# Assessing the effect of adding a variable using stepwise forward logistic regression using Stata?

I'd really appreciate help using Stata to perform a manual stepwise forward logistic regression.

I have 37 biologically plausible, statistically significant categorical variables linked to disease outcome. I need to end up with a final multivariable model.

I've added the first variable (most significant/most plausible) with corresponding OR output.

xi:logistic outcome i.variable1

. xi:logistic casecontrol i.breed_groupall
i.breed_group~l   _Ibreed_gro_0-7     (naturally coded; _Ibreed_gro_0 omitted)

Logistic regression                               Number of obs   =        995
LR chi2(6)      =      83.87
Prob > chi2     =     0.0000
Log likelihood = -422.36813                       Pseudo R2       =     0.0903

------------------------------------------------------------------------------
casecontrol | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ibreed_gr~2 |   1.757143   .6861797     1.44   0.149      .817345    3.777537
_Ibreed_gr~3 |   1.952381   .8811439     1.48   0.138     .8061249    4.728537
_Ibreed_gr~4 |   1.464286    .530121     1.05   0.292     .7202148    2.977074
_Ibreed_gr~5 |   6.192708   1.779109     6.35   0.000     3.526453    10.87485
_Ibreed_gr~6 |   3.880357   1.103611     4.77   0.000     2.222193    6.775816
_Ibreed_gr~7 |    .636646   .2555236    -1.13   0.261     .2899083    1.398091
------------------------------------------------------------------------------


What do I look for to see if adding the second variable I choose means that both variables should stay in, when, for example I type;

xi:logistic outcome i.variable1 i.variable2

. xi:logistic casecontrol i.breed_groupall i.height_category
i.breed_group~l   _Ibreed_gro_0-7     (naturally coded; _Ibreed_gro_0 omitted)
i.height_cate~y   _Iheight_ca_0-4     (naturally coded; _Iheight_ca_0 omitted)

Logistic regression                               Number of obs   =        992
LR chi2(10)     =     132.25
Prob > chi2     =     0.0000
Log likelihood = -396.05629                       Pseudo R2       =     0.1431

------------------------------------------------------------------------------
casecontrol | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ibreed_gr~2 |   1.002262   .4145417     0.01   0.996     .4455736    2.254465
_Ibreed_gr~3 |   1.185087    .557553     0.36   0.718     .4712828    2.980017
_Ibreed_gr~4 |   1.774162   .6616502     1.54   0.124     .8541793    3.685001
_Ibreed_gr~5 |   1.452416    .541494     1.00   0.317     .6994292     3.01605
_Ibreed_gr~6 |   1.256098   .4377793     0.65   0.513     .6343958    2.487064
_Ibreed_gr~7 |   .4238999   .1777699    -2.05   0.041     .1863361    .9643388
_Iheight_c~1 |   2.780857    .918967     3.09   0.002     1.455088    5.314572
_Iheight_c~2 |   5.402833   2.246817     4.06   0.000     2.391342    12.20679
_Iheight_c~3 |   13.50715   5.989787     5.87   0.000     5.663642    32.21303
_Iheight_c~4 |   16.85605   8.674745     5.49   0.000     6.147467    46.21846
------------------------------------------------------------------------------


How do I know if I want to keep one, or both of these variables, or that one, or both of them is no use to me?

If for example, I want to keep both of these and add the 3rd variable, how do I know which?

. xi:logistic casecontrol i.height_category i.breed_groupall i.combinedweight

i.height_cate~y   _Iheight_ca_0-4     (naturally coded; _Iheight_ca_0 omitted)
i.breed_group~l   _Ibreed_gro_0-7     (naturally coded; _Ibreed_gro_0 omitted)
i.combinedwei~t   _Icombinedw_0-5     (naturally coded; _Icombinedw_0 omitted)

Logistic regression                               Number of obs   =        891
LR chi2(14)     =     123.58
Prob > chi2     =     0.0000
Log likelihood = -346.82026                       Pseudo R2       =     0.1512

------------------------------------------------------------------------------
casecontrol | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Iheight_c~1 |   3.397418   1.235922     3.36   0.001     1.665316    6.931087
_Iheight_c~2 |   6.321891   3.119652     3.74   0.000     2.403289    16.62983
_Iheight_c~3 |   14.36312   7.797083     4.91   0.000     4.956448    41.62242
_Iheight_c~4 |   23.39157   15.34571     4.81   0.000      6.46607    84.62101
_Ibreed_gr~2 |   .7339708   .3482777    -0.65   0.515     .2895834    1.860303
_Ibreed_gr~3 |   1.060443   .5318773     0.12   0.907      .396787    2.834113
_Ibreed_gr~4 |   1.644423   .6502556     1.26   0.208      .757569    3.569479
_Ibreed_gr~5 |   1.246412   .4940969     0.56   0.578     .5731024     2.71076
_Ibreed_gr~6 |   1.262449   .4661338     0.63   0.528     .6122442    2.603172
_Ibreed_gr~7 |    .401331   .1782529    -2.06   0.040     .1680497    .9584456
_Icombined~1 |    1.21903   .7160999     0.34   0.736     .3854692    3.855132
_Icombined~2 |   1.238685   .3967314     0.67   0.504     .6612025    2.320531
_Icombined~4 |   1.764532   .5970935     1.68   0.093     .9090641    3.425031
_Icombined~5 |   2.107871   1.118772     1.40   0.160     .7448366    5.965227
------------------------------------------------------------------------------


Any help would be gratefully received.

(I am using STATA v9.1 I believe.)

-
You might find some useful pointers in the related thread at stats.stackexchange.com/questions/14500/…. –  whuber Sep 14 '11 at 18:49
What is the reason for the missing data? This could play an important role; it certainly affects how to interpret the statistical output. –  whuber Sep 15 '11 at 6:14
As noted in the answers below, stepwise variable selection, either automatic or manual, is an invalid strategy. If this doesn't make sense, it may be helpful to read my answer here: algorithms-for-automatic-model-selection. –  gung Nov 25 '12 at 17:35

I am assuming you know that the stepwise regression is a wrong approach (see Frank Harrell's terrific book, or just wait for his comments in this thread), and you are ready to face the criticism of the reviewers (or your dissertation committee, depending on your career stage). I am thus treating this as a programming exercise, rather than a rigorous methodological investigation.

Stata stepwise command does not support factor variables, as you have probably discovered already, so you'd have to rewrite its main functionality, at least at a descriptive level. I will make use of Ben Jann's estadd command published in Stata Journal.

    net sj 7-2 st0085_1
net install st0085_1
webuse nlswork, clear
foreach catvar of varlist race grade ind_code occ_code {
regress ln_wage age i.catvar'
levelsof catvar', local( thelevels )
tokenize thelevels'
local dotcat
while "1'"!="" {
local dotcat dotcat' 1'.catvar'
macro shift
}
test dotcat'
estimates store with_catvar'
}
estimates tab with_* , stats( pnew )
`

The last line gives you the answers (not terribly informative in this case, of course, as the sample sizes are quite a bit larger than yours).

Feel free to ask about specific commands in this code fragment. Of course, you'd modify this for your own data and estimation command of your liking. The above code assumes Stata 11 and factor variables; you have not stated what version of Stata you are using, which would've helped.

-
Stepwise algorithms are indeed lousy for revealing the best variables that can explain an outcome. But they can be quite useful if all one wants is to know are some good, not-too-correlated predictors of an outcome. –  rolando2 Sep 14 '11 at 19:48

As someone has already covered the programming aspects of the problem, I would urge you - and your supervisors - to consider an alternative variable selection tactic. A discussion of the failings of stepwise regression and other automated, "cookbook" systems can be found here:

http://aje.oxfordjournals.org/content/167/5/523.abstract

and

http://ajph.aphapublications.org/cgi/reprint/79/3/340

Stepwise selection is no longer a well-supported method of variable selection. Depending on where you'd like to publish your results, it will be a substantial burden to get past reviewers, especially if you'd like to head toward the epidemiological literature. 37 variables is also not a daunting enough task to necessitate an automated stepwise method simply because of the sheer number of variables.

-
Thank you for the response. I don't think stepwise logistic regression is wrong? I've been told to do that by my supervisors, and it is the only approach I've been taught in my statistics training. I'm doing it manually, rather than expecting the model to do it all. I've never come across another approach to build a multivariable logistic regression model based on categorical variables with a binary outcome - but please advise me what you think is correct? So my question, was how to assess each stage of manually adding the next most significant variable. –  user6316 Sep 14 '11 at 22:09
Epi--I'm a little daunted by the prospect of manually selecting among the $2^{37}$ = $137438953472$ choices. That would take a few days... –  whuber Sep 15 '11 at 6:05
@whuber There are ways to go about selecting regression variables without resorting to brute force combinations. Gathering more conceptual evidence using say, Directed Acyclic Graphs and the like. The articles linked above have alternate suggestions for model selection. If people analyzing data from massive population surveys, or insurance databases can manage without resorting to automated algorithms, so can the rest of us :) –  EpiGrad Sep 15 '11 at 6:42
My point is that those "ways" all involve a lot of automation (and assumptions), because they are selecting among those billions of choices, whether explicitly or not. The criticism of stepwise regression is not that it's automated, but that it frequently fails altogether to find a good set of variables and can even fail to select the best set of variables that it actually encounters during the process. –  whuber Sep 15 '11 at 16:25
@whuber Not necessarily, unless we are going so far as to call a group of colleagues, a white board and a marker "automation" (which is typically what I start with for variable selection via Directed Acyclic Graph analysis). The criticism is two-fold, one that it is particularly bad at selecting the right set, and the other is that the researcher should never simply abdicate the process to software. –  EpiGrad Sep 15 '11 at 21:22
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