Professor McCullagh will investigate a possible extension of generalized linear models to multivariate discrete responses. Early results suggest that the new class of models is an attractive alternative to log-linear models. In addition, Professor McCullagh proposes to extend earlier work on dispersion effects in linear modles to analogous effects in generalized linear models. Investigation of the uses of tensor methods in problems of theoretical statistics and statistical methodology will be continued. One such problem is to consider the Fourier decomposition of directional cumulants and derived invariants as tools in the problem of estimating cumulants based on residuals in generalized linear models. This research in statistics is part of a current thrust to provide theory for generalized linear models. Traditional linear models assume the response variables are normally distributed. This work is to extend the conceptual probabilistic constructs to apply to multivariate discrete response variables, and aims at developing appropriate statistics based on these models.
