A Multiplicative Mixed Model When the Variances Are Heterogeneous

¹ Department of Biometry, University of Nebraska, Lincoln 68583-0712
² Department of Animal Science, Cornell University, Ithaca, NY 14853

When animals are compared across environments, adjustment for differences among the environments is important. Not only are some environments more favorable than others, but the amount of variability may differ. A number of methods exist to account for heterogeneous variances. However, current methods have several potential disadvantages. A multiplicative mixed model that incorporates scaling factors is presented along with estimation procedures based on the model. A multiplicative mixed model differs from the usual mixed models in that the fixed and random effects are scaled by the scaling factor of each environment. A prior distribution, based on the chi-squared distribution, for the scaling factors is used. Marginal posterior mode estimators are given for estimation of the unknown parameters. An example data set is used to illustrate the procedure.

Key Words: heterogeneous • variance • mixed models

Submitted on June 11, 1992
Accepted on October 21, 1992