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# Re: Re-re-post: Stata 11 - Factor variables in a regression command

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: Re-re-post: Stata 11 - Factor variables in a regression command Date Sat, 01 May 2010 10:50:25 -0500

```At 01:42 AM 5/1/2010, Michael Norman Mitchell wrote:
```
```Dear Ricardo

The command

. logistic y a#b

```
includes just the interaction of "a by b", and does not include the main effect of a, nor the main effect of b. By contrast, the command
```
. logistic y a##b

```
includes the main effect of a, the main effect of b, as well as the a by b interaction. It is equivalent to typing
```
. logistic y a#b a b
```
```
```
I don't think this is quite right. As the original example shows, the fits produced by the first two syntaxes are identical. So, a#b and a##b are different ways of parameterizing the models. a##b gives you the main effect of a, the main effect of b, and the interaction, i.e. it is the same as entering a, b, and a*b in the model. a*b = 1 if a and b both equal 1, 0 otherwise. I believe this is equivalent to your 3rd syntax, except I would say i.a and i.b so Stata knows these are categorical variables.
```
```
With a#b, there are four possible combinations of values: 0 0, 0 1, 1 0, and 1 1. The first gets dropped and the other three are in the model.
```
```
These are two parameterizations of the same model; personally I prefer the a##b approach because it separates main effects from interaction effects.
```
```
The following example illustrates the 3 different approaches, and shows the equivalence of the last 2 approaches in Michael's example:
```
. use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
(77 & 89 General Social Survey)

. logit  warmlt2 yr89#male, nolog

Logistic regression                               Number of obs   =       2293
LR chi2(3)      =      64.74
Prob > chi2     =     0.0000
Log likelihood = -851.54241                       Pseudo R2       =     0.0366

------------------------------------------------------------------------------
warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89#male |
0 1  |   .1816812   .1431068     1.27   0.204     -.098803    .4621655
1 0  |  -1.295833    .229115    -5.66   0.000     -1.74489   -.8467762
1 1  |   -.659902   .2022755    -3.26   0.001    -1.056355   -.2634493
|
_cons |  -1.667376   .1021154   -16.33   0.000    -1.867518   -1.467233
------------------------------------------------------------------------------

. logit  warmlt2 yr89##male, nolog

Logistic regression                               Number of obs   =       2293
LR chi2(3)      =      64.74
Prob > chi2     =     0.0000
Log likelihood = -851.54241                       Pseudo R2       =     0.0366

------------------------------------------------------------------------------
warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.yr89 |  -1.295833    .229115    -5.66   0.000     -1.74489   -.8467762
1.male |   .1816812   .1431068     1.27   0.204     -.098803    .4621655
|
yr89#male |
1 1  |   .4542502   .3050139     1.49   0.136    -.1435661    1.052066
|
_cons |  -1.667376   .1021154   -16.33   0.000    -1.867518   -1.467233
------------------------------------------------------------------------------

. logit  warmlt2 i.yr89 i.male yr89#male, nolog

Logistic regression                               Number of obs   =       2293
LR chi2(3)      =      64.74
Prob > chi2     =     0.0000
Log likelihood = -851.54241                       Pseudo R2       =     0.0366

------------------------------------------------------------------------------
warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.yr89 |  -1.295833    .229115    -5.66   0.000     -1.74489   -.8467762
1.male |   .1816812   .1431068     1.27   0.204     -.098803    .4621655
|
yr89#male |
1 1  |   .4542502   .3050139     1.49   0.136    -.1435661    1.052066
|
_cons |  -1.667376   .1021154   -16.33   0.000    -1.867518   -1.467233
------------------------------------------------------------------------------

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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```