Adapting Mixture Models to Take into Account Measurement Non-Invariance Public Deposited

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  • March 22, 2019
  • Cole, Veronica
    • Affiliation: College of Arts and Sciences, Department of Psychology and Neuroscience
  • Researchers in the social sciences often use finite mixture models to find clusters of individuals on the basis of patterns of indicators. Though covariates are often incorporated in mixture models, it is most often assumed that these covariates exclusively affect class membership, rather than directly impacting the indicators themselves. Violation of this assumption indicates that the measurement of the latent classes by a given indicator is not constant across all individuals. Such violations, known as differential item functioning (DIF), have been well-studied in models for continuous latent variables, but virtually unexamined in models for categorical latent variables. The current study extends the analytic and testing framework developed in continuous latent variable models to the case of latent class analysis. First, a Monte Carlo simulation systematically examined the effects of omitted DIF on mixture model results, as well as the performance of tests to detect DIF. In the presence of DIF in the data-generating model, the omission of these effects in the fitted model was associated with overestimation of the number of classes, as well as biased estimates of covariate effects on class membership and model-implied endorsement probabilities, particularly when classes were poorly separated and DIF was large. Including DIF in the model, even if the nature of this DIF was misspecified, mitigated this bias considerably. Standard model-based procedures drawn from the continuous latent variable modeling literature were shown to detect DIF with high sensitivity and specificity. Finally, DIF was examined in an application of latent class analysis to alcohol use disorder (AUD) diagnostic criteria in an undergraduate sample. Researchers are advised to test comprehensively for DIF in applications of mixture models, in order to ensure that the results obtained are truly applicable to all individuals under study.
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Rights statement
  • In Copyright
  • Curran, Patrick
  • Gates, Kathleen
  • Bauer, Daniel
  • Zeng, Donglin
  • Bollen, Kenneth
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill
Graduation year
  • 2017

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