Selecting amongst multinomial models: An apologia for normalized maximum likelihood

The modeling of multinomial data has seen tremendous progress since Riefer and Batchelder's (1988) seminal paper. One recurring challenge, however, concerns the availability of relative performance measures that strike an ideal balance between goodness of fit and functional flexibility. One approach to the problem of model selection is Normalized Maximum Likelihood (NML), a solution derived from the Minimum Description Length principle. In the present work we provide an R implementation of a Gibbs sampler that can be used to compute NML for models of joint multinomial data. We discuss the application of NML in different examples, compare NML with Bayes Factors, and show how it constitutes an important addition to researchers’ toolboxes.