Title of the ESTIMATION AND MODEL SELECTION FOR Dissertation FINITE MIXTURES OF LATENT INTERACTION MODELS

Title of the ESTIMATION AND MODEL SELECTION FOR Dissertation FINITE MIXTURES OF LATENT INTERACTION MODELS Jui-Chen Hsu, Doctor of Philosophy, 2011 Directed by Professor Gregory R. Hancock, Department of Measurement, Statistics and Evaluation Professor Jeffrey R. Harring, Department of Measurement, Statistics and Evaluation Latent interaction models and mixture models have received considerable attention in social science research recently, but little is known about how to handle if unobserved population heterogeneity exists in the endogenous latent variables of the nonlinear structural equation models. The current study estimates a mixture of latent interaction models using an unconstrained product indicator approach. It also investigates the performance of the method in parameter recovery, classification quality, and identification of the correct number of latent classes using data simulated under a variety of conditions. The major findings of this study are (1) class separation in the factor means is a critical factor influencing parameter recovery and classification results; (2) the relative biases (or bias) for the class-specific interaction effects are larger than those of other parameters; (3) the precision of all structural parameter estimates for the conditions with larger separation are satisfactory; (4) entropy values, correct assignment probabilities, and convergence rates are improved for larger separation models; (5) AIC, BIC, and ABIC all support the two-class models over one-class models regardless data are generated from oneor two-class latent interaction models. ESTIMATION AND MODEL SELECTION FOR FINITE MIXTURES OF LATENT INTERACTION MODELS