East Carolina University
Department of Psychology
Stepwise Regression
= 

It is pretty cool, but not necessarily very useful, and just plain dangerous in the hands of somebody not well educated in the multiple regression techniques, including effects of collinearity, redundancy, and suppression. Here are some quotes from others I have collected from the now departed STATL.
Derksen, S. and H. J. Keselman. 1992. Backward, forward and stepwise automated subset selection algorithms: Frequency of obtaining authentic and noise variables. British Journal of Mathematical and Statistical Psychology, 45: 265282.
Date: Fri, 5 Mar 1993
18:26:18 GMT
Sender: STATISTICAL CONSULTING
<STATL@MCGILL1.BITNET>
From: Steve Blinkhorn <steve@PRD.CO.UK>
Subject: Re: Stepwise Procedure....
A brief abstract of the BJMSP article I referred to in my
earlier posting has been requested, so here is the abstract from the paper, plus
odd extracts from elsewhere:
The use of automated subset search algorithms is reviewed and
issues concerning model selection and selection criteria are discussed.
In addition, a Monte Carlo study is reported which presents data regarding the
frequency with which authentic and noise variables are selected by automated
subset algorithms. In particular, the effects of the correlation
between predictor variables, the number of candidate predictor variables, the
size of the sample, and the level of significance for entry and deletion of
variables were studied for
three automated subset selection algorithms: BACKWARD ELIMINATION, FORWARD
SELECTION and STEPWISE. Results indicated that:
Conclusions (mine, not theirs):
======================Frank Harrell Jr, 19 Feb 1996======ssc
Frank E Harrell Jr feh@biostat.mc.duke.edu
Associate Professor of Biostatistics
Division of Biometry Duke University Medical Center

Subject: Reasons not to do stepwise (or all possible regressions)
Here are SOME of the problems with stepwise variable selection.
1. It yields Rsquared values that are badly biased high
2. The F and chisquared tests quoted next to each variable on the printout do
not have the claimed distribution
3. The method yields confidence intervals for effects and predicted values that
are falsely narrow (See Altman and Anderson Stat in Med)
4. It yields Pvalues that do not have the proper meaning and the proper
correction for them is a very difficult problem
5. It gives biased regression coefficients that need shrinkage (the coefficients
for remaining variables are too large; see Tibshirani, 1996).
6. It has severe problems in the presence of collinearity
7. It is based on methods (e.g. F tests for nested models) that were intended to
be used to test prespecified hypotheses.
8. Increasing the sample size doesn't help very much (see Derksen and Keselman)
9. It allows us to not think about the problem
10. It uses a lot of paper
Note that 'all possible subsets' regression does not solve any of these
problems.
References

author = "Altman, D. G. and Andersen, P. K.", journal = "Statistics in
Medicine", pages = "771783", title = "Bootstrap investigation of
the stability of a {C}ox regression model", volume = "8", year
= "1989"
Shows that stepwise methods yields confidence limits that are far too narrow.
author = {Derksen, S. and Keselman, H. J.}, journal = {British Journal of
Mathematical and Statistical Psychology},
pages = {265282},
title = {Backward, forward and stepwise automated subset selection algorithms: {F}requency
of obtaining authentic and noise variables}, volume = {45}, year =
{1992},
author = {Roecker, Ellen B.}, journal = {Technometrics}, pages =
{459468}, title = {Prediction error and its estimation for
subsetselected models}, volume = {33}, year = {1991}
Shows that allpossible regression can yield models that are "too small".
author = {Mantel, Nathan}, journal = {Technometrics}, pages = {621625}, title = {Why stepdown procedures in variable selection}, volume = {12},year = {1970},
author = "Hurvich, C. M. and Tsai, C. L.", journal = American Statistician, pages = "214217", title = "The impact of model selection on inference in linear regression", volume = "44", year = "1990"
author = {Copas, J. B.}, journal = "Journal of the Royal Statistical Society B", pages = {311354}, title = {Regression, prediction and shrinkage (with discussion)}, volume = {45}, year = {1983},
Shows why the number of CANDIDATE variables and not the number in the final model is the number of d.f. to consider.
author = {Tibshirani, Robert}, journal = "Journal of the Royal Statistical Society B", pages = {267288}, title = {Regression shrinkage and selection via the lasso}, volume = {58}, year = {1996},
==========================Ira Bernstein, 29 Apr 1996==========
From: "IRA H BERNSTEIN" <BERNSTEI@albert.uta.edu>
Subject: Re: When should Stepwise reg be used?
I think that there are two distinct questions here: (a) _when_ is stepwise
selection appropriate and (b) _why_ is it so popular.
I would probably only argue slightly with "never" as an answer to the use of
stepwise selection since I don't know what knowledge we would lose if all papers
using stepwise regression were to vanish from journals at the same time programs
providing their use were to become terminally virusladen. However, I have been
in situations that looked like "I have good reason to look at variables A, B,
and C;
then look at D, and E, but I have no basis to favor F over G or vice versa past
that point." Older versions of SPSS (I haven't used newer versions since
switching to SAS a decade ago) allowed this mixture, and I would personally not
object to it as long as the strategy were defined in advance and made clear to
readers.
As to part (b), I think that there are two groups that are inclined to favor its
usage. One consists of individuals with little formal training in data analysis
who confuse knowledge of data analysis with knowledge of the syntax of SAS,
SPSS, etc. They seem to figure that "if its there in a program, its gotta be
good and better than actually thinking about what my data might look like". They
are fairly easy to spot and to condemn in a rightthinking group of welltrained
data analysts (like ourselves). However, there is also a second group who are
often well trained (and may be here in this group ready to flame me). They
believe in statistics uber allesgiven any properly obtained data base, a
suitable computer
program can objectively make substantive inferences without active consideration
of the underlying hypotheses. If stepwise selection is the parent of this line
blind data analysis, then automatic variable respecification in confirmatory
factor analysis is the child.
==========================Kent Campbell, 30 Apr 1996=========
From: campbell@acs.ryerson.ca (Kent Campbell)
Subject: Re: When should Stepwise reg be used?
try generating some random data sets and then analyzing them with stepwise
regression. It is quite likely that you will discover all sorts of "significant"
relationships. I have done this in a controlled manner and found that the type 1
error (using the default settings in spss) is much higher than 5%. So one reason
why stepwise is so popular is that it produces statistically significant results
when fed garbage.
Best wishes,
Kent.
============================Carl Huberty, 13 Feb 1996=========
From: carl huberty <CHUBERTY@UGA.CC.UGA.EDU>
Subject: Re: When are stepwise and backward regression methods appropriate?
About the only time stepwise methods are remotely appropriate is when you have a
large number of variables and you want to do some "pre screening" of the
variable set  and you would need a "large" N/p ratio to do such an analysis
then. There are MUCH better ways to assess variable ordering and to determine
good variable subsets. DOWN WITH STEPWISE!!
Carl
===========================Ronay M Conroy 7/5/96============
MessageID: <v02120d02adb60ca879df@[193.1.229.68]>
From: rconroy@rcsi.ie (Ronan M Conroy)
Subject: Re: When should Stepwise reg be used?
I am struck by the fact that Judd and McClelland in their excellent book "Data
Analysis: A Model Comparison Approach" (Harcourt Brace Jovanovich, ISBN
0155167650) devote less than 2 pages to stepwise methods. What they do say,
however, is worth repeating:
1. Stepwise methods will not necessarily produce the best model if there
are redundant predictors (common problem).
2. Allpossiblesubset methods produce the best model for each possible number
of terms, but larger models need not necessarily be subsets of smaller ones,
causing serious conceptual problems about the underlying logic of the
investigation.
3. Models identified by stepwise methods have an inflated risk of capitalising
on on chance features of the data. They frequently fail when
applied to new datasets. They are rarely tested in this way.
4. Since the interpretation of coefficients in a model depends on the other
terms included, "it seems unwise," to quote J and McC, "to let an automatic
algorithm determine the questions we do and do not ask about our data". RC adds
that stepwise methods abusers frequently would rather not think about their
data, for reasons that are funny to describe over a second Guinness.
5. I quote this last point directly, as it is sane and succinct:
"It is our experience and strong belief that better models and a better
understanding of one's data result from focused data analysis, guided by
substantive theory." (p 204)
They end with a quote from Henderson and Velleman's paper "Building multiple
regression models interactively". Biometrics 1981;37:391411
"The data analyst knows more than the computer"
and add "failure to use that knowledge produces inadequate data analysis."
Personally, I would no more let an automatic routine select my model than I
would let some bestfit procedure pack my suitcase.
Links
Stopping Stepwise: Why Stepwise and Similar Selection Methods are Bad, and What You Should Use
Why do we still use stepwise modelling in ecology and behaviour?
About a Million Other Hits when searching Google for "Problems with stepwise regression."
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Dr. Karl L. Wuensch
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