Ordinal latent variable models and their application in the study of newly licensed teenage drivers

In a unique longitudinal study of teen driving, risky driving behavior and the occurrence of crashes or near crashes are measured prospectively over the first 18 months of licensure. Of scientific interest is relating the two processes and developing a predictor of crashes from previous risky driving behavior. In this work, we propose two latent class models for relating risky driving behavior to the occurrence of a crash or near crash event. The first approach models the binary longitudinal crash/near crash outcome using a binary latent variable which depends on risky driving covariates and previous outcomes. A random effects model introduces heterogeneity among subjects in modeling the mean value of the latent state. The second approach extends the first model to the ordinal case where the latent state is composed of K ordinal classes. Additionally, we discuss an alternate hidden Markov model formulation. Estimation is performed using the expectation-maximization (EM) algorithm and Monte Carlo EM. We illustrate the importance of using these latent class modeling approaches through the analysis of the teen driving behavior.