Measurement Error Adjustment in the Offset Variable of a Poisson Model
Motor vehicle accidents is the main cause of death among teenagers in the US. Car crashes are the leading cause of death among teenagers. The Graduated Driver Licensing (GDL) program is one effective policy for reducing the number of teenage car crashes. Our study focuses on how the GDL program adopted by the state of Michigan in 1997 took effect. We use Poisson regression with spatially dependent random effects to model the county-level teenage car crash counts and consider a measurement error model for the offset as the offset variable is mismeasured. The total teenage population in the county-level is widely used to be a proxy for the teenage driver population when modelling the teenage driver fatality rate. In our case, the data for the teenage driver population are not available in the county-level but the state-level in Michigan. Thus, a measurement error issue arises in the offset variable of our Poisson model, we propose including a measurement error model to account for the difference between the teenage population and teenage driver population. To the best of our knowledge, there is no existing literature to adjust for an offset variable when it is measured with error, and limited research has addressed the measurement errors in the context of spatial data. In this thesis, a Berkson measurement error model with spatial random effects have been applied to adjust the offset variable in a Bayesian framework, and the Bayesian MCMC sampling is implemented in rstan. To check whether the adjustment for the offset variable will bring any differences to our model, we have conducted real data analysis. We found the coefficient of T (time) becomes less significant after the adjustment, which leads to a new finding for the GDL -- the reduction number of teen-drivers can help explain the partial effectiveness of this policy.
Graduated Driver Licensing, measurement errors, spatial random effects
Master of Science (M.Sc.)
Mathematics and Statistics