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Selecting the Number of Classes to Fit under Latent Class Regression Models

Guan-Hua Huang, Johns Hopkins University Department of Biostatistics

In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators' substantive associations with predictors are built directly and indirectly in unique model parameters. This talk includes two parts: first, I am going to present a latent class regression (LCR) model which allows mediated relationships between primary predictors and latent class membership, but also allows direct effects of secondary covariates on the indicators themselves. Theory and issues about model identification, parameter estimation, and diagnosis will be briefly discussed. In the second part, I will talk about how to choose the number of classes of the proposed model. To reduce complexity and enhance interpretability, one usually fixes the number of classes in a given LCR. Traditionally, goodness of fit methods are used as a selecting criterion of the number of classes to fit. We propose a new stratage which is based on the analogous method used in factor analysis and does not require repeatedly fitting LCR as in goodness of fit test. A Monte Carlo simulation study is presented to illustrate the behavior of the procedure.

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