Decomposable log-linear models

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Abstract

 The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphicalmodels, which can be characterized by a structured set of conditional independencies between some variables given some other variables. We term the new model class decomposable log-linear models, which is illustrated to be a much richer class than decomposable graphical models.It covers a wide range of non-hierarchical models, models with structural zeroes, models described by quasi independence and models for level merging. Also, they have a very natural interpretation as they may be formulated by a structured set of conditional independencies between two events given some other event. In relation to contingency tables we term such independencies as context specific independencies.
Original languageEnglish
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages21
Publication statusPublished - 2005
SeriesResearch Report Series
NumberR-2005-16
ISSN1399-2503

Keywords

  • Decomposable model
  • Log-linear model
  • Exact inference
  • Quasi independence
  • Level merging
  • Incomplete contingency table

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