Selecting amongst multinomial models: An apologia for normalized maximum likelihood

David Kellen, Karl Christoph Klauer

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number102367
JournalJournal of Mathematical Psychology
StatePublished - Aug 2020


  • Gibbs sampler
  • Minimum-description length
  • Model selection
  • Multinomial data
  • Normalized maximum likelihood

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics


Dive into the research topics of 'Selecting amongst multinomial models: An apologia for normalized maximum likelihood'. Together they form a unique fingerprint.

Cite this