Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models

Statistics in Biosciences
Zhenzhen ZhangBrisa N Sánchez

Abstract

Factor analysis models are widely used in health research to summarize hard to measure predictor or outcome variable constructs. For example, in the ELEMENT study, factor models are used to summarize lead exposure biomarkers which are thought to indirectly measure prenatal exposure to lead. Classic latent factor models are fitted assuming that factor loadings are constant across all covariate levels (e.g., maternal age in ELEMENT); that is, measurement invariance (MI) is assumed. When the MI is not met, measurement bias is introduced. Traditionally, MI is examined by defining subgroups of the data based on covariates, fitting multi-group factor analysis, and testing differences in factor loadings across covariate groups. In this paper, we develop novel tests of measurement invariance by modeling the factor loadings as varying coeffcients, i.e., letting the factor loading vary across continuous covariate values instead of groups. These varying coeffcients are estimated using penalized splines, where spline coeffcients are penalized by treating them as random coeffcients. The test of MI is then carried out by conducting a likelihood ratio test for the null hypothesis that the variance of the random spline coeffcients equals zero....Continue Reading

References

Nov 14, 1997·Pediatrics·T González-CossíoH Hu
Sep 24, 2004·American Journal of Epidemiology·Martha María Téllez-RojoHoward Hu
Dec 13, 2006·Psychological Methods·Reinoud D StoelGodfried van den Wittenboer
Apr 1, 2008·Biometrics·B N SánchezL M Ryan
Aug 5, 2009·Computational Statistics & Data Analysis·Jungsoon ChoiBrian J Reich
Sep 29, 2011·Biometrics·Oliver E Lee, Thomas M Braun

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