On the improved estimation of the normal mixture components for longitudinal data

When analyzing real data sets, statisticians often face the question that the data are heterogeneous and it may not necessarily be possible to model this heterogeneity directly. One natural option in this case is to use the methods based on finite mixtures. The key question in these techniques often is what is the best number of mixtures or, depending on the focus of the analysis, the best number of sub-populations when the model is otherwise fixed. Moreover, when the distribution of the response variable deviates from meeting the assumptions, it's common to employ an appropriate transformation to align the distribution with the model's requirements. To solve the problem in the mixture regression context we propose a technique based on the scaled Box-Cox transformation for normal mixtures. The specific focus here is on mixture regression for longitudinal data, the so-called trajectory analysis. We present interesting practical results as well as simulation experiments to demonstrate that our method yields reasonable results. Associated R-programs are also provided.