The Effect Screening platform uses the principle of effect sparsity (Box and Meyer, 1986). This principle asserts that relatively few of the effects that you study in a screening design are active. Most are inactive, meaning that their true effects are zero and that their estimates are random error.
1.
Open the Drug.jmp sample data table.
2.
Select Analyze > Fit Model.
3.
Select y and click Y.
4.
Select Drug and x and add these to the Construct Model Effects list.
5.
6.
Click Run.
7.
From the red triangle menu next to Response y, select Effect Screening > Scaled Estimates.
The report (Scaled Estimates Report) indicates that the continuous factor, x, is centered by its mean and scaled by its half-range.
Scaled Estimates Report
The model fits three parallel lines, one for each Drug group. The x values range from 3 to 21. The Scaled Estimate for x, 8.8846543, is half the difference between the predicted value for x = 21 and the predicted value for x = 3 for any one of the Drug groups. You can verify this fact by selecting Save Columns > Prediction Formula from the report’s red triangle menu. Then add rows to obtain predicted values for each of the Drug groups at x = 21 and x = 3.
So, over the range of x values in this particular data set, the impact of x is to vary the response over a range of about 17.8 units. Note that the parameter estimate for x based on the raw data is 0.9871838; it does not permit direct interpretation in terms of the response.
A Lenth PSE (pseudo standard error) table appears directly beneath the notes or option lists. (For a description of the PSE, see Lenth’s PSE.)
The option Using estimates standardized to have equal variances applies a normalizing transformation to standardize the variances. This option is selected by default when the variances are unequal.
The option Using estimates orthogonalized to be uncorrelated applies a transformation to remove correlation. This option is selected by default when the estimates are correlated. The transformation that is applied is identical to the transformation that is used to calculate sequential sums of squares. The estimates measure the additional contribution of the variable after all previous variables have been entered into the model.
The columns that appear in the table depend on the selections initially described in the notes or option lists. The report highlights any row corresponding to an estimate with a p-value of 0.15 or less. All versions of the report give Term, Estimate, and either t-Ratio and Prob>|t| or Pseudo t-Ratio and Pseudo p-Value.
Gives the p-value for the test. If a transformation is applied, this option gives the p-value for a test using the transformed data.
Appears when there are no degrees of freedom for error. The p-value is derived using a t distribution. The degrees of freedom are m/3, rounded down to the nearest integer, where m is the number of parameters.
If Using estimates standardized to have equal variances is selected and the note indicating that the parameter estimates are not correlated appears, the report shows a column called Standardized Estimate. This column provides estimates of the parameters resulting from the transformation used to transform the estimates to have equal variances.
If both Using estimates standardized to have equal variances and Using estimates orthogonalized to be uncorrelated are selected, the report gives a column called Orthog Coded. The following information is provided:
Appears if there are no degrees of freedom for error. It is a t ratio computed by dividing the orthogonalized estimate, Orthog Coded, by Coded Scale Lenth PSE.
Effect Screening Report for Equal Variance and Uncorrelated Estimates shows the Effect Screening report that you create by running the Fit Model script in the Bicycle.jmp sample data table. Note that you would select Effect Screening > Normal Plot in order to obtain this form of the report. The notes directly beneath the report title indicate that no transformation is required. Consequently, the Lenth PSE is displayed. Because there are no degrees of freedom for error, no estimate of residual error can be constructed. For this reason, Lenth’s PSE is used as an estimate of residual error to obtain pseudo t ratios. Pseudo p-values are given for these t ratios. Rows corresponding to the three estimates with p-values of 0.15 or less are highlighted.
Effect Screening Report for Equal Variance and Uncorrelated Estimates
In the Odor.jmp sample data table, run the Model script and click Run. To create the report shown in Effect Screening Report for Unequal Variances and Correlated Estimates, select Effect Screening > Normal Plot from the Response Y red triangle menu. You can also create the report by selecting the Bayes Plot or Pareto Plot options in the Response Y red triangle menu.
The report shows the t-Test Scale and Coded Scale Lenth PSEs. But, because there are degrees of freedom for error, the tests in the Parameter Estimate Population report do not use the Lenth PSEs. Rows corresponding to the three estimates with p-values of 0.15 or less are highlighted. A note at the bottom of the Parameter Estimate Population report indicates that orthogonalized estimates depend on their order of entry into the model.
Effect Screening Report for Unequal Variances and Correlated Estimates
The Correlations of Estimates report appears only if the estimates are correlated (Effect Screening Report for Unequal Variances and Correlated Estimates). The report provides the correlation matrix for the parameter estimates. This matrix is similar to the one that you obtain by selecting the Estimates > Correlation of Estimates red triangle option. However, to provide a more compact representation, the report does not show column headings. See Correlation of Estimates for details.
If a transformation to orthogonality has been applied, the vertical axis represents the Normalized Estimates. These are the Orthog t-Ratio values found in the Parameter Estimate Population report. (The Orthog t-Ratio values are the Orthog Coded estimates divided by the Coded Scale Lenth PSE.)
Because the estimates are normalized by an estimate of σ, the points corresponding to inactive effects should fall along a line of slope 1. A red line with slope 1 is shown on the plot, as well as a blue line with slope equal to the t-Test Scale Lenth PSE.
In all cases, estimates that deviate from normality at the 0.15 level, based on the p-values in the Parameter Estimate Population report, are labeled on the plot.
Normal Plot shows the Normal Plot report for the Bicycle.jmp sample data table. No transformation is needed for this model, so the plot shows the raw estimates plotted against their normal quantiles. A line with slope equal to Lenth’s PSE is shown on the plot. The plot suggests that Gear, Dynamo, and Seat are active factors.
1.
Open the Bicycle.jmp sample data table.
2.
Select Analyze > Fit Model.
3.
Select Y and click Y.
4.
Select HBars through Brkfast and click Add.
5.
Click Run.
6.
Normal Plot
The specifications window, showing default settings for a Bayes Plot for the Bicycle.jmp sample data table, is shown in Bayes Plot Specifications. Clicking Go in this window updates the report to show Posterior probabilities for each of the terms and a bar chart (Bayes Plot Report).
1.
Open the Bicycle.jmp sample data table.
2.
Select Analyze > Fit Model.
3.
Select Y and click Y.
4.
Select HBars through Brkfast and click Add.
5.
Click Run.
Bayes Plot Specifications
7.
Click Go to calculate the posterior probabilities.
Bayes Plot Report
The Pareto Plot report presents a Pareto chart of the absolute values of the estimates. Pareto Plot shows a Pareto Plot report for the Bicycle.jmp sample data table.
Pareto Plot