A major aim of longitudinal analyses of life course data is to describe the within- and between-individual variability in a behavioral outcome such as crime. Methods for life course data typically draw on mixed-effects growth and mixture models. For example, group-based trajectory modeling assumes a mixture of groups where each group is defined by a distinct polynomial relationship between age and behavior.
Here we take a different approach, assuming a common age-crime curve and allowing individual crime trajectories to differ by latent patterns of temporal misalignment and amplitudes. We analyze self- reported counts of yearly marijuana use from the Denver Youth Survey, assuming a unimodal age-crime curve. We employ a non- parametric Bayesian hierarchical curve registration approach to estimate the age-crime curve and individual amplitudes and time- transformation functions. Our approach captures individual heterogeneity in meaningful terms by allowing differences in the level of offending and in the timing of features such as age at desistance. We compare our results with those from a group-based trajectory analysis graphically and numerically with a cross- validation study. (Joint work with Donatello Telesca, Ross Matsueda, and Derek Kreager.)
