Transformations for compositional data with zeros with an application to forensic evidence evaluation

In forensic science likelihood ratios provide a natural way of computing the value of evidence under competing propositions such as “the compared samples have originated from the same object” (prosecution) and “the compared samples have originated from different objects” (defence). We use a two-level multivariate likelihood ratio model for comparison of forensic glass evidence in the form of elemental composition data under three data transformations: the logratio transformation, a complementary log–log type transformation and a hyperspherical transformation. The performances of the three transformations in the evaluation of evidence are assessed in simulation experiments through use of the proportions of false negatives and false positives.

► A likelihood ratio approach was used to obtain the evidential value of multivariate glass data. ► Multivariate normal random effects models and kernel density estimation were considered. ► Three distinct transformations for compositional data with zeros were considered. ► Dimension reduction was based on a graphical model approach. ► Kernel density estimation on spherically transformed data yielded remarkably accurate results.