Likelihood Ratios for categorical evidence; Comparison of LR models applied to gunshot residue data

In this article a 2-level multinomial model for the calculation of Likelihood Ratios (LRs) as a measure of the strength of evidence in the case of categorical evidence is introduced. In order to illustrate its usage, it is applied to gunshot residue (GSR) comparison data obtained in an experimental set-up and analysed using electron microscopy. The data consists of a number of gunshot residues divided in k categories depending on their elemental composition. For comparison a score-based model (the Pearson correlation) and a 1-level multinomial model estimated with Maximum Likelihood (ML) were also applied on the same data. Three variations of the 2-level multinomial model were tested, together with the other two models. The results show that all tested models can be applied on categorical data such as GSR. The 2-level multinomial model, the model that is introduced in the study, shows the least misleading evidence. Furthermore this article demonstrates a first step taken towards a system that calculates numerical LRs in GSR comparison studies.