Bayesian and multilevel approaches to modelling road traffic fatalities

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Smeed, in 1949, provided a regression model for estimating road traffic fatalities (RTFs). In this study, a modified form of Smeed’s model is proposed for which it was shown that the multiplicative error term is less than that of Smeed’s original model for most situations. Based on this Modified Smeed’s model, Bayesian and multilevel methods were developed to assess RTF risk across sub populations of a given geographical zone. These methods consider the parameters of the Smeed’s model to be random variables and therefore make it possible to compute variances across space provided there is significant intercept variation of the regression equation across such regions. Using data from Ghana, the robustness of the Bayesian estimates was indicated at low sample sizes with respect to the Normal, Laplace and Cauchy prior distributions. Thus the Bayesian and Multilevel methods performed at least as well as the traditional method of estimating parameters and beyond this were able to assess risk differences through variability of these parameters in space.
Thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematical Statistics, 2016