Mixed effects modelling for glass category estimation from glass refractive indices

520 Glass fragments were taken from 105 glass items. Each item was either a container, a window, or glass from an automobile. Each of these three classes of use are defined as glass categories. Refractive indexes were measured both before, and after a programme of re-annealing. Because the refractive index of each fragment could not in itself be observed before and after re-annealing, a model based approach was used to estimate the change in refractive index for each glass category. It was found that less complex estimation methods would be equivalent to the full model, and were subsequently used. The change in refractive index was then used to calculate a measure of the evidential value for each item belonging to each glass category. The distributions of refractive index change were considered for each glass category, and it was found that, possibly due to small samples, members of the normal family would not adequately model the refractive index changes within two of the use types considered here. Two alternative approaches to modelling the change in refractive index were used, one employed more established kernel density estimates, the other a newer approach called log-concave estimation. Either method when applied to the change in refractive index was found to give good estimates of glass category, however, on all performance metrics kernel density estimates were found to be slightly better than log-concave estimates, although the estimates from log-concave estimation prossessed properties which had some qualitative appeal not encapsulated in the selected measures of performance. These results and implications of these two methods of estimating probability densities for glass refractive indexes are discussed.