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Accepted (AM)Open Access (License Unspecified), Open
Journal article
Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models
Statistics in biosciences, v 10(3), pp 634-650
29 Sep 2018
PMID: 30805035
Featured in Collection : UN Sustainable Development Goals @ Drexel
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. We use a Monte-Carlo EM algorithm for estimation, and obtain the likelihood using Monte-Carlo in tegration. Using simulations, we compare the Type I error and power of our testing approach and the multi-group testing method. We apply the proposed methods to to summarize data on prenatal biomarkers of lead exposure from the ELEMENT study and find violations of MI due to maternal age.
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Details
- Title
- Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models
- Creators
- Zhenzhen Zhang - University of MichiganThomas M. Braun - University of MichiganKaren E. Peterson - University of MichiganHoward Hu - University of WashingtonMartha M. Téllez-Rojo - National Institute of Public HealthBrisa N. Sánchez - University of Michigan
- Publication Details
- Statistics in biosciences, v 10(3), pp 634-650
- Publisher
- Springer Nature
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Epidemiology and Biostatistics
- Web of Science ID
- WOS:000448224700008
- Other Identifier
- 991020100056304721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematical & Computational Biology