Summary A modification of the method of Nelder and Wedderburn (1972) is given for fitting models with the same error distributions as discussed there but with the systematic part of the models specified in terms of constraints. It is possible to fit these by the method described by Nelder and Wedderburn using iterative weighted regression, but it turns out to be simpler to replace each regression calculation of that method by another one with the property that the fitted values of one regression calculation are the residuals of the other and vice versa. The method is applied to testing for marginal homogeneity in contingency tables.
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R. W. M. Wedderburn (1974) studied this question.