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Re: st: Testing equality of odds ratios outside of logistic regression
From
Michael Norman Mitchell <[email protected]>
To
[email protected]
Subject
Re: st: Testing equality of odds ratios outside of logistic regression
Date
Sun, 09 May 2010 17:13:07 -0700
Dear Michael
I think the comment that you received is a good one. It is very
likely that your conclusions are correct, but they will be more
substantiated by including a direct test of the coefficients.
Fortunately, Stata is very good at this using the -suest- command. Here
is an example based on the -auto- dataset, where the question is asked
"Is the coefficient for -smtrunk- (small trunk size)" the same as the
coefficient for -smprice- (small price of car". The models are estimated
separately, and -estimates store- is used to store the results of each.
Then, -suest- is used to estimate the models together, and then -test-
to compare the coefficients in the two models.
I hope this is helpful,
Best regards,
Michael N. Mitchell
See the Stata tidbit of the week at...
http://www.MichaelNormanMitchell.com
---snip---
* make fake data
. sysuse auto, clear
(1978 Automobile Data)
. gen himpg = mpg > 20
. gen smtrunk = trunk < 14
. gen smprice = price < 5000
.
. * run model 1, predicing himpg from smtrunk
. logit himpg smtrunk
Iteration 0: log likelihood = -51.265861
Iteration 1: log likelihood = -35.88057
Iteration 2: log likelihood = -35.860081
Iteration 3: log likelihood = -35.860072
Iteration 4: log likelihood = -35.860072
Logistic regression Number of obs
= 74
LR chi2(1)
= 30.81
Prob > chi2 =
0.0000
Log likelihood = -35.860072 Pseudo R2 =
0.3005
------------------------------------------------------------------------------
himpg | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
smtrunk | 2.926739 .598858 4.89 0.000 1.752999
4.10048
_cons | -1.386294 .3952847 -3.51 0.000 -2.161038
-.6115506
------------------------------------------------------------------------------
. estimates store m1
.
. * run model 2, predicting himpg from smprice
. logit himpg smprice
Iteration 0: log likelihood = -51.265861
Iteration 1: log likelihood = -48.528905
Iteration 2: log likelihood = -48.527122
Iteration 3: log likelihood = -48.527122
Logistic regression Number of obs
= 74
LR chi2(1)
= 5.48
Prob > chi2 =
0.0193
Log likelihood = -48.527122 Pseudo R2 =
0.0534
------------------------------------------------------------------------------
himpg | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
smprice | 1.109541 .4832148 2.30 0.022 .1624577
2.056625
_cons | -.6131045 .3443686 -1.78 0.075 -1.288055
.0618456
------------------------------------------------------------------------------
. estimates store m2
.
. * estimate the two models together
. suest m1 m2
Simultaneous results for m1, m2
Number of obs
= 74
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
m1_himpg |
smtrunk | 2.926739 .6029459 4.85 0.000 1.744987
4.108492
_cons | -1.386294 .3979829 -3.48 0.000 -2.166327
-.6062622
-------------+----------------------------------------------------------------
m2_himpg |
smprice | 1.109541 .4865133 2.28 0.023 .1559929
2.06309
_cons | -.6131045 .3467193 -1.77 0.077 -1.292662
.0664528
------------------------------------------------------------------------------
.
. * Is the coefficient for "smtrunk" equal to "smprice"
. test [m1_himpg]smtrunk = [m2_himpg]smprice
( 1) [m1_himpg]smtrunk - [m2_himpg]smprice = 0
chi2( 1) = 7.68
Prob > chi2 = 0.0056
On 2010-05-09 4.49 PM, Michael I. Lichter wrote:
I'm assisting on a paper where we examine the relationship between
each of four dichotomous predictors variables and one dichotomous
outcome variable. Prediction is our primary objective. The predictors
are all measures of more or less the same thing, and we want to know
whether, *without controlling for any of the others*, they predict the
outcome equally well. We want to be able to say, "If you could only
pick one of these variables as a predictor of the outcome, it wouldn't
make any difference which one you selected."
For each of the predictors we calculate a odds ratio and a
corresponding confidence interval. The odds ratios are very similar in
magnitude and have confidence intervals that overlap almost entirely.
We did not do any formal tests, not knowing of any offhand, and,
because this isn't a central point, we didn't think it was very
important. When we reported that the odds ratios were essentially
equal, a reviewer objected that we had not tested for equality. Any
suggestions?
In logistic regression, by the way, two of the four variables emerged
as significant predictors and two did not, controlling for the others.
That is of interest, but it doesn't answer my initial question. At
least, I don't think it does.
*
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*
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