Methodological analysis demonstrates regressive logistic models for dependent binary observations, indicating that standard statistical software can readily fit complex multivariate data.
The likelihood of a set of binary dependent outcomes, with or without explanatory variables, is expressed as a product of conditional probabilities each of which is assumed to be logistic. The models are called regressive logistic models. They provide a simple but relatively unknown parametrization of the multivariate distribution. They have the theoretical and practical advantage that they can be analyzed and fitted as in logistic regression for independent outcomes, and with the same computer programs. The paper is largely expository and is intended to motivate the development and usage of the regressive logistic models. The discussion includes serially dependent outcomes, equally predictive outcomes, more specialized patterns of dependence, multidimensional tables, and three examples.
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George E. Bonney (1987) studied this question.
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