Sample- and segment-size specific Model Selection in Mixture Regression Analysis

As mixture regression models increasingly receive attention from both theory and practice, the question of selecting the correct number of segments gains urgency. A misspecification can lead to an under- or oversegmentation, thus resulting in flawed management decisions on customer targeting or product positioning. This paper presents the results of an extensive simulation study that examines the performance of commonly used information criteria in a mixture regression context with normal data. Unlike with previous studies, the performance is evaluated at a broad range of sample/segment size combinations being the most critical factors for the effectiveness of the criteria from both a theoretical and practical point of view. In order to assess the absolute performance of each criterion with respect to chance, the performance is reviewed against so called chance criteria, derived from discriminant analysis. The results induce recommendations on criterion selection when a certain sample size is given and help to judge what sample size is needed in order to guarantee an accurate decision based on a certain criterion respectively.