The Annals of Statistics

Marginalization and Collapsibility in Graphical Interaction Models

Morten Frydenberg

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Abstract

The behaviour of a graphical interaction model under marginalization is discussed. A graphical interaction model is called collapsible onto a set of variables if the class of marginal distributions is the same as that implied by the related subgraph. The necessary and sufficient condition for collapsibility is found and it is shown that collapsibility is equivalent to a range of other important statistical properties of the model.

Article information

Source
Ann. Statist., Volume 18, Number 2 (1990), 790-805.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347626

Digital Object Identifier
doi:10.1214/aos/1176347626

Mathematical Reviews number (MathSciNet)
MR1056337

Zentralblatt MATH identifier
0725.62057

JSTOR
links.jstor.org

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62J99: None of the above, but in this section

Keywords
Graphical models decomposition collapsibility maximum likelihood estimate contingency tables covariance selection marginalization cut

Citation

Frydenberg, Morten. Marginalization and Collapsibility in Graphical Interaction Models. Ann. Statist. 18 (1990), no. 2, 790--805. doi:10.1214/aos/1176347626. https://projecteuclid.org/euclid.aos/1176347626


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