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Generalized Multilevel Structural Equation Modeling

Published online by Cambridge University Press:  01 January 2025

Sophia Rabe-Hesketh ,
Anders Skrondal  and
Andrew Pickles
Sophia Rabe-Hesketh*
Affiliation:
University of California, Berkeley
Anders Skrondal
Affiliation:
Norwegian Institute of Public Health, Oslo
Andrew Pickles
Affiliation:
The University of Manchester
*
Requests for reprints should be sent to Sophia Rabe-Hesketh, Graduate School of Education, 3659 Tolman Hall, University of California, Berkeley, California 94720-1670, USA. E-Mail: sophiarh@berkeley.edu
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Abstract

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.

Keywords

multilevel structural equation modelsgeneralized linear mixed modelslatent variablesrandom effectshierarchical modelsitem response theoryfactor modelsadaptive quadratureempirical BayesGLLAMM
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 2 , June 2004 , pp. 167 - 190
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

gllamm can be downloaded from http://www.gllamm.org. The paper was written while Sophia Rabe-Hesketh was employed at and Anders Skrondal was visiting the Department of Biostatistics and Computing, Institute of Psychiatry, King's College London.

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