Random Effects Multidimensional Scaling Models

Keywords: MCMC, nonparametric mixed effects

Abstract: By assuming a distribution for the parameters associated with subject weights in individual differences multidimensional scaling models, the subject weights become random effects. Including random effects in multidimensional scaling models can offer several advantages over traditional models such as those fitted by the {\sc INDSCAL}, {\sc ALSCAL}, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, generalization of results to the sampled population of subjects is immediate. Here we define some random effects multidimensional scaling models, give computational algorithms, and provide an examples illustrating the use of our model and algorithms.