Generalized Multilevel Structural Equation Modeling

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a respon...

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Bibliographic Details
Published in:Psychometrika 2004-06, Vol.69 (2), p.167-190
Main Authors: Rabe-Hesketh, Sophia, Skrondal, Anders, Pickles, Andrew
Format: Article
Language:English
Subjects:
Biological and medical sciences
Factor Analysis
Factor Structure
Fundamental and applied biological sciences. Psychology
Item Response Theory
Latent Variables
Maximum Likelihood Statistics
Predictor Variables
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics
Psychometrics. Statistics. Methodology
Statistics. Mathematics
Structural Equation Models
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Summary:A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.
ISSN:0033-3123
1860-0980
DOI:10.1007/BF02295939