# (Automated) feature selection in multiple regression with categorical variables

I need a general guide on what are the appropriate approaches to automated feature selection in multiple regression with categorical variables.

In my case, I have several numeric and categorical independent variables. I want to predict a numeric value and I am going to make use of multiple regression, including these categorical variables according to the effect coding strategy (find effect coding ref. here).

My questions are:

• I am familiar with stepwise feature selection methods that I used in logistic regression models. Are they likely to be successful in this case, too?

• When is there a moment to apply such automated feature selection methods? I mean: if I run them after introducing effect-transformed variables, there is a possibility the method reject e.g. a part of effect-transformed variables, drawn from one categorical variable (this categorical variable is not fully represented then), isn't it? Is this a problem?

• What are the most popular automated feature selection methods when dealing with categorical variables?

If you absolutely do need to incorporate feature selection, choose a method that keeps together multiple parameters describing one predictor, such as $F$ tests with multiple numerator degrees of freedom or other simple translations of partial sums of squares.
• Feature selection has nothing to do with solving that problem. It is a mirage. You are actually "spending degrees of freedom" to do variable selection, and the large amount of resulting model uncertain undoes apparent advantages of variable selection. Think about it this way: I know of only 2 unbiased estimates of $\sigma^2$ in ordinary linear models. One involves the number of parameters in a pre-specified model and the other involves estimating the effective number of parameters upon data mining. This effective number is closer to the number of original candidates than # significant. – Frank Harrell Sep 29 '14 at 12:28