A multivariate logit model with marginal canonical association

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Abstract
In this work, a generalization of the Goodman Association Model to the case of q, q > 2, categorical variables which is based on the idea of marginal modelling discussed by Gloneck–McCullagh is introduced; the difference between the proposed generalization and two models, previously introduced by Becker and Colombi, is discussed. The Becker generalization is not a marginal model because it does not imply Logit Models for the marginal probabilities, and because it is based on the conditional approach of modelling the association. The Colombi model is only partially a marginal model because it uses simple logit models for the univariate marginal probabilities but is based on the conditional approach of modelling the association. It is also shown that the maximum likelihood estimation of the parameters of the new model is feasible and, to compute the maximum likelihood estimates, an algorithm is proposed, which is a numerically convenient compromise between the constrained optimization approach of Lang and the straightforward use of the Fisher Scoring Algorithm suggested by Glonek–McCullagh.Finally, the proposed model is used to analyze a data set concerning work accidents which occurred to workers at some Italian firms during the years 1994–1996.