RSM/MIX Suggested Model

Stat-Ease automatically defaults to the “Suggested” polynomial model which best fits the criteria discussed in the Fit Summary section.

After examining the summary statistics from the model fitting, you may choose to select different models for further study. For example, you could find that a subset of the cubic model provides the best fit to the data.

Stat-Ease uses the Fit Summary tables to calculate the Whitcomb Score (a heuristic scoring system) to select a default model. The Whitcomb Score has two components:

• Score1 = M ✕ L ✕ Pred R-squared

• Score2 = M ✕ L ✕ Adjusted R-squared

Where:

M is the Sequential Model Sum of Squares score:

• M = 1 if the p-value is less than or equal to 0.05

• M = 0.05/p-value if the p-value is greater than 0.05

• M = 0 if model is aliased

L is the Lack of Fit (LOF) score:

• L = 1 if the LOF p-value is greater than or equal to 0.10

• L = p-value/0.10 if the LOF p-value value is less than 0.10

The Predicted R-squared and Adjusted R-squared values are taken from the Fit Summary table.

The model(s) with the highest Score1 and Score2 are selected. In most cases, they will be the same model, in which case a single model will be recommended. If one model has the highest Score1 and a different model has the highest Score2, then both models will be “Suggested” and the experimenter must choose between them. The program will default to the higher-order model going forward in the analysis, although model selection may be beneficial.

If all the predicted R-squared values are negative, the Mean model will be suggested for an RSM or the Linear model for a mixture. If all model scores are less than or equal to zero, the program selects the mean model for an RSM or the Linear model for a mixture.