Generalized regression does not work with random effects like whole plot factors so, as random noise cannnot be removed, guess genreg can't be used to model split plot DOE results ?
I suggest you read:
Box, G.E.P., Stephen Jones (1992), “Split-plot designs for robust product experimentation”, Journal of Applied Statistics, Vol. 19, No. 1
I don't find a free version of this paper. JMP GENREG in 1992??
Hi @frankderuyck,
You can fit Generalized Regression models with random effects by choosing the Generalized Linear Mixed Model personality when launching the Fit Model platform (JMP Pro):
Hope this quick and practical answer will help you,
I know this Victor but it does not have this great Forward selection Aicc/penalize options like GENREG. Is there anywhere an "All Subsets" option available to get the best model?
Maybe start with GENREG without whole plot factor and select the stong effects using "Best Subset" then return to Fit Mixed with the strong effects + random whole plot?
No this option is not available, and is not recommended in DOE scenarii. The "All Subsets" option is more a data-mining, model-agnostic way of building models. If you remove the whole plot factor to use the GenReg platform, you'll lose the advantage of having a random effect, capturing the variance you are not interested in. Without the random effect, this variance will be considered as random, and may "hide" potentially active effects.
When building the DoE, you have assumed a model. Fit this model with the random effect(s) through the Generalized Linear Mixed Model, and evaluate the relevance and correctness of this model (residual analysis, model's metrics, etc...). You can then start to relaunch the model by removing some higher order terms (but still respecting effect heredity), and compare the different models you have : factors influences on the response(s), models metrics, residual analysis...
Or even better - as with whole plot random effect, factor levels can get correlated - start with genreg elastic net to select strongest effect first?
Thanks for interesting reply Victor, you have a point, without the random whole plot effect there will be significant noise however strong effects will peak more out of the noise. In the "best subset" result you shoud not be too severe on P-values, think a threshold of 0,1 is ok for selecting factors with stongest effect.
