Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data

• DOI: 10.1111/j.1467-9469.2008.00638.x
• Publication Date: 2009-04-22T09:13:43Z
• Authors: MONIA LUPPARELLI; GIOVANNI M. MARCH...; WICHER P. BERGSMA
• Keywords: FOS: Computer and information sciences; complete hierarchical parameterizations; connected set Markov property; constrained maximum likelihood; covariance graphs; marginal independence; marginal log-linear models; multivariate logistic transformation; variation independence; Statistics - Machine Learning; FOS: Mathematics; Mathematics - Statistics Theory; Machine Learning (stat.ML); Statistics Theory (math.ST); 0101 mathematics; 01 natural sciences

Abstract. We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi‐directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation‐independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.