mean model: E(y) = Xβ
variance model: log(Variance(y)) = Z λ,
Variance(y) = exp(Z λ)
A dispersion or log-variance effect can model changes in the variance of the response. This is implemented in the Fit Model platform by a fitting personality called the Loglinear Variance personality.
Log-linear variance effects are specified in the Fit Model dialog by highlighting them and selecting LogVariance Effect from the Attributes drop-down menu. &LogVariance appears at the end of the effect. When you use this attribute, it also changes the fitting Personality at the top to LogLinear Variance. If you want an effect to be used for both the mean and variance of the response, then you must specify it twice, once with the LogVariance option.
The effects you specify with the log-variance attribute become the effects that generate the Z’s in the model, and the other effects become the X’s in the model.