We apply the method of McCullagh & Tibshirani (1990) to a generalization of
the model for variance components in which the parameter of interest can a
ppear in both the mean and variance. We obtain the exact adjusted profile l
og-likelihood score function. For the variance components model, we obtain
the adjusted profile log-likelihood and show that it equals the restricted
log-likelihood of Patterson & Thompson (1971). We discuss an example due to
Kempton (1982) of a regression model with autoregressive terms in which th
e parameter of interest appears in both the mean and variance.