyestige Level

(I) Horizontal mobility

(II) Vertical mobility

Total

Interaction

25

27.9

55.1

8;.0

d.!. = 1

1 = 2.72

d.f. = 1

By subtraction

* Significant at .05 level** Significant at .01 level

*** Significant at .001 level

d.!•• 1

- -Table D. 4 Zero-Order Correlation Matrix for Unordered Pair Regression

. " e

- e

Table D. 5 Zero-Order Correlation Matrix for Ordered Pair Regression

, . e

• Table D. 6 Standard Partial Regression Coefficients

106

~ Independent Bacoalaureate Dootorate to Postdoctoralvariable to dootorate employment job

mobility mobility mobility

(I) Unordered pair regression

Distanoe -0.1208 -0.1209 -0.0482

Average of -0.0668 -0.0747 -0.0235prestige soores

Absolute differenoe -0.0040 -0.0426 -0.0087in prestige scores

Average of -0.0426 0.0100 0.0098oompensation

Absolute differenoe -0.0077 -0.0404 ..0.0229in oompensation

(II) Ordered pair re6#ession

North-South 0.0119 0.0015 0.0100distance

East-West 0.0228 0.0105 0.0110distanoe

Signed differenoe -0.0423 -0.0443 -0.0179in prestige soores

Signed differenoe 0.0862 -0.0117 0.0152in oompensation

• Table D. 7 ~a1ys1s of VariapQe Tables for UnorderedP41~ and Qrde~ed Pair Re~ession

107

Sum of Mean FType of Ana1ys~s SOlU'qe d.f. Sq,uares Sq\lare Va.lue

(I) Unordered Pair Re6Fess~on

(1) Baccalaureate to R~&Tession 5 22243.24 4448.65 20.43***doctora.te mobility

Re~id~al ~ 794412.00 217.71

Total ;654 816655.24

(2) Doctorate to Regr~~sion 5 37198.11 7439.62 21.92***emplo~ent ~ob~1~t1

ResidVta.l 2649 ·12~8635.34 339.45

~ot~l 3654 1275833.45

(3) Postdocto~al job R,gression 5 554.96 110.99 2.81*mobi;lity

Re~id,ua;L 3642 141222,81 39.53

Total ;654 144807.77

(II) Ordered Pair ReBfession

(1) ~acoa1aureate to RegJ;'ess,ion 4 3743.87 ~35.97 7.45***doctorate mo~il,ity

~~s~dual 1305 918268.95 125.70

~ota1 7309 922012.82

(2) Doctorate to ~eq,ress:Lon 4 7243.61 1810.90 5.22***emp1Qyme~t mobil,ity

Re~1d~1 7305 2534866.22 347.00;

Tol;al 7309 2542109.84

(3) Postdocto~a~ job . Reg;ress1on 4 147.04 36.76 0.64 •mobility

Res1d~ . 7~05 416724.02 57.05

.. Tot~l 7~09 416901.06

, ,e * Significant at .0' level** Signi~ioant a.t .01 :level

*** Signifio~lI a.t .0Ol;Level;