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Biometrika 1989 76(3):539-555; doi:10.1093/biomet/76.3.539
© 1989 by Biometrika Trust
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Decomposition of maximum likelihood in mixed graphical interaction models

MORTEN FRYDENBERG and L. LAURITZEN STEFFEN

Department of Theoretical Statistics, Aarhus University DK-8000 Aarhus, Denmark
Department of Mathematics and Computer Science, Aalborg University DK-9000 Aalborg, Denmark

We show how decompositions of marked graphs induce corresponding decompositions of maximum likelihood estimates in mixed graphical interaction models. We use this result to obtain explicit formulae for the estimates in decomposable models and to obtain factorizations of likelihood ratio statistics.

Key Words: Cut • Decomposition • Likelihood ratio • Marked graph • Multiplicative model


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