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I am currently building my model and I have chosen to use a step-wise backwards elimination method. I have many categorical variables and am using the "CLASS" statement in SAS within my regression model. How do I determine if a categorical variable should stay in? Is it based on the TYPE III Analysis of Effects p-value? or is it based on the P for trend value?

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Step-wise model selection methods are not recommended for either continuous or categorical variables. To understand why, you may find it helpful to read my answer here: algorithms-for-automatic-model-selection. – gung Dec 14 '12 at 21:46
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You can use penalized methods such as LASSO or LAR by using PROC GLMSELECT – Peter Flom Dec 14 '12 at 22:18
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See also my answer as to why to abandon stepwise approaches to model building here. – Alexis Feb 13 '15 at 16:11

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