FINITE MIXTURE REGRESSION MODELS AND APPLICATIONS: DETECTION LIMIT AND GOODNESS-OF-FIT TEST

Abstract

OF THE DISSERTATION Finite Mixture Regression Models and Applications: Detection Limit and Goodness-of-Fit Test by Junwu Shen Dissertation Director: Dr. Shou-En Lu Finite mixture models have been used to analyze data in a heterogeneous population. In this dissertation, we aimed to propose two statistical methodologies: one is the mixture regression model analysis accommodating repeated measures and observations under detection limits; the other is the GOF test for evaluating the model fit of mixture regression models, with and without random effects. Both methodologies were applied to the analysis of the 8-isoprostane data in the HEART study. A general framework for random effects finite mixture regression models was proposed to analyze repeatedly measured data with observations under a detection limit. The non-detectables were treated as left-censored observations and the regression parameters were estimated by the maximum likelihood method. Using normal mixture models as an example, we demonstrated that the parameter estimators are unbiased. In addition, we proposed a prototype goodness-of-fit test method based on the principle of cumulative residuals. Cumulative pseudo-residuals were defined based on the score functions and then a GOF test was proposed accordingly for two-component normal mixture models with and without random effects. Extensive simulation studies showed that the proposed GOF tests maintained the type I error rate, and had a reasonable power to detect model deviations.