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


Address for correspondence: John C. Jackson, Department of Mathematical Sciences, US Military Academy, Thayer Road, West Point, NY 10996, USA.


Summary.  In a unique longitudinal study of teen driving, risky driving behaviour 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 behaviour. In this work, we propose two latent class models for relating risky driving behaviour to the occurrence of a crash or near-crash event. The first approach models the binary longitudinal crash or near-crash outcome by using a binary latent variable which depends on risky driving covariates and previous outcomes. A random-effects model introduces heterogeneity among subjects in modelling 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 alternative hidden Markov model formulation. Estimation is performed by using the expectation–maximization algorithm and Monte Carlo expectation–maximization. We illustrate the importance of using these latent class modelling approaches through the analysis of the teen driving behaviour.

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