Overview of the Loglinear Variance Model
The loglinear-variance model (Harvey 1976, Cook and Weisberg 1983, Aitken 1987, Carroll and Ruppert 1988) provides a way to model the variance simply through a linear model. In addition to having regressor terms to model the mean response, there are regressor terms in a linear model to model the log of the variance:
mean model: E(y) = Xβ
variance model: log(Variance(y)) = Z λ,
Variance(y) = exp(Z λ)
where the columns of X are the regressors for the mean of the response, and the columns of Z are the regressors for the variance of the response. The regular linear model parameters are represented by β, and λ represents the parameters of the variance model.
Log-linear variance models are ...