© willett, harvard university graduate school of education, 8/4/2015s052/ii.2(b) – slide 1...
TRANSCRIPT
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 1
S052/II.2(b): Applied Data Analysis Roadmap of the Course – What Is Today’s Topic Area?
S052/II.2(b): Applied Data Analysis Roadmap of the Course – What Is Today’s Topic Area?
More details can be found in the “Course Objectives and Content” handout on the course webpage.More details can be found in the “Course Objectives and Content” handout on the course webpage.
Multiple RegressionAnalysis (MRA)
Multiple RegressionAnalysis (MRA) iiii XXY 22110
Do your residuals meet the required assumptions?
Test for residual
normality
Use influence statistics to
detect atypical datapoints
If your residuals are not independent,
replace OLS by GLS regression analysis
Use Individual
growth modeling
Specify a Multi-level
Model
If your sole predictor is continuous, MRA is
identical to correlational analysis
If your sole predictor is dichotomous, MRA is identical to a t-test
If your several predictors are
categorical, MRA is identical to ANOVA
If time is a predictor, you need discrete-
time survival analysis…
If your outcome is categorical, you need to
use…
Binomial logistic
regression analysis
(dichotomous outcome)
Multinomial logistic
regression analysis
(polytomous outcome)
Discriminant Analysis
If you have more predictors than you
can deal with,
Create taxonomies of fitted models and compare
them.Form composites of the indicators of any common
construct.
Conduct a Principal Components Analysis
Use Cluster Analysis
Transform the outcome or predictor
Use non-linear regression analysis.
If your outcome vs. predictor relationship
is non-linear,
Today’s Topic Area
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 2
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Printed Syllabus – What Is Today’s Topic?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Printed Syllabus – What Is Today’s Topic?
Please check inter-connections among the Roadmap, the Daily Topic Area, the Printed Syllabus, and the content of today’s class when you pre-read the day’s materials.
Please check inter-connections among the Roadmap, the Daily Topic Area, the Printed Syllabus, and the content of today’s class when you pre-read the day’s materials.
Today, I will: Introduce the multinomial logistic
regression model, distinguishing it from the binomial logistic regression model.
Fit a taxonomy of multinomial logistic regression models.
Compare and contrast the output obtained in a multinomial and a binomial logit analysis.
Explain an additional test (“Type III Analysis of Effects”) that is available in a multinomial logit analysis.
Test and interpret a fitted multinomial logistic regression model.
Today, I will: Introduce the multinomial logistic
regression model, distinguishing it from the binomial logistic regression model.
Fit a taxonomy of multinomial logistic regression models.
Compare and contrast the output obtained in a multinomial and a binomial logit analysis.
Explain an additional test (“Type III Analysis of Effects”) that is available in a multinomial logit analysis.
Test and interpret a fitted multinomial logistic regression model.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 3
Dataset ALT_RTS_GIRLS.txt
Overview Sub-sample of girls from the NELS:88 dataset in which girls are tracked as they exit from high school (by dropout, receipt of GED, or graduation) and enter college (no college, community college, four-year college).
Source Kurlaender, M. (2003). Reinforcing Disadvantage or Increasing Opportunity: Alternative Routes to Educational Attainment. Unpublished Doctoral Thesis, Harvard University Graduate School of Education, in process.
Sample size 5148 females
Info NELS:88 is a national longitudinal data-collection effort managed by the National Center for Education Statistics (NCES), providing longitudinal data on trends/transitions in young people’s lives as they develop, attend school, and embark on their careers. Data were collected from students, parents, teachers and high school principals, and from school records. The survey began with an 8th grade cohort in 1988. Cognitive tests (math, science, reading, history) were administered in the base year (1988), at first follow up (1990), and at second follow up (1992). Third and fourth follow up data were collected in 1994 and 2000. All school dropouts who could be located were retained in the study.
Information accompanying today’s dataset is in ALT_RTS_GIRLS_info.pdf ….Information accompanying today’s dataset is in ALT_RTS_GIRLS_info.pdf ….
Radcliffe, Class of ‘57
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Introducing the Alternative Routes to Education Dataset
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Introducing the Alternative Routes to Education Dataset
Broad Research Question:Broad Research Question:How is entry into college impacted
by race/ethnicity and socio-economic status?
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 4
Structure of Dataset
Col# Var Name Variable Description Variable Metric/Labels
1 ID Respondent’s NELS ID
2 COLLEGE Type of institution selected by the respondent for their initial postsecondary education
Polychotomous variable (1 = None, 2 = Tech/Voc or Community College, 3 = Four-Year College)
3 HSGRAD Respondent’s high school completion status Polychotomous variable (1 = HS Diploma,
2 = GED, 3 = Dropout)
4 READ Respondent’s performance on a standardized test of reading in 8th grade
Continuous variable (mean 53.22 and standard deviation 13.47, in the full sample)
5 MATH Respondent’s performance on a standardized test of math in 8th grade
Continuous variable (mean 53.40, and standard deviation 13.56, in the full sample)
6 WHITE Is the respondent Caucasian? Dichotomous: 0 = no; 1 = yes
7 BLACK Is the respondent African-American? Dichotomous: 0 = no; 1 = yes
8 LATINO Is the respondent Hispanic? Dichotomous: 0 = no; 1 = yes
9 SES Respondent’s composite socio-economic status in 8th grade (including: family income, parental education and occupation, household possessions).
Continuous variable (mean 2.92 and standard deviation .79 in the full sample)
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Printed Syllabus – What Is Today’s Topic?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Printed Syllabus – What Is Today’s Topic?
Polychotomous categorical outcomeoutcomevariable
Principle question question predictorspredictors
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 5
To model the relationship between a polychotomous outcome, like COLLEGE (which has three categories – “Four-Year College,” “Community College,” & “No College”) and a predictor like SES, we use the same “logit” approach that we have already developed …
To model the relationship between a polychotomous outcome, like COLLEGE (which has three categories – “Four-Year College,” “Community College,” & “No College”) and a predictor like SES, we use the same “logit” approach that we have already developed …
SESeCOLLEGEProb
101
1????
We still use the logistic regression function, containing usual parameters and predictors, to represent right hand side of the model
We still use the logistic regression function, containing usual parameters and predictors, to represent right hand side of the model
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis How Do You Model The Relationship Between A Polytomous Outcome & Predictors?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis How Do You Model The Relationship Between A Polytomous Outcome & Predictors?
But, because the outcome is no longer a dichotomy, we have to do something about the left-hand side
of the model.
But, because the outcome is no longer a dichotomy, we have to do something about the left-hand side
of the model.
Under the multinomial logit approach, we simultaneously model the relationship between predictors and two outcome probabilities: Probability of going to
community college vs. not going to college,
Probability of going to 4-year college vs. not going to college.
0
1
1
P(4-Year vs. No Coll)
P(Comm Coll vs. No Coll)
SES
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 6
So, the hypothesized multinomial logit model simply becomes a simultaneous collection of two parts …So, the hypothesized multinomial logit model simply becomes a simultaneous collection of two parts …
Both parts of the new multinomial model are fitted
simultaneously to the data, with parameter estimates and goodness-of-fit statistics
interpreted in the usual way …
Both parts of the new multinomial model are fitted
simultaneously to the data, with parameter estimates and goodness-of-fit statistics
interpreted in the usual way …
SESe
CollegeNovsCollege
yearProb )3(
1
)3(
01
1.4
SESeCollegeNovsCollege
CommunityProb )2(1
)2(01
1.
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis How Do You Model The Relationship Between A Polytomous Outcome & Predictors?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis How Do You Model The Relationship Between A Polytomous Outcome & Predictors?
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 7
*---------------------------------------------------------------------------------*Input the data, name and label the variables in the dataset*---------------------------------------------------------------------------------*; DATA ALT_RTS_GIRLS; INFILE 'C:\DATA\S052\ALT_RTS_GIRLS.txt'; INPUT ID COLLEGE HSGRAD READ MATH WHITE BLACK LATINO SES; LABEL COLLEGE = 'Institution Selected for Postsec Ed' BLACK = 'Is respondent African-American?' LATINO = 'Is respondent Hispanic?' WHITE = 'Is respondent Caucasian?‘ SES = 'Socio-economic status'; * Create a single categorical variable to represent race/ethnicity; IF BLACK=1 THEN RACE=1; IF LATINO=1 THEN RACE=2; IF WHITE=1 THEN RACE=3; * Create the required two-way interactions between RACE and SES; BxSES = BLACK*SES; LxSES = LATINO*SES; WxSES = WHITE*SES; PROC FORMAT; VALUE CFMT 1='No Postsec Ed' 2='Tech/Voc or Comm Coll' 3='4-Year College'; VALUE RFMT 1='Black' 2='Latino' 3='White';
*---------------------------------------------------------------------------------*Input the data, name and label the variables in the dataset*---------------------------------------------------------------------------------*; DATA ALT_RTS_GIRLS; INFILE 'C:\DATA\S052\ALT_RTS_GIRLS.txt'; INPUT ID COLLEGE HSGRAD READ MATH WHITE BLACK LATINO SES; LABEL COLLEGE = 'Institution Selected for Postsec Ed' BLACK = 'Is respondent African-American?' LATINO = 'Is respondent Hispanic?' WHITE = 'Is respondent Caucasian?‘ SES = 'Socio-economic status'; * Create a single categorical variable to represent race/ethnicity; IF BLACK=1 THEN RACE=1; IF LATINO=1 THEN RACE=2; IF WHITE=1 THEN RACE=3; * Create the required two-way interactions between RACE and SES; BxSES = BLACK*SES; LxSES = LATINO*SES; WxSES = WHITE*SES; PROC FORMAT; VALUE CFMT 1='No Postsec Ed' 2='Tech/Voc or Comm Coll' 3='4-Year College'; VALUE RFMT 1='Black' 2='Latino' 3='White';
Data-Analytic Handout II_2b_1 …Data-Analytic Handout II_2b_1 …
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Reading The Alternative Routes Data Into PC-SAS
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Reading The Alternative Routes Data Into PC-SAS
Standard input statementsStandard input statements
Creates a set of two-way interactions needed in subsequent
logistic regression analyses.
Creates a set of two-way interactions needed in subsequent
logistic regression analyses.
Create a categorical variable representing race/ethnicity for use
in subsequent tabulations
Create a categorical variable representing race/ethnicity for use
in subsequent tabulations
Format selected categorical variables for use in subsequent
tabulations
Format selected categorical variables for use in subsequent
tabulations
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 8
*---------------------------------------------------------------------------------*Obtaining statistics on COLLEGE choice for the different racial/ethnic groups*---------------------------------------------------------------------------------*;* Cross-tabulation of COLLEGE and RACE; PROC FREQ DATA=ALT_RTS_GIRLS; TABLE COLLEGE*RACE / NOROW CHISQ CELLCHI2; FORMAT RACE RFMT. COLLEGE CFMT.;
* Distribution of SES by COLLEGE and RACE; PROC TABULATE DATA=ALT_RTS_GIRLS; CLASS COLLEGE RACE; VAR SES; TABLE (COLLEGE*(RACE ALL)),(SES*(P5 MEDIAN P95)); FORMAT RACE RFMT. COLLEGE CFMT.;
*---------------------------------------------------------------------------------*Obtaining statistics on COLLEGE choice for the different racial/ethnic groups*---------------------------------------------------------------------------------*;* Cross-tabulation of COLLEGE and RACE; PROC FREQ DATA=ALT_RTS_GIRLS; TABLE COLLEGE*RACE / NOROW CHISQ CELLCHI2; FORMAT RACE RFMT. COLLEGE CFMT.;
* Distribution of SES by COLLEGE and RACE; PROC TABULATE DATA=ALT_RTS_GIRLS; CLASS COLLEGE RACE; VAR SES; TABLE (COLLEGE*(RACE ALL)),(SES*(P5 MEDIAN P95)); FORMAT RACE RFMT. COLLEGE CFMT.;
First, let’s conduct exploratory analyses to examine the bivariate relationships between the polychotomous outcome COLLEGE and predictors RACE and SES using classical contingency table analysis …First, let’s conduct exploratory analyses to examine the bivariate relationships between the polychotomous outcome COLLEGE and predictors RACE and SES using classical contingency table analysis …
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Programming Exploratory Data Analysis In The Alternative Routes Dataset
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Programming Exploratory Data Analysis In The Alternative Routes Dataset
Compute statistics by RACE, and for ALL
the sample.
Estimate the 5th %ile, median and 95th %ile of
SES for each group
Obtaining descriptive statistics on continuous
variable SES within each of the COLLEGE by RACE
subgroups (this is useful for subsequent plotting of
prototypical fitted trend lines).
Obtaining descriptive statistics on continuous
variable SES within each of the COLLEGE by RACE
subgroups (this is useful for subsequent plotting of
prototypical fitted trend lines).
Compute the 2 statistic
Compute the cell contributions to the 2 statisticEliminate row percentages
Standard two-way contingency-table analysis of
the bivariate relationship between categorical variables
COLLEGE and RACE.
Standard two-way contingency-table analysis of
the bivariate relationship between categorical variables
COLLEGE and RACE.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 9
COLLEGE(Institution Selected for Postsec Ed)
RACEFrequency ‚Cell Chi-Square ‚Percent ‚Col Pct ‚Black ‚Latino ‚White ‚ TotalƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆNo Postsec Ed ‚ 120 ‚ 192 ‚ 716 ‚ 1028 ‚ 1.1294 ‚ 16.74 ‚ 4.6433 ‚ ‚ 2.21 ‚ 3.54 ‚ 13.22 ‚ 18.97 ‚ 20.91 ‚ 25.46 ‚ 17.51 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTech/Voc or Comm ‚ 225 ‚ 365 ‚ 1467 ‚ 2057 Coll ‚ 0.2297 ‚ 21.656 ‚ 4.7421 ‚ ‚ 4.15 ‚ 6.74 ‚ 27.08 ‚ 37.97 ‚ 39.20 ‚ 48.41 ‚ 35.87 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ4-Year College ‚ 229 ‚ 197 ‚ 1907 ‚ 2333 ‚ 1.3351 ‚ 50.206 ‚ 12.077 ‚ ‚ 4.23 ‚ 3.64 ‚ 35.20 ‚ 43.06 ‚ 39.90 ‚ 26.13 ‚ 46.63 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTotal 574 754 4090 5418 10.59 13.92 75.49 100.00 Statistics for Table of COLLEGE by RACE Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 4 112.7585 <.0001Likelihood Ratio Chi-Square 4 117.5525 <.0001Mantel-Haenszel Chi-Square 1 41.2598 <.0001
COLLEGE(Institution Selected for Postsec Ed)
RACEFrequency ‚Cell Chi-Square ‚Percent ‚Col Pct ‚Black ‚Latino ‚White ‚ TotalƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆNo Postsec Ed ‚ 120 ‚ 192 ‚ 716 ‚ 1028 ‚ 1.1294 ‚ 16.74 ‚ 4.6433 ‚ ‚ 2.21 ‚ 3.54 ‚ 13.22 ‚ 18.97 ‚ 20.91 ‚ 25.46 ‚ 17.51 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTech/Voc or Comm ‚ 225 ‚ 365 ‚ 1467 ‚ 2057 Coll ‚ 0.2297 ‚ 21.656 ‚ 4.7421 ‚ ‚ 4.15 ‚ 6.74 ‚ 27.08 ‚ 37.97 ‚ 39.20 ‚ 48.41 ‚ 35.87 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ4-Year College ‚ 229 ‚ 197 ‚ 1907 ‚ 2333 ‚ 1.3351 ‚ 50.206 ‚ 12.077 ‚ ‚ 4.23 ‚ 3.64 ‚ 35.20 ‚ 43.06 ‚ 39.90 ‚ 26.13 ‚ 46.63 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTotal 574 754 4090 5418 10.59 13.92 75.49 100.00 Statistics for Table of COLLEGE by RACE Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 4 112.7585 <.0001Likelihood Ratio Chi-Square 4 117.5525 <.0001Mantel-Haenszel Chi-Square 1 41.2598 <.0001
Standard test associated with a two-way contingency analysis:
1. The sample 2 statistic compares the observed frequencies to the frequencies expected under the null hypothesis.
2. The statistic is computed as follows:
Standard test associated with a two-way contingency analysis:
1. The sample 2 statistic compares the observed frequencies to the frequencies expected under the null hypothesis.
2. The statistic is computed as follows:
cellsall Exp
ExpObsStatistic Pearson
2
2
H0: COLLEGE and RACE are not related, in the population.
Test statistic & p-value: 2 = 112.75 ( p<.0001)
Decision: Reject H0
Conclusion: In the population, race/ethnicity is an important predictor of a girl’s choice of type of college.
H0: COLLEGE and RACE are not related, in the population.
Test statistic & p-value: 2 = 112.75 ( p<.0001)
Decision: Reject H0
Conclusion: In the population, race/ethnicity is an important predictor of a girl’s choice of type of college.
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Classical Contingency Table Analysis In The Alternative Routes Dataset
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Classical Contingency Table Analysis In The Alternative Routes Dataset
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 10
COLLEGE(Institution Selected for Postsec Ed)
RACEFrequency ‚Cell Chi-Square ‚Percent ‚Col Pct ‚Black ‚Latino ‚White ‚ TotalƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆNo Postsec Ed ‚ 120 ‚ 192 ‚ 716 ‚ 1028 ‚ 1.1294 ‚ 16.74 ‚ 4.6433 ‚ ‚ 2.21 ‚ 3.54 ‚ 13.22 ‚ 18.97 ‚ 20.91 ‚ 25.46 ‚ 17.51 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTech/Voc or Comm ‚ 225 ‚ 365 ‚ 1467 ‚ 2057 Coll ‚ 0.2297 ‚ 21.656 ‚ 4.7421 ‚ ‚ 4.15 ‚ 6.74 ‚ 27.08 ‚ 37.97 ‚ 39.20 ‚ 48.41 ‚ 35.87 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ4-Year College ‚ 229 ‚ 197 ‚ 1907 ‚ 2333 ‚ 1.3351 ‚ 50.206 ‚ 12.077 ‚ ‚ 4.23 ‚ 3.64 ‚ 35.20 ‚ 43.06 ‚ 39.90 ‚ 26.13 ‚ 46.63 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTotal 574 754 4090 5418 10.59 13.92 75.49 100.00 Statistics for Table of COLLEGE by RACE Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 4 112.7585 <.0001Likelihood Ratio Chi-Square 4 117.5525 <.0001Mantel-Haenszel Chi-Square 1 41.2598 <.0001
COLLEGE(Institution Selected for Postsec Ed)
RACEFrequency ‚Cell Chi-Square ‚Percent ‚Col Pct ‚Black ‚Latino ‚White ‚ TotalƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆNo Postsec Ed ‚ 120 ‚ 192 ‚ 716 ‚ 1028 ‚ 1.1294 ‚ 16.74 ‚ 4.6433 ‚ ‚ 2.21 ‚ 3.54 ‚ 13.22 ‚ 18.97 ‚ 20.91 ‚ 25.46 ‚ 17.51 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTech/Voc or Comm ‚ 225 ‚ 365 ‚ 1467 ‚ 2057 Coll ‚ 0.2297 ‚ 21.656 ‚ 4.7421 ‚ ‚ 4.15 ‚ 6.74 ‚ 27.08 ‚ 37.97 ‚ 39.20 ‚ 48.41 ‚ 35.87 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ4-Year College ‚ 229 ‚ 197 ‚ 1907 ‚ 2333 ‚ 1.3351 ‚ 50.206 ‚ 12.077 ‚ ‚ 4.23 ‚ 3.64 ‚ 35.20 ‚ 43.06 ‚ 39.90 ‚ 26.13 ‚ 46.63 ‚ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTotal 574 754 4090 5418 10.59 13.92 75.49 100.00 Statistics for Table of COLLEGE by RACE Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 4 112.7585 <.0001Likelihood Ratio Chi-Square 4 117.5525 <.0001Mantel-Haenszel Chi-Square 1 41.2598 <.0001
A useful diagnostic tool that can help you determine where the detected relationship really resides….
A useful diagnostic tool that can help you determine where the detected relationship really resides….
12.07750.20621.65616.740
3351.17421.42297.06433.41294.1
7585.112
2
2
2
onscontributi cell the of Sum Table
Exp
ExpObs to onContributi Cell
cell that for
Examine each cell for a “large” contribution to the 2 statistic: The story is really about Latinos:
• More Latinos than expected are going to community college, or not going to college at all.
• Fewer Latinos than expected are going to 4 year college.
However, there are a few more Whites than expected going to 4-year college.
Examine each cell for a “large” contribution to the 2 statistic: The story is really about Latinos:
• More Latinos than expected are going to community college, or not going to college at all.
• Fewer Latinos than expected are going to 4 year college.
However, there are a few more Whites than expected going to 4-year college.
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Classical Contingency Table Analysis In The Alternative Routes Dataset
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Classical Contingency Table Analysis In The Alternative Routes Dataset
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 11
„ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ† ‚ ‚ Socio-economic status ‚ ‚ ‡ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ P5 ‚ Median ‚ P95 ‚ ‡ƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Institut-‚RACE ‚ ‚ ‚ ‚ ‚ion ‚ ‚ ‚ ‚ ‚ ‚Selected ‚ ‚ ‚ ‚ ‚ ‚for ‚ ‚ ‚ ‚ ‚ ‚Postsec ‚ ‚ ‚ ‚ ‚ ‚Ed ‚ ‚ ‚ ‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚No ‚Black ‚ 0.99‚ 1.96‚ 3.19‚ ‚Postsec ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Ed ‚Latino ‚ 1.06‚ 1.81‚ 2.99‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 1.45‚ 2.38‚ 3.42‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.34‚ 2.28‚ 3.34‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Tech/Voc ‚RACE ‚ ‚ ‚ ‚ ‚or Comm ‡ƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚Coll ‚Black ‚ 1.30‚ 2.41‚ 3.55‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚Latino ‚ 1.42‚ 2.33‚ 3.68‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 1.79‚ 2.84‚ 3.81‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.62‚ 2.74‚ 3.76‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚4-Year ‚RACE ‚ ‚ ‚ ‚ ‚College ‡ƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚ ‚Black ‚ 1.63‚ 2.98‚ 4.15‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚Latino ‚ 1.49‚ 2.68‚ 4.13‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 2.20‚ 3.37‚ 4.39‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.97‚ 3.28‚ 4.36‚ Šƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒŒ
„ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ† ‚ ‚ Socio-economic status ‚ ‚ ‡ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ P5 ‚ Median ‚ P95 ‚ ‡ƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Institut-‚RACE ‚ ‚ ‚ ‚ ‚ion ‚ ‚ ‚ ‚ ‚ ‚Selected ‚ ‚ ‚ ‚ ‚ ‚for ‚ ‚ ‚ ‚ ‚ ‚Postsec ‚ ‚ ‚ ‚ ‚ ‚Ed ‚ ‚ ‚ ‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚No ‚Black ‚ 0.99‚ 1.96‚ 3.19‚ ‚Postsec ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Ed ‚Latino ‚ 1.06‚ 1.81‚ 2.99‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 1.45‚ 2.38‚ 3.42‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.34‚ 2.28‚ 3.34‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚Tech/Voc ‚RACE ‚ ‚ ‚ ‚ ‚or Comm ‡ƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚Coll ‚Black ‚ 1.30‚ 2.41‚ 3.55‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚Latino ‚ 1.42‚ 2.33‚ 3.68‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 1.79‚ 2.84‚ 3.81‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.62‚ 2.74‚ 3.76‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚4-Year ‚RACE ‚ ‚ ‚ ‚ ‚College ‡ƒƒƒƒƒƒƒƒƒ‰ ‚ ‚ ‚ ‚ ‚Black ‚ 1.63‚ 2.98‚ 4.15‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚Latino ‚ 1.49‚ 2.68‚ 4.13‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚White ‚ 2.20‚ 3.37‚ 4.39‚ ‚ ‡ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒ‰ ‚ ‚All ‚ 1.97‚ 3.28‚ 4.36‚ Šƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒ‹ƒƒƒƒƒƒƒƒƒƒƒƒŒ
Useful to know, when we produce prototypical fitted plots….
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Tabulation of SES, by COLLEGE and RACE
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Tabulation of SES, by COLLEGE and RACE
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 12
*---------------------------------------------------------------------------------*Fitting A Taxonomy Of Nested Multinomial Logit Models*---------------------------------------------------------------------------------*;PROC LOGISTIC DATA=ALT_RTS_GIRLS; M1: MODEL COLLEGE(ref='1')= BLACK LATINO / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M2: MODEL COLLEGE(ref='1')= SES / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M3: MODEL COLLEGE(ref='1')= BLACK LATINO SES / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M4: MODEL COLLEGE(ref='1')= BLACK LATINO SES BxSES LxSES / LINK=GLOGIT EXPB RSQUARE;
*---------------------------------------------------------------------------------*Fitting A Taxonomy Of Nested Multinomial Logit Models*---------------------------------------------------------------------------------*;PROC LOGISTIC DATA=ALT_RTS_GIRLS; M1: MODEL COLLEGE(ref='1')= BLACK LATINO / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M2: MODEL COLLEGE(ref='1')= SES / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M3: MODEL COLLEGE(ref='1')= BLACK LATINO SES / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC DATA=ALT_RTS_GIRLS; M4: MODEL COLLEGE(ref='1')= BLACK LATINO SES BxSES LxSES / LINK=GLOGIT EXPB RSQUARE;
PROC LOGISTIC can fit models for several categorical outcomes:Binomial logit (by default, if the outcome is
dichotomous),Ordinal logit (by default, if the outcome is ordinal
and more than two categories),Multinomial logit, if you choose the GLOGIT
(“generalized logit”) “link” function.
PROC LOGISTIC can fit models for several categorical outcomes:Binomial logit (by default, if the outcome is
dichotomous),Ordinal logit (by default, if the outcome is ordinal
and more than two categories),Multinomial logit, if you choose the GLOGIT
(“generalized logit”) “link” function.
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Fitting A Taxonomy of Multinomial Logit Models To The Alternative Routes DataS052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis
Fitting A Taxonomy of Multinomial Logit Models To The Alternative Routes Data
When fitting a multinomial model, you must specify the common reference category that will be used in each of the simultaneous binomial comparisons: Here, I have chosen “1” or “no college” as
the reference category. Any of the available categories can be
selected – it’s a substantive choice, not a statistical one.
When fitting a multinomial model, you must specify the common reference category that will be used in each of the simultaneous binomial comparisons: Here, I have chosen “1” or “no college” as
the reference category. Any of the available categories can be
selected – it’s a substantive choice, not a statistical one.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 13
The LOGISTIC Procedure Model Information Data Set WORK.ALT_RTS_GIRLSResponse Variable COLLEGE Institution Selected for Postsec EdNumber of Response Levels 3Number of Observations 5418Model generalized logitOptimization Technique Fisher's scoring Response Profile Ordered Total Value COLLEGE Frequency 1 1 1028 2 2 2057 3 3 2333 Logits modeled use COLLEGE=1 as the reference category. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.
The LOGISTIC Procedure Model Information Data Set WORK.ALT_RTS_GIRLSResponse Variable COLLEGE Institution Selected for Postsec EdNumber of Response Levels 3Number of Observations 5418Model generalized logitOptimization Technique Fisher's scoring Response Profile Ordered Total Value COLLEGE Frequency 1 1 1028 2 2 2057 3 3 2333 Logits modeled use COLLEGE=1 as the reference category. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.
Examine the output for Model M1, containing the main effects of only predictors BLACK and LATINO …Examine the output for Model M1, containing the main effects of only predictors BLACK and LATINO …
The history of the fitting process looks very similar to
that produced in regular logistic regression analysis,
but contains interesting distinguishing information
The history of the fitting process looks very similar to
that produced in regular logistic regression analysis,
but contains interesting distinguishing information
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis 1st Page Of Output For Any Model Confirms That A Multinomial Logit Model Has Been Fit
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis 1st Page Of Output For Any Model Confirms That A Multinomial Logit Model Has Been Fit
Confirms that a multinomial logit multinomial logit modelmodel has been fitted
Confirms that a multinomial logit multinomial logit modelmodel has been fitted
Confirms that the “no college” option (COLLEGE=1) is being used as the reference categoryreference category.
Confirms that the “no college” option (COLLEGE=1) is being used as the reference categoryreference category.
Tells you that three levelsthree levels have been detected in the outcome variable.
Tells you that three levelsthree levels have been detected in the outcome variable.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 14
Model Fit Statistics Intercept Intercept and Criterion Only Covariates -2 Log L 11333.060 11215.508 R-Square 0.0215 Max-rescaled R-Square 0.0245
Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSqLikelihood Ratio 117.5525 4 <.0001
Model Fit Statistics Intercept Intercept and Criterion Only Covariates -2 Log L 11333.060 11215.508 R-Square 0.0215 Max-rescaled R-Square 0.0245
Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSqLikelihood Ratio 117.5525 4 <.0001
H0: The simultaneous effect of all predictors in Model M1 (race predictors, BLACK and LATINO) on a girl’s choice of college is zero, in the population.
Test Statistic: 2 = 117.55 (df=4), p< .0001
Decision: Reject H0
Conclusion: In the population, a girl’s college choice depends on her race.
H0: The simultaneous effect of all predictors in Model M1 (race predictors, BLACK and LATINO) on a girl’s choice of college is zero, in the population.
Test Statistic: 2 = 117.55 (df=4), p< .0001
Decision: Reject H0
Conclusion: In the population, a girl’s college choice depends on her race.
51.112152LL:M1 Model
06.113332LL:Model Null
55.117)2( LL
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Overall Fit Of The Model Is Assessed In The Usual Way By The -2LL Statistic
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Overall Fit Of The Model Is Assessed In The Usual Way By The -2LL Statistic
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 15
Analysis of Maximum Likelihood Estimates Standard Wald Parameter COLLEGE DF Estimate Error Chi-Square Pr > ChiSq Exp(Est) Intercept 2 1 0.7173 0.0456 247.5623 <.0001 2.049 Intercept 3 1 0.9796 0.0438 499.5382 <.0001 2.663 BLACK 2 1 -0.0887 0.1219 0.5294 0.4668 0.915 BLACK 3 1 -0.3334 0.1209 7.6013 0.0058 0.717 LATINO 2 1 -0.0749 0.1001 0.5594 0.4545 0.928 LATINO 3 1 -0.9539 0.1105 74.5501 <.0001 0.385
Analysis of Maximum Likelihood Estimates Standard Wald Parameter COLLEGE DF Estimate Error Chi-Square Pr > ChiSq Exp(Est) Intercept 2 1 0.7173 0.0456 247.5623 <.0001 2.049 Intercept 3 1 0.9796 0.0438 499.5382 <.0001 2.663 BLACK 2 1 -0.0887 0.1219 0.5294 0.4668 0.915 BLACK 3 1 -0.3334 0.1209 7.6013 0.0058 0.717 LATINO 2 1 -0.0749 0.1001 0.5594 0.4545 0.928 LATINO 3 1 -0.9539 0.1105 74.5501 <.0001 0.385
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Parameter Estimates, And Ancillary Statistics, Are Present To Excess
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Parameter Estimates, And Ancillary Statistics, Are Present To Excess
All parameter estimates are present in pairs
because there were two outcome comparisons
All parameter estimates are present in pairs
because there were two outcome comparisons
Under “COLLEGE” is recorded the label of the “upper” category: “2” represents
community college, “3” represents 4-
year college.
Under “COLLEGE” is recorded the label of the “upper” category: “2” represents
community college, “3” represents 4-
year college.
There are two sets of parameter estimates, one for each facet of the multinomial model:There are two sets of parameter estimates, one for each facet of the multinomial model:
)954.0333.0980.0(
)075.0089.0717.0(
1
1ˆ
1
1 ˆ
LB, Coll.
Novs.
Coll.
Year-4
LB,
LATINOBLACK
LATINOBLACK
ep
ep
Coll.
Novs.
Coll.
Comm.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 16
Odds Ratio Estimates Point 95% WaldEffect COLLEGE Estimate Confidence Limits BLACK 2 0.915 0.721 1.162BLACK 3 0.717 0.565 0.908LATINO 2 0.928 0.763 1.129LATINO 3 0.385 0.310 0.478
Odds Ratio Estimates Point 95% WaldEffect COLLEGE Estimate Confidence Limits BLACK 2 0.915 0.721 1.162BLACK 3 0.717 0.565 0.908LATINO 2 0.928 0.763 1.129LATINO 3 0.385 0.310 0.478
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Antilogged Parameter Estimates Are Also Provided, To Be Interpreted As Odds-Ratios
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Antilogged Parameter Estimates Are Also Provided, To Be Interpreted As Odds-Ratios
“The fitted odds that a Caucasian girl will go to Four-Year college (vs.
choosing no college at all) is 2.6 times the fitted odds that a Latino girl will have
the same outcome”
“The fitted odds that a Caucasian girl will go to Four-Year college (vs.
choosing no college at all) is 2.6 times the fitted odds that a Latino girl will have
the same outcome”
60.2385.0
1
The fitted odds that a Caucasian girl will go to Four-Year College (vs. not going to college at all) is 1.39 times the fitted odds that an African –American girl will have
the same outcome.
The fitted odds that a Caucasian girl will go to Four-Year College (vs. not going to college at all) is 1.39 times the fitted odds that an African –American girl will have
the same outcome.
394.1717.0
1
When odds-ratios are less than unity, it’s best to invert them, for
interpretive purposes, but remember to invert the interpretation too
When odds-ratios are less than unity, it’s best to invert them, for
interpretive purposes, but remember to invert the interpretation too
Both these confidence intervals cover unity (the “null” value for an odds-ratio), and so:We cannot reject the null
hypothesis in either case.There are no statistically
significant differences in the probability of going to community college/vocational training (e.g., outcome = 2) among girls of all three race/ethnicities.
Both these confidence intervals cover unity (the “null” value for an odds-ratio), and so:We cannot reject the null
hypothesis in either case.There are no statistically
significant differences in the probability of going to community college/vocational training (e.g., outcome = 2) among girls of all three race/ethnicities.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 17
Taxonomy of fitted multinomial logit models of the relationship between a girl’s choice of postsecondary institution and her race/ethnicity and socioeconomic status (n=5148).
Model
Null M1 M2 M3 M4
Technical/Vocational and Community College vs. None
Intercept 0.717*** -1.594*** -1.964*** -2.032***
BLACK -0.089 0.375** 0.748~
LATINO -0.075 0.449*** 0.523
SES 0.917*** 1.017*** 1.051***
BLACKSES -0.188
LATINO SES -0.067
Four Year College vs. None
Intercept 0.980*** -4.854*** -5.129*** -5.682***
BLACK -0.333** 0.568*** 1.844***
LATINO -0.954*** 0.120 2.317***
SES 2.053*** 2.127*** 2.318***
BLACKSES -0.495*
LATINO SES -0.846***
-2LL 11333.1 11215.5 9937.5 9901.5 9864.7
Key: ~ p<.10; * p<.05; ** p<.01; *** p<.001
Test statistic: difference in –2LL
2 = (9901.5-9864.7) = 36.8
Critical value: 2(df=4;=.05) = 9.49
Decision: Reject H0
Conclusion: Controlling for the main effects of race/ethnicity and socioeconomic status, the post-secondary education choices of African-American, Latina and Caucasian girls depend on their socioeconomic status, in the population.
Test statistic: difference in –2LL
2 = (9901.5-9864.7) = 36.8
Critical value: 2(df=4;=.05) = 9.49
Decision: Reject H0
Conclusion: Controlling for the main effects of race/ethnicity and socioeconomic status, the post-secondary education choices of African-American, Latina and Caucasian girls depend on their socioeconomic status, in the population.
.0
,0
,0
,0:
}Coll No vs.Coll.4Year {SESLATINA
}Coll No vs.Coll.4Year {SESBLACK
Coll} No vs.Coll. {CommSESLATINA
Coll} No vs.Coll. {CommSESBLACK0
H
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Final Taxonomy Of Fitted Multinomial Logit Models
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Final Taxonomy Of Fitted Multinomial Logit Models
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 18
Taxonomy of fitted multinomial logit models of the relationship between a girl’s choice of postsecondary institution and her race/ethnicity and socioeconomic status (n=5148).
Model
Null M1 M2 M3 M4
Technical/Vocational and Community College vs. None
Intercept 0.717*** -1.594*** -1.964*** -2.032***
BLACK -0.089 0.375** 0.748~
LATINO -0.075 0.449*** 0.523
SES 0.917*** 1.017*** 1.051***
BLACKSES -0.188
LATINO SES -0.067
Four Year College vs. None
Intercept 0.980*** -4.854*** -5.129*** -5.682***
BLACK -0.333** 0.568*** 1.844***
LATINO -0.954*** 0.120 2.317***
SES 2.053*** 2.127*** 2.318***
BLACKSES -0.495*
LATINO SES -0.846***
-2LL 11333.1 11215.5 9937.5 9901.5 9864.7
Key: ~ p<.10; * p<.05; ** p<.01; *** p<.001
Type III Analysis of Effects WaldEffect DF Chi-Square Pr > ChiSq
BLACK 2 12.4539 0.0020LATINO 2 29.8929 <.0001SES 2 789.6798 <.0001BxSES 2 6.4279 0.0402LxSES 2 36.1789 <.0001
Type III Analysis of Effects WaldEffect DF Chi-Square Pr > ChiSq
BLACK 2 12.4539 0.0020LATINO 2 29.8929 <.0001SES 2 789.6798 <.0001BxSES 2 6.4279 0.0402LxSES 2 36.1789 <.0001
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis There Are Additional “Type III” Tests,
If You Want To Test The Impact Of A Single Predictor On The Joint Outcome
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis There Are Additional “Type III” Tests,
If You Want To Test The Impact Of A Single Predictor On The Joint Outcome
Test Statistic: 2 = 6.43, df=2, p=0.04
Decision: Reject H0
Conclusion: Postsecondary education choices of Black and White girls differ by their SES, in the population.
0
0:}{
0
Coll No vs. Coll. 4Year
SESBLACK
Coll} No vs. Coll. {CommSESBLACK
H
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 19
Taxonomy of fitted multinomial logit models of the relationship between a girl’s choice of postsecondary institution and her race/ethnicity and socioeconomic status (n=5148).
Model
Null M1 M2 M3 M4
Technical/Vocational and Community College vs. None
Intercept 0.717*** -1.594*** -1.964*** -2.032***
BLACK -0.089 0.375** 0.748~
LATINO -0.075 0.449*** 0.523
SES 0.917*** 1.017*** 1.051***
BLACKSES -0.188
LATINO SES -0.067
Four Year College vs. None
Intercept 0.980*** -4.854*** -5.129*** -5.682***
BLACK -0.333** 0.568*** 1.844***
LATINO -0.954*** 0.120 2.317***
SES 2.053*** 2.127*** 2.318***
BLACKSES -0.495*
LATINO SES -0.846***
-2LL 11333.1 11215.5 9937.5 9901.5 9864.7
Key: ~ p<.10; * p<.05; ** p<.01; *** p<.001
Type III Analysis of Effects WaldEffect DF Chi-Square Pr > ChiSq
BLACK 2 12.4539 0.0020LATINO 2 29.8929 <.0001SES 2 789.6798 <.0001BxSES 2 6.4279 0.0402LxSES 2 36.1789 <.0001
Type III Analysis of Effects WaldEffect DF Chi-Square Pr > ChiSq
BLACK 2 12.4539 0.0020LATINO 2 29.8929 <.0001SES 2 789.6798 <.0001BxSES 2 6.4279 0.0402LxSES 2 36.1789 <.0001
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis There Are Additional “Type III” Tests,
If You Want To Test The Impact Of A Single Predictor On The Joint Outcome
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis There Are Additional “Type III” Tests,
If You Want To Test The Impact Of A Single Predictor On The Joint Outcome
Test Statistics: 2 = 36.18 (df=2), p<.0001
Decision: Reject H0
Conclusion: Postsecondary education choices of Latina and White girls differ by their SES, in the population.
0
0:}{
0
Coll No vs. Coll. 4YearSESLATINA
Coll} No vs. Coll. {CommSESLATINA
H
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 20
Model
Null M1 M2 M3 M4
Technical/Vocational and Community College vs. None
Intercept 0.717*** -1.594*** -1.964*** -2.032***
BLACK -0.089 0.375** 0.748~
LATINO -0.075 0.449*** 0.523
SES 0.917*** 1.017*** 1.051***
BLACKSES -0.188
LATINO SES -0.067
Four Year College vs. None
Intercept 0.980*** -4.854*** -5.129*** -5.682***
BLACK -0.333** 0.568*** 1.844***
LATINO -0.954*** 0.120 2.317***
SES 2.053*** 2.127*** 2.318***
BLACKSES -0.495*
LATINO SES -0.846***
-2LL 11333.1 11215.5 9937.5 9901.5 9864.7
AIC 11337.1 11227.5 9945.5 9917.5 9888.7
R2 0 0.022 0.227 0.232 0.237
We can recover prototypical fitted equations in the usual way…but,
now there are two sets …
We can recover prototypical fitted equations in the usual way…but,
now there are two sets …
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Writing Down Fitted Models Is Straightforward
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Writing Down Fitted Models Is Straightforward
)***85.0*50.0***32.2***32.2***84.1***68.5(
)07.019.0***05.152.075.0***03.2(
1
1ˆ
1
1ˆ
Coll. No
vs.
Coll.4Year
Coll. No
vs.
Coll. Comm.
~
SESLATINOSESBLACKSESLATINOBLACK
SESLATINOSESBLACKSESLATINOBLACK
ep
ep
)***85.0*50.0***32.2***32.2***84.1***68.5(
)07.019.0***05.152.075.0***03.2(
1
1ˆ
1
1ˆ
Coll. No
vs.
Coll.4Year
Coll. No
vs.
Coll. Comm.
~
SESLATINOSESBLACKSESLATINOBLACK
SESLATINOSESBLACKSESLATINOBLACK
ep
ep
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 21
White Black Latino White Black Latino
1 0.396277 0.1176371.1 0.417097 0.394939 0.137917 0.1485781.2 0.438217 0.418679 0.161055 0.1681771.3 0.459564 0.442801 0.187232 0.1897861.4 0.481059 0.467197 0.216565 0.2134591.5 0.388054 0.502625 0.491751 0.099302 0.249085 0.2392131.6 0.413285 0.524181 0.516344 0.122046 0.284713 0.2670191.7 0.438981 0.545648 0.540859 0.149135 0.323245 0.2967961.8 0.465007 0.566946 0.565177 0.180998 0.364335 0.3284071.9 0.491226 0.587999 0.589186 0.217925 0.407502 0.3616522 0.517493 0.608735 0.612777 0.259994 0.452147 0.396277
2.1 0.543663 0.629087 0.635851 0.306996 0.497575 0.4319742.2 0.569595 0.648989 0.658316 0.358381 0.543043 0.4683922.3 0.595151 0.668387 0.680093 0.413237 0.587805 0.505152.4 0.620201 0.68723 0.701112 0.470335 0.631161 0.5418522.5 0.644626 0.705473 0.721316 0.52822 0.672497 0.5781052.6 0.668321 0.723082 0.74066 0.585356 0.711319 0.6135362.7 0.691192 0.740025 0.759109 0.640285 0.747269 0.6478042.8 0.713164 0.756282 0.776641 0.691768 0.780126 0.6806152.9 0.734173 0.771835 0.793245 0.738889 0.809798 0.711733 0.754174 0.786675 0.808919 0.781085 0.836307 0.740967
3.1 0.773135 0.8008 0.823668 0.818141 0.85976 0.7682043.2 0.791039 0.81421 0.837508 0.850127 0.880334 0.7933773.3 0.807881 0.826912 0.850458 0.877332 0.898247 0.816468
SES
ComColl vs None 4-Year Coll vs. None
0
0.5
1
0.5 1.5 2.5 3.5 4.5Family SES
Fit
ted
Pro
babi
lity
0
0.5
1
0.5 1.5 2.5 3.5 4.5Family SES
Fit
ted
Pro
babi
lity
White Black Latino White Black Latino
1 0.396277 0.1176371.1 0.417097 0.394939 0.137917 0.1485781.2 0.438217 0.418679 0.161055 0.1681771.3 0.459564 0.442801 0.187232 0.1897861.4 0.481059 0.467197 0.216565 0.2134591.5 0.388054 0.502625 0.491751 0.099302 0.249085 0.2392131.6 0.413285 0.524181 0.516344 0.122046 0.284713 0.2670191.7 0.438981 0.545648 0.540859 0.149135 0.323245 0.2967961.8 0.465007 0.566946 0.565177 0.180998 0.364335 0.3284071.9 0.491226 0.587999 0.589186 0.217925 0.407502 0.3616522 0.517493 0.608735 0.612777 0.259994 0.452147 0.396277
2.1 0.543663 0.629087 0.635851 0.306996 0.497575 0.4319742.2 0.569595 0.648989 0.658316 0.358381 0.543043 0.4683922.3 0.595151 0.668387 0.680093 0.413237 0.587805 0.505152.4 0.620201 0.68723 0.701112 0.470335 0.631161 0.5418522.5 0.644626 0.705473 0.721316 0.52822 0.672497 0.5781052.6 0.668321 0.723082 0.74066 0.585356 0.711319 0.6135362.7 0.691192 0.740025 0.759109 0.640285 0.747269 0.6478042.8 0.713164 0.756282 0.776641 0.691768 0.780126 0.6806152.9 0.734173 0.771835 0.793245 0.738889 0.809798 0.711733 0.754174 0.786675 0.808919 0.781085 0.836307 0.740967
3.1 0.773135 0.8008 0.823668 0.818141 0.85976 0.7682043.2 0.791039 0.81421 0.837508 0.850127 0.880334 0.7933773.3 0.807881 0.826912 0.850458 0.877332 0.898247 0.816468
SES
ComColl vs None 4-Year Coll vs. None
0
0.5
1
0.5 1.5 2.5 3.5 4.5Family SES
Fit
ted
Pro
babi
lity
0
0.5
1
0.5 1.5 2.5 3.5 4.5Family SES
Fit
ted
Pro
babi
lity
Community Collegevs. No College
4-Year Collegevs. No College
W
W
BL
B
L
Among female adolescents who do not go to four-year college: High SES youth are more likely to enroll in community college than low
SES youth. At each level of SES, with an effect larger at low SES, B & L youth have a
similar and higher probability of enrolling in community college than W youth.
Among female adolescents who do not go to four-year college: High SES youth are more likely to enroll in community college than low
SES youth. At each level of SES, with an effect larger at low SES, B & L youth have a
similar and higher probability of enrolling in community college than W youth.
Among female adolescents who do not go to community college:
High SES youth are more likely to go to 4-yr college than low SES youth, and these differences are greater than corresponding effects for enrollment in community college.
At low SES, all youth have a lower probability of going to four-year college than to community college, but B & L youth have a similar and higher probability of enrolling in a 4-yr college than W youth.
At high SES, B & W youth have a similar and higher probability of enrolling in a four-year college than do L youth.
Among female adolescents who do not go to community college:
High SES youth are more likely to go to 4-yr college than low SES youth, and these differences are greater than corresponding effects for enrollment in community college.
At low SES, all youth have a lower probability of going to four-year college than to community college, but B & L youth have a similar and higher probability of enrolling in a 4-yr college than W youth.
At high SES, B & W youth have a similar and higher probability of enrolling in a four-year college than do L youth.
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Producing Fitted Plots For Prototypical Individuals Is Just The Same
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Producing Fitted Plots For Prototypical Individuals Is Just The Same
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 22
WhitesLatinosLatinosWhites
1
WhitesLatinosLatinosWhites
1
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix I: An Algebraic Aside On The Inversion Of Odds-ratios
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix I: An Algebraic Aside On The Inversion Of Odds-ratios
Odds-ratios can be inverted, you just have to get the interpretation correct …Odds-ratios can be inverted, you just have to get the interpretation correct …
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 23
*--------------------------------------------------------------------------------*Input the data, name and label the variables in the dataset*--------------------------------------------------------------------------------*; DATA ALT_RTS_GIRLS; INFILE 'C:\DATA\S052\ALT_RTS_GIRLS.txt'; INPUT ID COLLEGE HSGRAD READ MATH WHITE BLACK LATINO SES; LABEL COLLEGE = 'Institution Selected for Postsec Ed' BLACK = 'Is respondent African-American?' LATINO = 'Is respondent Hispanic?' WHITE = 'Is respondent Caucasian?' SES = 'Socio-economic status'; * Create the required two-way interactions between RACE and SES; BxSES = BLACK*SES; LxSES = LATINO*SES; * Create a pair of new dichotomous outcomes to replace polytomous COLLEGE; IF COLLEGE=2 THEN COMCOLL=1; ELSE COMCOLL=0; IF COLLEGE=3 THEN FOURYR=1; ELSE FOURYR=0; * Format the new outcomes; PROC FORMAT; VALUE CCFMT 0='No Postsec Ed' 1='Tech/Voc or Comm Coll'; VALUE FYFMT 0='No Postsec Ed' 1='4-Year College'; *-------------------------------------------------------------------------------- Are the New Binomial Outcomes Independent?*--------------------------------------------------------------------------------; PROC FREQ DATA=ALT_RTS_GIRLS; FORMAT COMCOLL CCFMT. FOURYR FYFMT.; TABLES COMCOLL*FOURYR /CHISQ;
*--------------------------------------------------------------------------------*Input the data, name and label the variables in the dataset*--------------------------------------------------------------------------------*; DATA ALT_RTS_GIRLS; INFILE 'C:\DATA\S052\ALT_RTS_GIRLS.txt'; INPUT ID COLLEGE HSGRAD READ MATH WHITE BLACK LATINO SES; LABEL COLLEGE = 'Institution Selected for Postsec Ed' BLACK = 'Is respondent African-American?' LATINO = 'Is respondent Hispanic?' WHITE = 'Is respondent Caucasian?' SES = 'Socio-economic status'; * Create the required two-way interactions between RACE and SES; BxSES = BLACK*SES; LxSES = LATINO*SES; * Create a pair of new dichotomous outcomes to replace polytomous COLLEGE; IF COLLEGE=2 THEN COMCOLL=1; ELSE COMCOLL=0; IF COLLEGE=3 THEN FOURYR=1; ELSE FOURYR=0; * Format the new outcomes; PROC FORMAT; VALUE CCFMT 0='No Postsec Ed' 1='Tech/Voc or Comm Coll'; VALUE FYFMT 0='No Postsec Ed' 1='4-Year College'; *-------------------------------------------------------------------------------- Are the New Binomial Outcomes Independent?*--------------------------------------------------------------------------------; PROC FREQ DATA=ALT_RTS_GIRLS; FORMAT COMCOLL CCFMT. FOURYR FYFMT.; TABLES COMCOLL*FOURYR /CHISQ;
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
A comparison of results obtained when fitting a multinomial logit versus a pair of binomial logit models to the same data can be found in Data-Analytic Handout II_2b_2 …A comparison of results obtained when fitting a multinomial logit versus a pair of binomial logit models to the same data can be found in Data-Analytic Handout II_2b_2 …
Create a pair of new dichotomous outcomes: COMCOLL indicates
whether the student went to community college,
FOURYR indicates whether the student went to a four-year college.
Comparison group is the “no postsecondary education” group, in each case
Create a pair of new dichotomous outcomes: COMCOLL indicates
whether the student went to community college,
FOURYR indicates whether the student went to a four-year college.
Comparison group is the “no postsecondary education” group, in each case
Use contingency-table analysis to examine the relationship
between the two new dichotomous outcomes,
COMCOLL and FOURYR
Use contingency-table analysis to examine the relationship
between the two new dichotomous outcomes,
COMCOLL and FOURYR
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 24
Table of COMCOLL by FOURYR COMCOLL FOURYR Frequency ‚ Percent ‚ Row Pct ‚ Col Pct ‚No Posts‚4-Year C‚ Total ‚ec Ed ‚ollege ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ No Postsec Ed ‚ 1028 ‚ 2333 ‚ 3361 ‚ 18.97 ‚ 43.06 ‚ 62.03 ‚ 30.59 ‚ 69.41 ‚ ‚ 33.32 ‚ 100.00 ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Tech/Voc or Comm ‚ 2057 ‚ 0 ‚ 2057 Coll ‚ 37.97 ‚ 0.00 ‚ 37.97 ‚ 100.00 ‚ 0.00 ‚ ‚ 66.68 ‚ 0.00 ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 3085 2333 5418 56.94 43.06 100.00 Statistics for Table of COMCOLL by FOURYR Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 1 2507.6352 <.0001Likelihood Ratio Chi-Square 1 3267.1645 <.0001Continuity Adj. Chi-Square 1 2504.8049 <.0001Mantel-Haenszel Chi-Square 1 2507.1723 <.0001Phi Coefficient -0.6803
Table of COMCOLL by FOURYR COMCOLL FOURYR Frequency ‚ Percent ‚ Row Pct ‚ Col Pct ‚No Posts‚4-Year C‚ Total ‚ec Ed ‚ollege ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ No Postsec Ed ‚ 1028 ‚ 2333 ‚ 3361 ‚ 18.97 ‚ 43.06 ‚ 62.03 ‚ 30.59 ‚ 69.41 ‚ ‚ 33.32 ‚ 100.00 ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Tech/Voc or Comm ‚ 2057 ‚ 0 ‚ 2057 Coll ‚ 37.97 ‚ 0.00 ‚ 37.97 ‚ 100.00 ‚ 0.00 ‚ ‚ 66.68 ‚ 0.00 ‚ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 3085 2333 5418 56.94 43.06 100.00 Statistics for Table of COMCOLL by FOURYR Statistic DF Value ProbƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒChi-Square 1 2507.6352 <.0001Likelihood Ratio Chi-Square 1 3267.1645 <.0001Continuity Adj. Chi-Square 1 2504.8049 <.0001Mantel-Haenszel Chi-Square 1 2507.1723 <.0001Phi Coefficient -0.6803
Notice the interesting relationship between the two newly-created dichotomous outcomes …Notice the interesting relationship between the two newly-created dichotomous outcomes …
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
Same baseline group appears in both binomial comparisons.
Same baseline group appears in both binomial comparisons.
Empty cell.Empty cell.
Reject H0 and conclude that COMCOLL and FOURYR are not independent, in the
population.
Reject H0 and conclude that COMCOLL and FOURYR are not independent, in the
population.
The phi coefficient is equivalent to a Pearson’s correlation coefficient, for a pair of
dichotomous variables: r = -0.63
So, we conclude that the two new dichtomous outcomes are strongly correleated
The phi coefficient is equivalent to a Pearson’s correlation coefficient, for a pair of
dichotomous variables: r = -0.63
So, we conclude that the two new dichtomous outcomes are strongly correleated
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 25
*--------------------------------------------------------------------------------* Fit a binomial logit model for the community college vs. no postsec comparison;*--------------------------------------------------------------------------------*;* Pick out the sub-sample for the community college vs. no postsec comparison; DATA ALT_RTS_GIRLS_COMCOLL; SET ALT_RTS_GIRLS; IF COLLEGE NE 3;* Fit the associated binomial logit model; PROC LOGISTIC DATA=ALT_RTS_GIRLS_COMCOLL; M4A: MODEL COMCOLL(event='1')= BLACK LATINO SES BxSES LxSES; *---------------------------------------------------------------------------------* Fit the binomial logit model for the four-year college vs. no postsec comparison;*--------------------------------------------------------------------------------*;* Pick out the sub-sample for the four year vs. no postsec comparison; DATA ALT_RTS_GIRLS_FOURYR; SET ALT_RTS_GIRLS; IF COLLEGE NE 2;* Fit the associated binomial logit model; PROC LOGISTIC DATA=ALT_RTS_GIRLS_FOURYR; M4B: MODEL FOURYR(event='1')= BLACK LATINO SES BxSES LxSES;
*--------------------------------------------------------------------------------* Fit a binomial logit model for the community college vs. no postsec comparison;*--------------------------------------------------------------------------------*;* Pick out the sub-sample for the community college vs. no postsec comparison; DATA ALT_RTS_GIRLS_COMCOLL; SET ALT_RTS_GIRLS; IF COLLEGE NE 3;* Fit the associated binomial logit model; PROC LOGISTIC DATA=ALT_RTS_GIRLS_COMCOLL; M4A: MODEL COMCOLL(event='1')= BLACK LATINO SES BxSES LxSES; *---------------------------------------------------------------------------------* Fit the binomial logit model for the four-year college vs. no postsec comparison;*--------------------------------------------------------------------------------*;* Pick out the sub-sample for the four year vs. no postsec comparison; DATA ALT_RTS_GIRLS_FOURYR; SET ALT_RTS_GIRLS; IF COLLEGE NE 2;* Fit the associated binomial logit model; PROC LOGISTIC DATA=ALT_RTS_GIRLS_FOURYR; M4B: MODEL FOURYR(event='1')= BLACK LATINO SES BxSES LxSES;
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
Two separate binomial logistic regression analyses: COMCOLL vs no
postsecondary education. FOURYR vs no
postsecondary education.
Two separate binomial logistic regression analyses: COMCOLL vs no
postsecondary education. FOURYR vs no
postsecondary education.
© Willett, Harvard University Graduate School of Education, 04/19/23 S052/II.2(b) – Slide 26
Estimates Standard Errors
Multi-nomial
Twin
Binomial
Multi
-nomialTwin
Binomial
Technical/Vocational and Community College vs. None
Intercept -2.03 -2.25 0.206 0.218
BLACK 0.75 0.84 0.447 0.468
LATINO 0.52 0.62 0.388 0.407
SES 1.05 1.13 0.079 0.083
BLACKSES -0.19 -0.22 0.193 0.202
LATINO SES -0.07 -0.09 0.169 0.177
Four Year College vs. None
Intercept -5.68 -5.27 0.243 0.262
BLACK 1.84 1.70 0.531 0.559
LATINO 2.32 2.03 0.465 0.494
SES 2.32 2.18 0.087 0.094
BLACKSES -0.50 -0.46 0.213 0.225
LATINO SES -0.85 -0.76 0.189 0.201
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
S052/II.2(b): Extensions of the Basic Logit Approach/Multinomial Logit Analysis Appendix II: Does Using Multinomial Logistic Regression Have Advantages
Over Using Multiple Binomial Logistic Regressions?
Sample size is the largest in the multinomial analysis..
So, the standard errors are always smaller in the multinomial analysis.
Sample size is the largest in the multinomial analysis..
So, the standard errors are always smaller in the multinomial analysis.
Different samples are employed in the multinomial and the twin binomial
approaches..
The parameter estimates are not particularly affected in any systematic way -- some estimates are higher for
one outcome, some higher for the other.
Different samples are employed in the multinomial and the twin binomial
approaches..
The parameter estimates are not particularly affected in any systematic way -- some estimates are higher for
one outcome, some higher for the other.