Modeling and Multivariate Methods - SAS

314 Fitting Dispersion Effects with the Loglinear Variance Model Chapter 12
Profiling the Fitted Model
Figure 12.8 Profiler to Match Target and Minimize Variance
One of the best ways to see the relationship between the mean and the variance (both modeled with the
LogVariance personality) is through looking at the individual prediction confidence intervals about the
mean. Regular confidence intervals (those shown by default in the Profiler) do not show information about
the variance model as well as individual prediction confidence intervals do. Prediction intervals show both
the mean and variance model in one graph.
If Y is the modeled response, and you want a prediction interval for a new observation at x n, then:
s 2 2 2
x n
= s Y xn + s xn
Ŷ
where:
s 2 |x n is the variance for the individual prediction at x n
s 2 Y |x n is the variance of the distribution of Y at x n
s Ŷ
2 xn
is the variance of the sampling distribution of Ŷ , and is also the variance for the mean.
Because the variance of the individual prediction contains the variance of the distribution of Y, the effects of
the changing variance for Y can be seen. Not only are the individual prediction intervals wider, but they can
change shape with a change in the variance effects.