國立成功大學 統計與資料科學學系

In regression modeling combined with unsupervised clustering, the explanatory variables are first clustered,and separate regression models are then built for each cluster. The resulting models are often evaluated using in-cluster prediction criteria, such as the AIC and the BIC.Out-of-cluster prediction is explored for evaluating regression models, particularly in selecting the number of clusters. A model exclusion procedure is developed that makes use of the reduced accuracy of out-of-cluster prediction compared with in-cluster prediction, under the assumption that regression models differ between clusters, to exclude redundant models before applying model selection. The model exclusion procedure is considered within standard

regression frameworks, including generalized linear and Cox regression models. For Cox regression models, a normalized partial log-likelihood is proposed to avoid divergence issues that arise when the standard partial log-likelihood is used for model selection. Selecting the number of clusters using AIC combined with the proposed model exclusion procedure achieves model selection consistency. The improved performance of the proposed exclusion procedure is confirmed through extensive simulation studies involving Gaussian linear, logistic, and Cox regression models combined with K-means clustering.