Maximum likelihood methods for linear and log-linear models in categorical data (Q1071434)

This work considers two types of models for categorical data: the linear model \(A\pi =X\beta\) and the generalized log-linear model A log \(\pi\) \(=X\beta\), where \(\pi\) is an array of cell probabilities corresponding to a multinomial or a product multinomial sampling scheme. For both models we derive maximum likelihood estimators of \(\pi\) and \(\beta\), as well as large-sample estimators of Var \({\hat \beta}\). Three examples are used to compare the results produced by the maximum likelihood and weighted least squares methods.