Re: Minitab 15 - Best quadratic subset for analyzing a response surface design
Hello weisse,
welcome to the Cove
There are many selection criterions or criterions for model comparison. R^2 is a very popular one, but it has three disadvantages:
- The more complex a models is, the higher R^2 gets, independent of the quality of the model. You can increase R^2 by adding terms, even if they are not significant and don't have any impact on the response.
- R^2-based model selection comes with a high risk of overfitting (adding terms without improving the amount of information from a model).
- Models with different numbers of terms shouldn't be compared using R^2, because R^2 doesn't reflect the information quality of a model but the fit quality.
One method to find the best model (=explains most based on the smallest number of terms) is a
stepwise_regression. To check whether a model is better compared to another model, an information criterion can be used (e.g. AIC:
Akaike_Information_Criterion).
Information criterions do reflect the information quality of a model, but the disadvantage is that they aren't limited to a specific range of values. R^2 could fall between 0 and 100%, whereas the information criterions are only numbers and could be (the smaller the number, the higher the information quality).
Minitab provides a stepwise regression only for linear effects (main effects in a DoE): Stat > Regression > Stepwise
This is done via the F-test with specified alpha values to add or remove a term.
AFAIK there exist no Minitab macro which supports model selection for a response surface model (linear, interaction, quadratic terms). Hopefully it will be included in the next release (R17), but this is just one out of several points on my wish list and I don't know if Minitab found that relevant, too.
Other software packages do provide these methods, e.g.
R (function step),
DesignExpert and
JMP.
Hope this helps
Barbara