Analysis of truck accident rates using loglinear models

Abstract
Alternative approaches for the analysis of factors affecting truck accident rates are assessed. The scope of the discussion is methodological in nature, with emphasis on exploring the limitations of each approach. Several important statistical concerns associated with the weighted least squares algorithm for calibrating loglinear models are addressed, including reduced cell membership in the contingency tables of accidents, scaling factors for measuring truck exposure, incompatibility between continuous exposure variables and categorical accident data, and sensitivity of calibrated coefficients to changes in accident characteristics for different data sets. An alternative approach for fitting loglinear models is proposed, which makes use of the generalized linear interactive models (GLIM) package. This approach assumes that the dependent variables in the contingency table of accidents behave in a Poisson-like process with values ranging from 0 to infinity. The calibration of the beta parameters in the loglinear expressions uses maximum likelihood techniques. Continuous exposure variates are incorporated into these models as offsets. As in the classical weighted least squares algorithm, this approach permits a stepwise statistical analysis of higher-order interactions for categorical accident frequency data, while adjusting directly for continuous measures of exposure. The results of a calibration of loglinear expressions for Ontario truck accident data are presented. Key words: truck accident rate, exposure, loglinear calibration, causal interaction.