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The framework allows an arbitrary number of hierarchical levels to be specified and structural relations among factors and/or random coefficients at different levels to be included

Generalized multilevel structural equation modeling

Psychometrika, no. 2 (2004): 167-190

Cited by: 664|Views8

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 ...More

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Introduction
  • Among the milestones in the development of statistical modeling are undoubtedly the advent of comprehensive methodologies for structural equation modeling (e.g., J6reskog, 1973) and multilevel modeling (e.g., Goldstein, 1986) and the concomitant implementation in widely available software such as LISREL (JOreskog & SOrbom, 1989) and MLwiN (Rasbash, Browne, Goldstein, Yang, Plewis, Healy, et al, 2000).
  • Developed separately and for different purposes, the modeling approaches have striking similarities.
  • Both include latent variables in the models in order to induce, and explain, correlations among the responses.
  • The latent variables, or random effects, can be interpreted as unobserved heterogeneity at the different levels inducing dependence among all lower-level units in the same higher-level unit.
  • Whereas random intercepts represent heterogeneity between clusters in the gllamm can be downloaded from http ://www.
Highlights
  • Among the milestones in the development of statistical modeling are undoubtedly the advent of comprehensive methodologies for structural equation modeling (e.g., J6reskog, 1973) and multilevel modeling (e.g., Goldstein, 1986) and the concomitant implementation in widely available software such as LISREL (JOreskog & SOrbom, 1989) and MLwiN (Rasbash, Browne, Goldstein, Yang, Plewis, Healy, et al, 2000)
  • Multilevel regression models are used when the data structure is hierarchical with elementary units at level 1 nested in clusters at level 2, which in turn may be nested inclusters at level 3, and so on
  • Whereas random intercepts represent heterogeneity between clusters in the gllamm can be downloaded from http ://www. gllamm, org
  • In this paper we introduce a unifying framework for multilevel structural equation models
  • We explore multilevel structural equation models as special cases of the framework
  • The framework allows an arbitrary number of hierarchical levels to be specified and structural relations among factors and/or random coefficients at different levels to be included
Results
  • The multilevel design was highly unbalanced with 49% of subjects responding to at least one item in all four panel waves, 12% in three waves, 13% in two waves and 25% in one wave.
  • Unit nonresponse was common, but if an interview took place, item nonresponse occurred in only 7% of cases
Conclusion
  • A unifying framework for multilevel structural equation modeling has been developed.
  • The framework allows an arbitrary number of hierarchical levels to be specified and structural relations among factors and/or random coefficients at different levels to be included.
  • Important special cases of the general framework were outlined and potential applications described.
  • These models in no way exhaust the possibilities of the framework
Tables
  • Table1: Estimates for the Multilevel Variance Components Logit Factor Model
Download tables as Excel
Funding
  • The multilevel design was highly unbalanced with 49% of subjects responding to at least one item in all four panel waves, 12% in three waves, 13% in two waves and 25% in one wave
  • Unit nonresponse was therefore common, but if an interview took place, item nonresponse occurred in only 7% of cases
Study subjects and analysis
individuals: 734
The data have a multilevel structure with panel waves nested in individuals nested in polling districts. There were 14143 responses to the seven items over the four panel waves from 734 individuals in 57 polling districts. The multilevel design was highly unbalanced with 49% of subjects responding to at least one item in all four panel waves, 12% in three waves, 13% in two waves and 25% in one wave

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