Modeling and Multivariate Methods - SAS

Chapter 12
Fitting Dispersion Effects with the Loglinear
Variance Model
Using the Fit Model Platform
The Loglinear Variance personality of the Fit Model platform enables you to model both the expected value
and the variance of a response using regression models. The log of the variance is fit to one linear model and
the expected response is fit to a different linear model simultaneously.
Note: The estimates are demanding in their need for a lot of well-designed, well-fitting data. You need
more data to fit variances than you do means.
For many engineers, the goal of an experiment is not to maximize or minimize the response itself, but to aim
at a target response and achieve minimum variability. The loglinear variance model provides a very general
and effective way to model variances, and can be used for unreplicated data, as well as data with replications.
Modeling dispersion effects is not very widely covered in textbooks, with the exception of the Taguchi
framework. In a Taguchi-style experiment, this is handled by taking multiple measurements across settings
of an outer array, constructing a new response which measures the variability off-target across this outer
array, and then fitting the model to find out the factors that produce minimum variability. This kind of
modeling requires a specialized design that is a complete cartesian product of two designs. The method of
this chapter models variances in a more flexible, model-based approach. The particular performance statistic
that Taguchi recommends for variability modeling is STD = -log(s). In JMP’s methodology, the log(s 2 ) is
modeled and combined with a model that has a mean. The two are basically equivalent, since log(s 2 )=2
log(s).