Open Access
May 2017 Type II chain graph models for categorical data: A smooth subclass
Federica Nicolussi, Roberto Colombi
Bernoulli 23(2): 863-883 (May 2017). DOI: 10.3150/15-BEJ762


The Probabilistic Graphical Models use graphs in order to represent the joint distribution of $q$ variables. These models are useful for their ability to capture and represent the system of independence relationships among the variables involved, even when complex. This work concerns categorical variables and the possibility to represent symmetric and asymmetric dependences among categorical variables. For this reason we use the Chain Graphical Models proposed by Andersson, Madigan and Perlman (Scand. J. Stat. 28 (2001) 33–85), also known as Chain Graphical Models of type II (GMs II). The GMs II allow for symmetric relationships typical of log-linear models and, at the same time, asymmetric dependences typical of Graphical Models for Directed Acyclic Graphs. In general, GMs II are not smooth, however this work provides a subclass of smooth GMs II by parametrizing the probability function through marginal log-linear models. Furthermore, the proposed models are applied to a data-set from the European Value Study for the year 2008 (EVS (2010)).


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Federica Nicolussi. Roberto Colombi. "Type II chain graph models for categorical data: A smooth subclass." Bernoulli 23 (2) 863 - 883, May 2017.


Received: 1 October 2014; Revised: 1 July 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 1381.62226
MathSciNet: MR3606753
Digital Object Identifier: 10.3150/15-BEJ762

Keywords: categorical variables , Chain Graph Models , conditional indipendence models , marginal models

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 2 • May 2017
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