Bias in Multivariate Generalized Linear Models

Abstract

In this article, an expression is derived for the bias associated with maximum likelihood estimates of the parameters in a multivariate generalized linear model (MGLM). This expression represent.s an extension of the bias formula in the case of a univariate generalized linear model. One important objective of the proposed extension is to obtain an expression for the mean squared error of prediction matrix, which can be used as a criterion for comparing response surface designs for a MGLM. An application of the bias formula is presented in the special case of the bivariate binary distribution. A numerical example is given to illustrate this particular application.