Abstract
Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.
Highlights
1.1 BackgroundThe main cause of death among teenagers in the USA is from motor vehicle accidents (Chen et al, 2014)
To the best of our knowledge, no work has been conducted to adjust for the measurement error in an offset variable in combination with spatial random effects
Embedding the measurement error model to account for the difference between Dij and nij, we have proposed the following models: Oij|m∗ij ∼ Poisson(m∗ij), log(m∗ij) = β0 + β1X1ij + β2X2i + β3Tj + log(nij) + log(Rij)
Summary
The main cause of death among teenagers in the USA is from motor vehicle accidents (Chen et al, 2014). Stage II: Intermediate stage of GDL, teenagers are allowed to drive independently with restrictions on driving at night and passengers. Stage III: Full-license stage of GDL, grants experienced teenager drivers full driving privileges without restrictions. The key difference is that we distinguish the population of teenagers and the population of teen drivers, while they are considered approximately the same in Chen et al (2014). We embed a measurement error model on the offset variable in a Poisson regression model to reflect the difference between the aforementioned two populations
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