Information identities based on the product multinomial likelihood are proposed to illustrate the association between categorical variables. These identities are built upon the Pythagorean law of decomposed mutual inf...
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Information identities based on the product multinomial likelihood are proposed to illustrate the association between categorical variables. These identities are built upon the Pythagorean law of decomposed mutual information and examined to yield valid inference of log-linear and logistic models. For practical contingency tables, an optimal selection scheme of the information identity is formulated to yield proper log-linearmodels and logistic models, giving proper logarithmic odds ratios as maximum likelihood parameter estimates. Comparison of the proposed geometric information analysis with the classical AIC model selection is examined using empirical study of a medical data.
We describe a novel stochastic search algorithm for rapidly identifying regions of high posterior probability in the space of decomposable, graphical and hierarchical log-linear models. Our approach is based on the Di...
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We use reversible jump Markov chain Monte Carlo methods (Green, 1995) to develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linearmodels for high-dimensional con...
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We use reversible jump Markov chain Monte Carlo methods (Green, 1995) to develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linearmodels for high-dimensional contingency tables. Even for tables of moderate size, these, sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a three-way table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a six-way contingency table for which exact methods are infeasible, because of the large number of possible. models. We identify the most;probable hierarchical, graphical and decomposable models, and compare the results with alternative approaches.
The iterative proportional fitting (IPF) algorithm is simple to use for fitting hierarchical log-linear models of any size whether their maximum likelihood estimates are given in a closed form or not. This paper shows...
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The iterative proportional fitting (IPF) algorithm is simple to use for fitting hierarchical log-linear models of any size whether their maximum likelihood estimates are given in a closed form or not. This paper shows that the algorithm can be extended toward a class of nonhierarchical log-linear models.
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