Often when a longitudinal change is studied in a population of interest we find that changes over time are heterogeneous (in terms of time and/or covariates' effect) and a traditional linear mixed effect model [Laird and Ware, 1982] on the entire population assuming common parametric form for covariates and time may not be applicable to the entire population. This is usually the case in studies when there are many possible predictors influencing the response trajectory. For example, Raudenbush [2001] used depression as an example to argue that it is incorrect to assume that all the people in a given population would be experiencing either increasing or decreasing levels of depression. In such cases, a group-averaged trajectory can mask important subgroup differences. Our aim is to identify and characterize longitudinally homogeneous subgroups based on the combination of baseline covariates. We achieve this goal by constructing regression tree through binary partitioning. We propose two steps procedure for binary partitioning: 1) first, choose the most significant partitioning variable and 2) then choose the best split by repetitive evaluation of a goodness of fit criterion at all the splits of chosen partitioning variable. To remedy for the problem of multiple testing, we propose a single test to identify the instability of parameter(s) in longitudinal models for a given partitioning variable. We obtain asymptotic results and examine finite sample behavior of our method through simulation studies. Finally, we apply our method to study the changes in brain metabolite levels of HIV infected patients.



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