Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 85
Effect Screening
Half-Normal Plot
Below the Normal Plot report title, select Half Normal Plot from the list to plot the absolute values of the
estimates against the normal quantiles for the absolute value normal distribution (shown in Figure 3.23).
Figure 3.23 Half Normal Plot
Bayes Plot
Another approach to resolving which effects are important (sometimes referred to as active contrasts) is
computing posterior probabilities using a Bayesian approach. This method, due to Box and Meyer (1986),
assumes that the estimates are a mixture from two distributions. Some portion of the effects is assumed to
come from pure random noise with a small variance. The remaining terms are assumed to come from a
contaminating distribution that has a variance K times larger than the error variance.
An effect’s prior probability is the chance you give that effect of being nonzero (or being in the
contaminating distribution). These priors are usually set to equal values for each effect. 0.2 is a commonly
recommended prior probability value. The K contamination coefficient is often set at 10. This value
indicates that the contaminating distribution has a variance that is 10 times the error variance.
The Bayes plot is done with respect to normalized estimates (JMP lists as Orthog t-Ratio), which have been
transformed to be uncorrelated and have equal variance.
Example of a Bayes Plot
1. Open the Reactor.jmp sample data table.
2. Select Analyze > Fit Model.
3. Select Y and click Y.
4. Make sure that the Degree box has a 2 in it.
5. Select F, Ct, A, T, and Cn and click Macros > Factorial to Degree.
6. Click Run.
7. From the red triangle menu next to Response Y, select Effect Screening > Bayes Plot.