Person-oriented methodology: II. Methodological considerations

Lars R. BergmanStockholm University

Workshop given at the PATHWAYS meeting, London, December 8, 2009

Overview of talk

• Focus on typical patterns: Motivation, some methods, LICUR, empirical example

• Measurement issues: Quasi-absolute scaling, scale level and nonlinear relationships

• (The individual in focus)

The pattern perspective

• The difference between the theoretical pattern focus and the methodological pattern focus.

• From the viewpoint of methodology, a p-o theoretical framework most often leads to the use of methods for the analysis of patterns.

• This is most often done using classification-based methods, searching for typical patterns but it can sometimes be done in a variable-oriented framework, e.g. by creating a dummy variable out of an interesting value pattern.

The pattern perspective: Motivation for the expectation that typical patterns will

emerge• In most processes the components are organized to optimize the

survival value of the system and only a limited number of system states (~ typical patterns) achieve this.

• Examples: Species, ecotypes, severe mental illness, occupation, social class, externalizing problems.

• A typology might exist – but it must be tested. • Typical patterns can form a complete or partial classification

structure. Carl von Linné: “Nature is so wisely constructed that you cannot take out one

part and it anyway works.”Gunilla Pettersson: “The object of the study should primarily be the totality; the

language system (la langue).”

Example where all pairwise relationships are zero but strong configurational patterns exist: Meehl´s

paradox for three binary variables

X1

X2

CC

10 0

1

0

1

Fictional data illustrating Meehl´s paradox (n=80, 3 binary variables)

All pairwise cross-tables lookPattern Obs. Exp. like this: 20 20X1 X2 X3 freq. freq. 20 200 0 0 0 10.00 0 1 20 10.0 All pairwise relationships=00 1 0 20 10.0 but strong 3-way interactions exist.0 1 1 0 10.01 0 0 20 10.01 0 1 0 10.01 1 0 0 10.01 1 1 20 10.0Conclusion: Pattern structuresmay not be picked up by pairwiserelationships

Examples of major classes of methods for (more or less) person-oriented analysis• The study of the single individual using p-technique

(e.g. Nesselroade).

• Model-based classification analysis (e.g. LPA, Collins´LTA).

• Exploratory classification analysis (e.g. cluster analysis-based methods, the configural frequency analysis of Lienert and von Eye).

• The study of nonlinear dynamical systems (e.g. Kelso, Thelen & Smith).

• Study of individualized growth curves (e.g. McArdle, Muthén, Nagin).

Model-based vs exploratory classification

Model-based classification: A statistical model is assumed and its parameters are estimated from the sample. This means that confidence intervals can be given and model fit tested.

Exploratory classification: The pattern data are summarized by some method like cluster analysis.

If all essential assumptions are approximately fulfilled, a model-based approach is often preferable – but in certain contexts the power to reject a bad model can be low for moderate sample sizes.

Four different cluster analysis-based approaches

• Direct classification of longitudinal patterns.• Separate classifications at each age followed by

linking across age (LICUR).• Age-invariant classification system (ISOA).• Focus only on typical patterns (TYFO).

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Reference: Bergman, L.R., Magnusson, D & El-Khouri, B.M. (2003). Studyingindividual development in an interindividual context. Erlbaum.

IDA: Individual Development and AdaptationTwo school grade cohorts followed to mid age (N=ca 2000)

Director: Lars R. Bergman Founding director: David Magnusson

Empirical example: The study of stability and change in boys patterns of school adjustment between ages 10 and 13• Sample taken from IDA• Variables in value pattern:

Aggression treated superficially

Motor Restlessness detailed example after break

TimidityDisharmonyLack of ConcentrationLow School Motivation.

• N=449 in longitudinal analysis

Results of cluster analyses using LICUR

• 7 clusters were obtained at age 10 and 9clusters at age 13.

• Cluster homogeneity was good.• Almost all clusters at age 10 were well

matched to a cluster at age 13.• Both cluster solutions were significant and

replicated on a random half.

1.5x

CL. A3L1 n = 117

CL. A6L1n = 119

5.2x***CL. A3L12n = 48

CL. A6L14n = 38

2.6x*

CL. A3L10n = 50

CL. A6L10n = 58

***

***

CL. A3L18n = 72

CL. A6L3n = 42

*** 2.5x

CL. A3L5n = 73

CL. A6L11n = 32

* 2.1x

CL. A3L17n = 70

CL. A6L13n = 37

2.2x

3.5x

*

*

Variables in profile: Aggr., Motor Restl., Tim., Dish., Lack of Conc., Low School Mot.

SUMMARY

Based on IDA data

(From Bergman, Magnusson & El-Khouri, 2003)

Variables as markers of patterns

The relationships between of dichotomized Aggression and Motor Restlessness to criminality and alcohol abuse at age 18-23 were fairly strong (p<.001 in both cases).

When severe multi-problem children were removed, only the relationship for Motor Restlessness remained significant.

The statement can, of course, be turned around to “patterns as markers of variables”.

Fictitious data illustrating configural frequency analysis (CFA)Ref: von Eye in Applied Psychology: An International Review, October 1996

ValuePattern Obs. Exp. Chi-square Table sign. Bin. prob.0 0 0 4 1.40 4.83 .05 .05 t1 0 0 4 5.60 0.46 ns .320 1 0 0 2.80 2.80 ns .053 at?1 1 0 13 11.20 0.29 ns .300 0 1 0 0.60 0.60 ns .55 t = type at = antitype1 0 1 2 2.40 0.07 ns .570 1 1 2 1.20 0.53 ns .341 1 1 5 4.80 0.01 ns .54Total 30 30.00

Margin percentages: 1..= 0.80 .1.= 0.67 ..1= 0.300. .= 0.20 .0.= 0.33 ..0= 0.70

Computations for pattern 0 0 0: exp. = 0.20 x 0.33 x 0.70 x 30 = 1.4chi-sq. = (o-e)2/e = (4-1.4)2/1.4 = 4.83

More about CFA

• CFA is a robust methodology, often suitable when theinvolved variables can be reduced to a few categoricalvalues. Major work has been done by Alexander von Eye.

• CFA-based methods have been developed for handlinglongitudinal prediction analysis and time series analysis.

• Recently a method has been developed for mediationanalysis*

--------------------------------------------------*von Eye, A,, Mun, E. U., & Mair, P. (in press). What carries a mediation

process? Configural analysis of mediation. Integrative Psychological AndBehavioral Science.

ISOA – I-States as Objects of AnalysisStandard situation: The same variables are measured for a sample

several times during a fairly short developmental period.It is assumed that the same typical patterns exist at all time points

although perhaps with varying frequencies.Assume n subjects, v variables, and k time points. Each subject has

k i-states (i.e. k variable profiles, one from each time point).In total there are n x k observed i-states who in Step 1 are classified.In Step 2 all subjects´ sequences of class membership are created

and it is looked for frequency stability and change and individualstability and change across time.

Bergman, L.R., Magnusson, D., & El-Khouri, B.M. (2003). Studying individual development in an interindividual context: A person-oriented approach.Mahwah, NJ: Erlbaum.

Using standard variables to study functional relations

• Functional relations are often of interest (e.g. between the number of risk factors and a bad outcome). Strong nonlinear relationships are rarely demonstrated.

• Is the apparent linearity sometimes caused by imperfect measures hiding a “true” nonlinear relationship?

• Obviously, this issue can be of relevance in v-o research but it is also of importance in p-o research.

• Many measures are not on an interval scale level, they are more similar to ordinal measures with ties. This might obscure a nonlinear relationship that holds for high quality measures. Especially relevant for monotonic nonlinear relationships?

Of Bad Outcome (interval scaled) as a function of # risk factors. Artificial data

• Bad Outcome (interval scaled) as a functiosk R2linear=0.80

R2quadratic=0.99

Bad Outcome (ordinal scaled) as a function of # risk factors (artificial data)

IDA data of the relationship between # crimes 0-20 yrs and conduct problems at age 13

R2linear=0.076R2quadr=0.101

Measurements for use in person-oriented analyses

The most important aspect is that the variables together give a balanced view of the system under study.

The use of scales created within a variable-oriented environment may create problems.

Reliability issues are more important than normally is the case in standard analyses.

It is important that the variables are on comparable scales.Most often z-transformed variables are preferable but

sometimes quasi-abosolute measurements are better.

Quasi-absolute scores and z-scores

Should we measure change directly?

• In a Swedish series of studies done during the 70´ theworkers experiences of insufficient light, disturbing noice,etc. at the workplace was measured. Over a decade, adeterioration was reported but when, in the last study, itwas asked for experienced change, large improvementswere reported.

• The human cognitive system is hard-wired to detectchange – maybe we should use this ability in ourmeasurements?

Are standard variables useful for studying individual development?

Many variables in developmental psychology have been developed for thestudy of group or average development and may there do well. Butthey are often used also for studying individual development, whichcan be questionable.

Example from medicine: The Body Mass Index* (BMI) was mainlydeveloped to indicate over weight at the population level. It has comeinto use as an individual risk factor for CHD but is less informativethan the waist-to-hip ratio (w/h)**. Hence, individual risk is betterdetermined by w/h*** than by BMI but at the group level, e.g. as anindicator of population trends, BMI might work fine.

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*Weight in kg/(Tallness in m)2 **See Lancet, Nov 5, 2005***w/h >0.90 for men and >0.85 for women indicates a risk.

Break!Some references to our work

Bergman, L. R., & Magnusson, D. (1997). A person-oriented approach in research in developmental psychopathology. Development and Psychopathology, 9, 291-319.

Bergman, L.R., Magnusson, D., & El-Khouri, B.M. (2003). Studying individual development in an interindividual context: A person-oriented approach.Mahwah, NJ: Erlbaum.

Bergman, L.R. (2001). (Guest Ed.). Modern interactionism. In Special Issue of European Psychologist 6, 151-152.

Lövdén, M., Bergman, L.R., Adolfsson, R., Lindenberger, U., & Nilsson, L.-G. (2005). Studying individual aging in an interindividual context: Typical paths of age-related, dementia-related, and mortality-related cognitive development in old age. Psychology and Aging, 20, 303-316.

von Eye, A., & Bergman, L.R. (2003). Research strategies in developmental psychopathology: Dimensional identity and the person-oriented approach. Development and Psychopathology, 15, 553-580.

Wångby, M., Bergman, L.R., & Magnusson, D. (1999). Development of adjustment problems in girls: What syndrome emerge? Child Development, 70, 678-699.

Zettergren, P., Bergman, L.R., & Wångby, M. (in press). Girls’ stable peer status and their adulthood adjustment: A longitudinal study from age 10 to age 43. International Journal of Behavioral Development.

Group level findings may not hold at the individual level

1. The ecological correlation fallacy (Robinson).2. For group findings to be informative of individuals´

developmental processes, the process must be ergodic. This assumption is often violated according to Molenaar. His solution: Study each individual´s process separately and generalize bottom-up.

3. “A set of variables can be defined as displaying dimensional identity if the interrelations among the variables in this set remains unchanged across the levels or categories of other variables.” (von Eye & Bergman, 2003).

Examples of 1., 2., and 3.

1. The individual correlation between nativity and illiteracy is .12, the ecological correlation is -.63 (Robinson, 1950)

2. The correlation between Agg10 and Agg13 is .43. But for 274 individuals out of 916 (30%), high<>high or low<>low is strongly violated.

3. For the IDA sample, r between extrinsic job satisfaction and income is .24***. For those with above/below median education r=.37*** and r=.06, respectively. dimensional identity is violated. r between intrinsic JS and income is similar for both educational groups dimensional identity holds.

Simple example: Studying individual development in school grades between age

10 and 13

• IDA data for both sexes combined areanalyzed.

• First some standard variable-oriented analysesare done. Then the findings are examined atthe individual level.

Some basic findingsCorrelation matrix

Swe10 Math10 Swe13 Math13Swe10 1 .66 .75 .59

Math10 .66 1 .61 .72Swe13 .75 .61 1 .69

Math13 .59 .72 .69 1VerbIQ .66 .49 .67 .53

NonverbIQ .54 .56 .55 .62ParentEd. .26 .26 .34 .30

Predicting school grade at age 13

• Two stepwise regression analyses (p<.01) were run with eitherSwe13 or Math13 as the dependent variable and all age 10information as the independent variables.

• In this way, factors influencing grade change could be studied.

Swe13 Math13BetaSwe10 .43 -BetaMath10 .13 .50BetaVerbIQ .27 .12BetaNonverbIQ - .26BetaParentEd. .09 .08

R2 .65 .61

Cross-tabulation between age 10 and age 13 for school grade in Swedish

Swe131 2 3 4 5 All

1 10 30 3 0 0 432 17 116 59 4 0 196

Swe10 3 4 58 225 65 0 3524 0 6 67 159 22 2545 0 0 3 30 36 69

All 31 210 357 258 58 91460% completely stable 98% almost stable

Cross-tabulation between age 10 and age 13 for school grade in Mathematics

Math131 2 3 4 5 All

1 9 16 2 1 0 282 24 101 53 2 0 180

Math10 3 8 91 205 62 5 3714 0 5 75 134 52 2665 0 0 4 22 43 69

All 41 213 339 221 100 91454% completely stable 97% almost stable

Examining the whole individual developmental grade pattern

Only two highlights are given:• Of those with an age 10 grade not above 3 3, only 1 out of

494 (0.2%) achieves a 5 in any subject at age 13.• Of those who start low (1 1, 1 2 or 2 1), only 1 out of 46

(2%) reach the average grade level three years later, goingfrom 1 1 to 3 4.

• What characterizes this person? Very low ParentEd,very low IQ, like school at both ages, conduct problemsgrow, concentration and school motivation improves.

What explains this child´s extremely unexpected positivedevelopment? Qualitative analysis needed.

IDA data: Change between age 10 and age 13 in Verbal test score related to change in

Opposites sub test scoreChange in Opposites

Yes NoChange in Yes 32 11 43Verbal No 41 813 854

73 824 897

Note. Change = Yes if Z-score difference > 1

IDA data: Change between age 10 and 13 in Verbal test score and Opposites sub test score related to change in Achievement Swedish (Z-score change)

Change in OppositesYes No

Change in Yes .41 .58 Dependent variable:

Verbal No .09 -.04 Change in Achievement

Swedish Z-scores

Two-way ANOVA with fix effects indicates Change inVerbal has a significant effect (p<.001) and Change inOpposites has a non significant effect (rough analysis).

The importance of considering nonlinear relations and interactions

They are expected to be freqeuent and cannot be ignored

Linear models ignoring such features are prevalent

The variance-covariance matrix may not adequately represent the datamatrix

Yet it is precisely because of the convenience of linear models … … that researchers often seriously depart from isomorphic parallels between social theory and nonlinear algebraic formalisms, leading them into the most dangerous of terrains.

Studying the dynamics of change at a pattern level

Important to study, if a person-oriented paradigm is acceptedThe failure to consider mechanism of change and to try toformulate them in models of the processes we investigate,however primitive the result may be, has importantconsequences for the state of sociological research.(Sörensen, 1998)

A standard person-oriented methodology to a certain extentenables on to study the dynamics of change