Multivariate linear intervention models with random parameters to estimate the effectiveness of safety treatments: Case study of intersection device program

A novel intervention model that analyzes time-series crash data was recently introduced in the road safety statistical field. The model allows the computation of components related to direct and indirect treatment effects using a linearized time-series intervention model. The isolation of a component corresponding to the direct treatment effects, known as the crash modification function (CMFunction), enables the assessment of safety countermeasures over time. To gain new insights into how crash counts are influenced by covariates and to account for the fact that many components affecting crash occurrence are not easily available (unobserved heterogeneity), the linear intervention models with random parameters are implemented to evaluate the safety impacts of a specific treatment. Both matched-pair and full random parameter models were applied. In addition, the analysis was carried out in a multivariate context to account for possible correlation between dependent variables. The safety treatment selected for this study was the Intersection Safety Device (ISD) program implemented in the City of Edmonton (Alberta, Canada). The safety impacts were estimated by assessing the change in crash severity (property-damage-only vs. fatal-plus-injury) over time. Overall, the results showed a lower deviance information criterion (better goodness of fit) of the multivariate linear intervention model with random parameters compared to the univariate form with fixed parameters. The difference of the indexes of treatment effectiveness between the proposed modeling framework and the univariate model with fixed parameters was estimated up to 2.7%, which indicates the importance of accounting for unobserved heterogeneity.