Cyclist-vehicle crash modeling with measurement error in traffic exposure

Exposure measures are always among the explanatory variables of any crash model. Regardless of the technique used to model crash, the mean crash frequency will increase with an increase in exposure since more crashes are likely to occur at higher exposure. For cyclist-vehicle crash models, bike and vehicle exposure measures are essential for an accurate and reliable estimate of the cyclist crash risk. However, traffic exposure measures are an example of variables that are measured with error. Generally, measurement error in regression estimates has three effects: 1) produce bias in parameter estimation for statistical models, 2) lead to a loss of explanation power, 3) mask important features of the data. This study proposes a full Bayesian Poisson Lognormal crash models that account for measurement error in traffic exposure measures (i.e., Vehicle Kilometers Travelled and Bike Kilometers Travelled). The underlying approach is to adjust the traffic exposure measures for measurement error to improve the accuracy of the crash model and crash model estimates. The full Bayesian models are developed using data for 134 traffic analysis zones (TAZs) in the city of Vancouver, Canada. The results show that Poisson Lognormal models that account for measurement error have a better fit for the modeled cyclist-vehicle crash data compared to traditional Poisson Lognormal models. The estimates of the Poisson Lognormal model that accounts for measurement error are consistent, with traditional Poisson Lognormal models' estimates except for the BKT and VKT estimates. Estimates of the BKT and VKT increased after introducing measurement error, which indicates an underestimation (downward bias) to BKT and VKT estimates in case of overlooking measurement error.