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Date:   Thu, 26 Oct 2006 11:33:01 -0700
Reply-To:   Vadim Pliner <Vadim.Pliner@VERIZONWIRELESS.COM>
Sender:   "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:   Vadim Pliner <Vadim.Pliner@VERIZONWIRELESS.COM>
Subject:   Re: Stepwise Regression
Comments:   To:
In-Reply-To:   <uHS%g.9638$>
Content-Type:   text/plain; charset="iso-8859-1"

. Paige Miller wrote: > On 10/23/2006 6:00 PM, Vadim Pliner wrote: > > Michael, > > > > risking to be slaughtered on SAS-L, let me give you a scenario where I > > think stepwise regression could be used. > > 1. You are trying to predict something. > > 2. You have a lot of independent variables and the selection of > > variables presents a problem for you.

> Partial Least Squares is a better solution

a. What do you mean by "better"? Here is my definition of "better" in this context: if my objective is purely prediction and method X gives me closer fit to the actual values on validation data than method Y, then method X is better for me. b. I was not talking specifically about linear stepwise regression. AFAIK, Partial Least Squares is not applicable to the case when dependent variable is binary. I know there are alternatives to stepwise logistic regression for selecting variables that you might consider "better" as well, but see a. above.

> > 3. You have enough data points to split your data into a large enough > > training data set (where you build the model) and a large enough test > > or validation data set where you can select the best model.

> Partial Least Squares still is a better solution

See a. above again.

> > 4. You build a number of competing models, one of which is created with > > stepwise regression. > > This does nothing to eliminate the drawbacks of stepwise. Lots of data > does not eliminate the drawbacks of stepwise. Having a large tes tdata > set does not eliminate the drawbacks of stepwise. Creating additional > models does not eliminate the drawbacks of stepwise.

I agree, but what lots of data does is an opportunity to test which of the competing methods predicts best in practice on your specific data rather than in theory.

> > 5. If on the set aside test data set stepwise regression gives you the > > best predictions, select this model.

> So, you are saying that there are cases where, simply by random > chance, stepwise gives you better predictions, then this is a reason > to continue to use stepwise.

This is not exactly what I was saying. Yes, a couple of times in my experience stepwise logistic regression outperformed competing methods (3 or 4 neural networks and a decision tree). I doubt it was "by random chance", because the sample sizes were too big to believe in chance. I didn't say this was a reason to continue to use stepwise, I just gave a scenario where you could justify the use of stepwise regression, and this was, as far as I remember, the OP's question.

> > > > Do I think it's realistic to expect stepwise regression can produce the > > best model? Yes, it can. Would you prefer a model that is theoretically > > sound or the one that gives you better predictions? I'd prefer the > > latter if prediction were my sole goal.

> But you haven't shown that stepwise is a theoretically good way to get > better predictions (it is not), or that it is even a method that will > give you better predictions in a reasonable percentage of the cases. > > Frank and Friedman (Technometrics, 1992 I think) showed that in the > situations they studied OLS based methods (including stepwise) are the > worst thing to use when you have many variables -- worst meaning that > the MSE of the predictions, and the MSE of the coefficients are very > very large compared to the much smaller MSEs associated with Principal > Components Regression, Ridge Regression and oh yes Partial Least > Squares Regression.

I was NOT saying that "stepwise is a theoretically good way to get better predictions." On the contrary, I said that if you had two methods, say, X and Y, and Y is theoretically better (this is not stepwise, I admit) but X gives better predictions on validation data, I would select method X.

Vadim Pliner

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