Construct Nonparametric Confidence Intervals for Variance Components
If you prefer to skip the steps in this section, select Help > Sample Data Library and open Design Experiment/Catalyst Design.jmp. In the Catalyst Design.jmp data table, click the green triangle next to the DOE Simulate script. Then go to Fit the Model.
1.
Select DOE > Custom Design.
3.
Click Add Factor > Continuous.
4.
Double-click to rename these factors Temperature, Time, and Catalyst.
5.
For Temperature, click Easy and select Very Hard.
This defines Temperature to be a whole plot factor.
6.
For Time, click Easy and select Hard for Time.
This defines Time to be a subplot factor.
7.
Click Continue.
8.
Note: Setting the Random Seed in step 10 and Number of Starts in step 11 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
10.
(Optional) Click the Custom Design red triangle and select Set Random Seed. Type 12345 and click OK.
11.
(Optional) Click the Custom Design red triangle and select Number of Starts. Type 1000 and click OK.
12.
Click Make Design.
13.
Click Make Table.
Note: The entries in your Y and Y Simulated columns will differ from those that appear in Figure 9.151.
Figure 9.151 Design Table
Figure 9.152 Simulate Responses Window
The design table and a Simulate Responses window appear. Notice that the design table contains a DOE Simulate script. At any time, you can run this script to specify different parameter values.
1.
In the Distribution panel (Figure 9.152), next to Whole Plots σ, type 2.
2.
Next to Subplots σ, type 1.5.
3.
Click Apply.
In the data table, the formula for Y Simulated updates to reflect your specifications. To view the formula, click on the plus sign to the right of the column name in the Columns panel.
5.
Click the Y variable next to the Y button and click Remove.
6.
Click Y Simulated and click the Y button.
This action replaces Y with a column that contains a simulation formula.
7.
Click Run.
Note: Because the values in Y Simulated are randomly generated, the entries in your report will differ from those that appear in Figure 9.153.
Figure 9.153 REML Report Showing Wald Confidence Intervals
Figure 9.154 Simulate Window
In your simulations, you replace the column Y Simulated, which you used to run your model, with a new instance of the column Y Simulated, which generates a new column of simulated values for each simulation. The column on which you right-clicked and that appears as selected, Var Component, will be simulated for each effect listed in the Parameter Estimates table.
2.
Next to Number of Samples, enter 200.
3.
(Optional) Next to Random Seed, enter 456.
This reproduces the values shown in Figure 9.155, except for the values in row 1.
4.
Figure 9.155 Table of Simulated Results for Var Component (Partial View)
5.
Run the Distribution script.
Figure 9.156 Distribution Plots for Variance Components (Partial View)
For each variance component, confidence intervals at various confidence levels are shown in the Simulation Results report (Figure 9.156). Compare the 95% intervals in the Alpha=0.05 row of each table to the intervals given in the REML report (Figure 9.153):

Help created on 7/12/2018