these-courvoisier

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• Publié par: Nazil
• Nombre de lectures: 22
• Langue: English

Extrait

Unfolding the constituents of psychological
scores:
Development and application of mixture and
multitrait-multimethod LST models
Delphine S. Courvoisier
University of Geneva
Faculty of Psychology and Educational Sciences
Section of Psychology
Thesis director: Michael Eid
November 30, 2006Contents
Thanks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1 Introduction 10
2 Basic ideas of latent state-trait models 14
2.1 Latent state-trait models . . . . . . . . . . . . . . . . . . . . . 14
2.2 Indicator-speciflc latent state-trait
models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Limitations of LST models . . . . . . . . . . . . . . . . . . . . 21
3 Mixture latent state-trait models 24
3.1 Mixture models . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Testing mixture SEM models . . . . . . . . . . . . . . 27
4 Application of mixture LST models: Well-being 29
4.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Results: LST models . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Mixture LST models . . . . . . . . . . . . . . . . . . 32
4.4 Mixture LST models with covariates of change . . . . . . . . . 41
4.5 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6 General results . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.6.1 Behavior of the adjusted Likelihood Ratio Test (aLRT) 48
4.6.2 Class sizes . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.6.3 Parameter estimates within classes . . . . . . . . . . . 50
4.6.4 Further evidence for two classes . . . . . . . . . . . . . 57
4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.7.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Multitrait-multimethod latent state-trait models 62
5.1d models . . . . . . . . . . . . . . . . . 62
15.2 Correlated trait correlated method¡1
(CTCM¡1) models . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Existing models for analyzing multitrait multimethod multi-
occasion data . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Deflnition of multitrait multimethod latent state-trait models. 71
5.4.1 Probability space . . . . . . . . . . . . . . . . . . . . . 72
5.4.2 Observed random variables . . . . . . . . . . . . . . . . 74
5.4.3 Latent true-score and residual variables . . . . . . . . . 74
Step 1: Deflnition of general latent true-score variables 75
Step2: Deflnitionoflatentpersonand latentsituation
variables . . . . . . . . . . . . . . . . . . . . . 75
5.4.4 ExtensionofLSTtheorytomultitrait-multimethodLST
theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Step 3: Deflnition of common and method-speciflc la-
tent trait variables . . . . . . . . . . . . . . . 76
Step 4: Deflnition of common and method-speciflc la-
tent occasion-speciflc variables . . . . . . . . 76
5.4.5 Decomposition of variance . . . . . . . . . . . . . . . . 77
Trait coe–cients . . . . . . . . . . . . . . . . . . . . . 78
Occasion-speciflc coe–cients . . . . . . . . . . . . . . . 79
5.4.6 Deflnition of the multitrait-multimethod LST model . . 81
5.4.7 Variance components . . . . . . . . . . . . . . . . . . . 87
5.4.8 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.9 Meaningfulness . . . . . . . . . . . . . . . . . . . . . . 92
5.4.10 Testability . . . . . . . . . . . . . . . . . . . . . . . . . 98
Null covariances based on model deflnition . . . . . . . 99
Covariancestructure: MM-LSTmodelwithconditional
regressive independence . . . . . . . . . . . . 105
Interpretation of non-zero covariances . . . . . . . . . . 107
5.4.11 Identiflability . . . . . . . . . . . . . . . . . . . . . . . 110
6 Application: Depression and anxiety in school children 121
6.1 Multiconstruct LST models . . . . . . . . . . . . . . . . . . . 121
6.1.1 Application of the multiconstruct LST model . . . . . 124
Design and sample . . . . . . . . . . . . . . . . . . . . 124
Measures . . . . . . . . . . . . . . . . . . . . . . . . . 124
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.2 Multitrait-multimethod LST models. . . . . . . . . . . . . . . 132
6.2.1 Application of the multitrait-multimethod LST model . 134
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
27 Conclusions 144
7.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.2 Study design. . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography 154
A Mplus Script for a mixture LST model without covariates 165
B Mplus Script for a mixture LST model with covariates 168
C Results of the simulation studies for the models with and
without covariates of change 174
D Elements of ! 190
E Mplus Script for an MM-LST model 192
3Thanks
This should be the longest chapter of my thesis. However, since I must keep
it short, I apologize in advance to any people I forget.
First of all, I would like to thank Fridtjof Nussbeck for his support and
help. Withouthim,Iwouldnothaveevenbegunthisthesis. Nextofcourse,I
thankMichaelEidbecause,withouthim,Iwouldnothaveflnishedthisthesis.
He was invaluable as a supervisor and was also an example of the \always
happy" people described in chapter 3. Two other people helped me improve
this thesis. Christian Geiser’s comments made it more understandable (and
readerswillneverrealizehowgratefultheyshouldbe). RolfSteyerhasallmy
appreciationforinspiringmetoreadmyflrstbookinGerman. Ididn’tthink
I would begin with a 500-page book, but he wrote the most complete work
I have seen on causal regression models. It would have been much harder to
mathematically deflne the models without his habilitation. Also, of course,
I also thank Rolf Steyer and David Cole for allowing me to use their data
to illustrate the models in this thesis. The content of my thesis was much
improved because of all these people. For the form of my thesis, I would
especially like to thank Olivier Renaud for his endless patience when I asked
Ahim to help me with LT Xproblems. S¶ebastien Courvoisier also helped meE
Awith LT X, but even more with the graphical illustrations of all models.E
I thank all my friends and colleagues who ofiered their support during
these years. They commiserated with me over my problems and then told
me to get back to work. Finally, my thanks go to my family and husband
who endured more talk about statistics during family reunions and romantic
dinners than any sane person should wish for.
It was because of all these people that writing my thesis was as much
pleasure as it was work.
PS. Etienne Roesch’s help in flnding a sexier title may at least double
the number of people who will read or at least peruse this thesis. Thanks to
him, also.
4Summary
Any measure is the product of many difierent in uences. This is especially
trueforsocialsciencescores. Inthisthesis,Ifocusonflvedifierentin uences:
1. stable internal in uences
2. momentary situational in uences
3. method of measurement in uences
4. measurement error
5. individual speciflcity
Several models have already been developed that decompose observed scores
intosomeofthesein uences. Inthisthesis,Ipresenttwoexistingmodels: the
latent state-trait (LST) models and the correlated trait correlated method
¡1 (CTCM¡1). Moreover, I also present a way of estimating and modeling
population heterogeneity with mixture modeling. Each of these three tech-
niques uses latent variables to decompose observed scores. They also have
speciflc advantages and conditions of application. The LST and CTCM¡1
models both allow for variance components and, thus, for a quantiflcation
of the sources of in uence (Steyer, Ferring, & Schmitt, 1992; Eid, 2000).
The principal advantage of the LST model is that it can evaluate if a score
measures mostly a trait or a state. An important condition of application
of the classical LST model is the assumption that the trait does not change
1lastingly between occasions of measurement . The principal advantage of
the CTCM¡1 model is that it can estimate convergent and discriminant
validity on the trait level. However, this model is more appropriate if one
method can be chosen as a standard (Eid, Lischetzke, & Nussbeck, 2006)
for theoretical reasons; the other methods are then considered as deviation
fromthisstandard. Ifthisistheoreticallyinappropriate,forexampleifraters
1Extension of LST models for lastingly changing traits have been developed by Cole &
Martin (2005).
5are exchangeable (i.e., two employees rating their supervisor), the CTCM¡1
model should not be used. Finally, mixture modeling relaxes the assumption
of population homogeneity by modeling one or several observed or latent
variable as a mixture of distributions (McLachlan & Peel, 2000). However,
the latent class modeled by a mixture distribution can be interpreted in two
ways. AmixturecouldmeanthatthereareC subpopulationswiththedistri-
butionspecifledinthemixture. Or, itcouldmeanthatthetotaldistribution
is not normal and