By the way, section 9.3 of Amazon.com: SAS for Mixed Models, Second Edition: 9781590475003: Littell, Ramon C., Milliken, George... provides demonstrations and examples of dealing with heteroscedasticity in mixed models. In short, this is dealt with two approaches that in essence both belong to the joint mean and variance modeling approach. They are termed as "Power-of-X" and "Power-of-the-Mean" models.
For Power-of-X models, the variance of residuals are modeled in this manner: Var(ei)=σ^2*exp(xγ), with γ being the regression coefficient. In SAS, this can be modeled by codes like:
proc mixed data=xxx;
/*other statements omitted*/
repeated /local=exp(x);
run;
Or
proc nlmixed data=xxx;
/*other statements omitted*/
model y ~ normal(mean,sig2*exp(gamma*x));
run;
The Power-of-the-Mean model assumes that the residuals are proportional to y_hat. Let yi_hat=β0+β1xi1+...+βkxik be the predicted dependent variable for the ith observation. The residuals are assumed to take the form Var(ei)=σ^2*|yi_hat|^θ, where θ is an unknown power parameter. SAS codes for this modeling approach are also documented in the book but are not displayed here because of their complexity. Refer to the book for more details.
By the way, this book now has a newer edition: SAS for Mixed Models: Introduction and Basic Applications: Stroup PH D, Walter W, Milliken PhD, Geor.... However, it is stated in the preface of the newer edition that contents regarding heterogeneous variance models are removed in that edition and are reserved to a later publication. For the time being, however, I have not found this publication.
