Graphical modeling of multinomial data is considered using the natural parametrization for which the maximum likelihood estimates will attain finite values under arbitrary models regardless of the sample size. The likelihood ratio test statistic or the divergence for decomposable models is shown to equal a simple expression involving only entropies. A general estimation technique is introduced for nondecomposable models in which models in a class of decomposable supermodels of the model under consideration are sequentially fitted to the observed distribution. Use of weighted divergence is considered in situations where different outcomes are of unequal importance with respect to the model fit. As an example, more powerful tests of independence for ordinal categorical data against dependence of a linear or monotone type are shown to be obtained by using an unequal weighting for the divergence. Such power comparisons are given both for simulated and real data.

Key words: Decomposability, entropy, graphical models, information divergence, iterative fitting, nondecomposable models, weighted divergence.

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Last update: 1999-09-16/CE