切換式的韋伯迴歸估計之研究

Mixture regressions are also known as switching regressions. They are used to determine the relationship between variables from several unknown latent groups. It has been widely applied in many areas such as econometrics, biology, epidemiology, and engineering and has been a longstanding topic in the research of model-based clustering. The Weibull distribution is well known in the applications of survival analysis, life insurance, and reliability analysis. There is a great demand for research in the area of Weibull regression models. Specifically, there are few studies on switching regression models of Weibull distributions. We develop a Weibull regression model and propose an EM-based algorithm for switching Weibull regressions. The mixture likelihood approach is a popular clustering method, in which the EM algorithm is used most often for deriving the maximum likelihood estimates. It is well known that, in mixture models, the performance of the EM algorithm heavily depends on the choice of initial values and its convergence speed is relatively low. Hence, in using EM for switching Weibull regressions, the selection of good initial values or the summarization of the outcomes from different sets of initial values are important. In this research, we proposed switching regression models for the Weibull distribution, developed the EM-based algorithms to estimate model parameters. Several simulation results show the proposed methods are feasible in modeling the Weibull distributed data. A real example is used to show the practicability of the proposed method.