Speaker: Dr. Jolynn Pek, York University
Department of Psychology
Title: Exploring and Diagnosing Latent Nonlinear Relations with Mixtures

Abstract: The functional form of a latent regression is typically unknown during early phases of research, highlighting the advantage of using semiparametric models (SPM) over parametric counterparts to model potential nonlinearity. An indirect application of structural equation mixture models (Bauer, 2005) can flexibly recover and describe the unknown form of the latent relationship with minimal distributional assumptions. As the recovered function is determined by a set of parameters, its description requires visualization. To make inferences about the unspecified latent function, approximate confidence sets may be constructed. Simultaneous confidence intervals and simultanous confidence envelopes, based on the delta method and parameter bootstrap, are developed and evaluted by Monte Carlo. To diagnose nonlinearity, a line finding algorithm to be used in conjunction with these CEs is also developed as an implementation of an informal test to diagnose nonlinearity. Targeted simulations were used to evaluate performance of the algorithm in terms of rates of detecting nonlinearity. Recommendations for the use of this method to explore nonlinearity are suggested.

Suggested Readings:
Bauer, D.J. (2005). A semiparametric approach to modeling nonlinear relations among latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 4, 513-535. doi:10.1207/s15328007sem1204_1