Statistical methods for developing and distinguishing multinominal response models in the traumatological analysis of simulated automobile impacts

This report describes the statistical analysis of injury data involving two sets of data taken from simulated car-to-car side impact studies. Predictors include exogenous biomechanical factors as well as anthropometric variables, such as age. The response is measured on a scale of injury score and is therefore multinomial. It is the aim of a statistical analysis of such data to devise a multinomial response model that explains possible patterns of injury as a function of a suitable set of predictor variables. Several approaches for modelling such a multinomial response relationship have been proposed in the literature, among them the logistic and the weibull regression models. Two major questions in applying such models are as follows: what model is appropriate and how should different models be compared. Another problem is how the quality of a given model should be presented for varying sets of predictors. In this paper we discuss the first question by constructing a goodness-of-fit test based on bootstrapping flexible, non-parametric alternatives to a given parametric candidate model. Secondly, we present several graphical techniques that allow relatively simple comparisons of different models.