Estimating the effect of friction on crash risk: Reducing the effect of omitted variable bias that results from spatial correlation.

Omitted variable bias is one of the main factors that lead to incorrect estimates of the effect of a variable on the expected number of crashes using regression modeling. We propose to use differencing of the (spatially adjacent) variables to reduce the effect of omitted variable bias. Differencing is a linear transformation that preserves the structure of the (generalized) linear model but can often result in significantly reducing the correlation between the variables. It is special case of (generalized) partial linear model regression which itself is a special case of a generalized additive model (GAM). In the spatial context used in this paper, differencing is similar to the well-known approach of including a spatial correlation structure (spatial error term) in the analysis of crash data. It is generally not clear how to interpret the results of models that include a spatial correlation structure and whether and how the added spatial correlation structure reduces the bias in the estimated regression parameters. However, for the case of differencing, it becomes clear how the effect of omitted variable bias is reduced by reducing the correlation between the variable of interest and the omitted variables. The order of differencing determines the dominant spatial scales of the variables considered in the model which affect how much the correlation is reduced. This reveals that omitted variable bias can be reduced when there are spatial scales at which the covariate of interest varies but the omitted variables either 1) are relatively homogeneous or 2) have variations that are not correlated to those of the variable of interest.