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Limited information estimation and testing of discretized multivariate normal structural models

Published online by Cambridge University Press:  01 January 2025

Albert Maydeu-Olivares
Albert Maydeu-Olivares*
Affiliation:
University of Barcelona
*
Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de Hebrön, 171, 08035 Barcelona, Spain. E-mail: amaydeu@ub.edu
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Abstract

Discretized multivariate normal structural models are often estimated using multistage estimation procedures. The asymptotic properties of parameter estimates, standard errors, and tests of structural restrictions on thresholds and polychoric correlations are well known. It was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators. It is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy. A test of the overall model specification is proposed, as well as a test of the distributional specification (i.e., discretized multivariate normality). Also, the small sample performance of overall, distributional, and structural tests, as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and/or distributional misspecification. It is found that relatively small samples are needed for parameter estimates, standard errors, and structural tests. Larger samples are needed for the distributional and overall tests. Furthermore, parameter estimates, standard errors, and structural tests are surprisingly robust to distributional misspecification.

Keywords

GLSWLS estimationLISRELcategorical data analysisdata sparsenessgoodness-of-fitlimited information estimationpseudo-maximum likelihood estimationIRTpolychoric correlationsstructural equation models
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 1 , March 2006 , pp. 57 - 77
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

This research was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grants BSO2000-0661 and BSO2003-08507 of the Spanish Ministry of Science and Technology.

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