Goodness-of-Fit Methods of Finite Mixture Models Based on Cumulative Pseudo-Residuals

• Activity Number: 581
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Junwu Shen*+ and Shou-En Lu
• Companies: Merck & Co., Inc. and University of Medicine and Dentistry of New Jersey
• Keywords: Goodness-of-fit ; Mixture models ; Cumulative residuals

Abstract

One of the challenges in the application of finite mixture models is to evaluate the adequacy of the model. Many different methods including likelihood ratio test, AIC, and BIC have been used extensively to compare the relative goodness-of-fit for different mixture models. However, there was limited literature on how to evaluate the discrepancy between observed data and a specific mixture model. In this paper, we proposed a model checking technique extended from the principle of cumulative residuals (D.Y. Lin, et al. 2002) to evaluate the goodness-of-fit for a mixture regression model. Using this method, both the component means and the mixing proportions modeled by linear and logistic regressions can be tested separately and jointly. For each of these tests, we can both visually and numerically evaluate the functional form of a covariate or the link functions. Simulation studies showed that the proposed tests perform well in terms of type I error and have a reasonable power. In addition, the proposed goodness-of-fit tests can also be extended to mixture models with random effects. The proposed method was applied to the data analysis for an environmental health study.