title: A TWO-STATE MIXED HIDDEN MARKOV MODEL FOR RISKY TEENAGE DRIVING BEHAVIOR.
abstract: 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 theforward-backwardalgorithm 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.
authors.affiliation: Department of Mathematical Sciences, United States Military Academy, Thayer Hall, West Point, New York 10996, USA.
authors.forename: John C
authors.initials: JC
authors.lastname: Jackson
authors.affiliation: Biostatistics and Bioinformatics, Division of Intramural Population, Health Research, Eunice Kennedy Shriver National Institute, of Child Health and Human Development, 6100 Executive Blvd, Bethesda, Maryland 20892, USA.
authors.forename: Paul S
authors.initials: PS
authors.lastname: Albert
authors.affiliation: Biostatistics and Bioinformatics, Division of Intramural Population, Health Research, Eunice Kennedy Shriver National Institute, of Child Health and Human Development, 6100 Executive Blvd, Bethesda, Maryland 20892, USA.
authors.forename: Zhiwei
authors.initials: Z
authors.lastname: Zhang
keywords: Adaptive quadrature; hidden Markov model; joint model; random effects