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 the 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.
Parameterizations and fitting of bi-directed graph models to categorical data / M. Lupparelli; G. Marchetti; W. Bergsma. - In: SCANDINAVIAN JOURNAL OF STATISTICS. - ISSN 0303-6898. - ELETTRONICO. - 36:(2009), pp. 559-576. [10.1111/j.1467-9469.2008.00638.x]
Parameterizations and fitting of bi-directed graph models to categorical data
M. Lupparelli;MARCHETTI, GIOVANNI MARIA;
2009
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 the 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.File | Dimensione | Formato | |
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