  This paper proposes a joint model for longitudinal binary and count outcomes.
We apply the model to a unique longitudinal study of teen driving where 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 predicting crash and near crash outcomes. We
propose a two-state mixed hidden Markov model whereby the hidden state
characterizes the mean for the joint longitudinal crash/near crash outcomes and
elevated g-force events which are a proxy for risky driving. Heterogeneity is
introduced in both the conditional model for the count outcomes and the hidden
process using a shared random effect. An estimation procedure is presented
using the forward-backward algorithm along with adaptive Gaussian quadrature to
perform numerical integration. The estimation procedure readily yields hidden
state probabilities as well as providing for a broad class of predictors.
