Fuzzy Clusterwise Growth Curve Models via Generalized Estimating Equations: An Application to the Antisocial Behavior of Children.

The growth curve model has been a useful tool for the analysis of repeated measures data. However, it is designed for an aggregate-sample analysis based on the assumption that the entire sample of respondents are from a single homogenous population. Thus, this method may not be suitable when heterogeneous subgroups exist in the population with qualitatively distinct patterns of trajectories. In this paper, the growth curve model is generalized to a fuzzy clustering framework, which explicitly accounts for such group-level heterogeneity in trajectories of change over time. Moreover, the proposed method estimates parameters based on generalized estimating equations thereby relaxing the assumption of correct specification of the population covariance structure among repeated responses. The performance of the proposed method in recovering parameters and the number of clusters is investigated based on two Monte Carlo analyses involving synthetic data. In addition, the empirical usefulness of the proposed method is illustrated by an application concerning the antisocial behavior of a sample of children.