Context-specific independencies in hierarchical multinomial marginal models

This paper focuses on studying the relationships among a set of categorical (ordinal) variables collected in a contingency table. Besides the marginal and conditional (in)dependencies, thoroughly analyzed in the literature, we consider the context-specific independencies holding only in a subspace of the outcome space of the conditioning variables. To this purpose we consider the hierarchical multinomial marginal models and we provide several original results about the representation of context-specific independencies through these models. The theoretical results are supported by an application concerning the innovation degree of Italian enterprises.

[1]  Ioannis Ntzoufras,et al.  Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence , 2013, Comput. Stat. Data Anal..

[2]  Roberto Colombi,et al.  Modelling two way contingency tables with recursive logits and odds ratios , 2008, Stat. Methods Appl..

[3]  J. Albert.  Bayesian selection of log-linear models , 1996 .

[4]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[5]  Craig Boutilier,et al.  Context-Specific Independence in Bayesian Networks , 1996, UAI.

[6]  M. Drton.  Likelihood ratio tests and singularities , 2007, math/0703360.

[7]  P. McCullagh,et al.  Multivariate Logistic Models , 1995 .

[8]  P. Dellaportas,et al.  Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models , 1999 .

[9]  Antonio Forcina,et al.  A class of smooth models satisfying marginal and context specific conditional independencies , 2012, J. Multivar. Anal..

[10]  Antonio Forcina,et al.  Smoothness of conditional independence models for discrete data , 2012, J. Multivar. Anal..

[11]  I. Ntzoufras,et al.  Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models , 2018, Bayesian Analysis.

[12]  F. Nicolussi,et al.  Context-specific independencies for ordinal variables in chain regression models , 2017, 1712.05229.

[13]  Alberto Roverato,et al.  Graphical Models for Categorical Data , 2017 .

[14]  Sabrina Giordano,et al.  hmmm: An R Package for Hierarchical Multinomial Marginal Models , 2014 .

[15]  Alessandro Rinaldo,et al.  Markov Properties of Discrete Determinantal Point Processes , 2018, AISTATS.

[16]  Jukka Corander,et al.  Context-specific independence in graphical log-linear models , 2014, Comput. Stat..

[17]  Francesco Bartolucci,et al.  An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints , 2007 .

[18]  Jukka Corander,et al.  Stratified Graphical Models - Context-Specific Independence in Graphical Models , 2013, 1309.6415.

[19]  Wicher P. Bergsma,et al.  Marginal models for categorical data , 2002 .

[20]  Søren Højsgaard,et al.  Statistical Inference in Context Specific Interaction Models for Contingency Tables , 2004 .

[21]  R. Colombi,et al.  Marginal Nested Interactions for Contingency Tables , 2014 .

[22]  Wicher P. Bergsma,et al.  Marginal log-linear parameterization of conditional independence models , 2010 .