Likelihood estimation for exchangeable multinomial data

In this article, maximum likelihood estimates of an exchangeable multinomial distribution using a parametric form to model the parameters as functions of covariates are derived. The non linearity of the exchangeable multinomial distribution and the parametric model make direct application of Newton Rahpson and Fisher\u27s scoring algorithms computationally infeasible. Instead parameter estimates are obtained as solutions to an iterative weighted least-squares algorithm. A completely monotonic parametric form is proposed for defining the marginal probabilities that results in a valid probability model