Modeling and Multivariate Methods - SAS

626 Visualizing, Optimizing, and Simulating Response Surfaces Chapter 24
Statistical Details
Table 24.5 Strata Intervals (Continued)
Strata Number Inside Distance Outside Distance
2
i
d + 2d
d + 2 2d
d + ( i–
1) 2d d+
i 2d
N Strata – 1
previous
∞
The default number of strata is 12. To change the number of strata, a hidden command N Strata is available
if you hold the Shift key down while clicking on the red triangle next to Simulator.
Figure 24.79 Showing the N Strata Menu Option
Increase the sample size as needed to maintain an even number of strata.
For each simulation run,
1. Select a strata as mod(i – 1, N Strata ) for run i.
2. Determine a random n-dimensional direction by scaling multivariate Normal (0,1) deviates to unit
norm.
3. Determine a random distance using a chi-square quantile appropriate for the strata of a random uniform
argument.
4. Scale the variates so the norm is the random distance.
5. Scale and re-center the variates individually to be as specified for each factor.
The resulting factor distributions are multivariate normal with the appropriate means and standard
deviations when estimated with the right weights. Note that you cannot use the Distribution standard
deviation with weights, because it does not estimate the desired value. However, multiplying the weight by a
large value, like 10 12 , and using that as a Freq value results in the correct standard deviation.