Group-Based criminal trajectory analysis using cross-validation criteria

In this paper, we discuss the challenge of determining the number of classes in a family of finite mixture models with the intent of improving the specification of latent class models for criminal trajectories. We argue that the traditional method of using either the Proc Traj or Mplus package to compute and maximize the Bayesian Information Criterion (BIC) is problematic: Proc Traj and Mplus do not always compute the MLE (and hence the BIC) accurately, and furthermore BIC on its own does not always indicate a reasonable-seeming number of groups even when computed correctly. As an alternative, we propose the new freely available software package, crimCV, written in the R-programming language, and the methodology of cross-validation error (CVE) to determine the number of classes in a fair and reasonable way. In the present paper, we apply the new methodology to two samples of N = 378 and N = 386 male juvenile offenders whose criminal behavior was tracked from late childhood/early adolescence into adulthood. We show how using CVE, as implemented with crimCV, can provide valuable insight for determining the number of latent classes in these cases. These results suggest that cross-validation may represent a promising alternative to AIC or BIC for determining an optimal number of classes in finite mixture models, and in particular for setting the number of latent classes in group-based trajectory analysis.