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# st: RE: Testing equality of coefficients in different logistic models

 From "Feiveson, Alan H. \(JSC-SK311\)" To Subject st: RE: Testing equality of coefficients in different logistic models Date Wed, 13 Sep 2006 11:50:32 -0500

```For the two binary responses, if you would settle for a probit link
function then Stata's bivariate probit command -biprobit- should give
you what you need to make the comparison, allowing for dependence
between mstair_1 and mstair2.

. biprobit h1 h2 = x5

Bivariate probit regression                       Number of obs   =
15
Wald chi2(2)    =
1.75
Log likelihood = -16.681705                       Prob > chi2     =
0.4170

------------------------------------------------------------------------
------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
h1           |
x5 |   .0459239   .0417967     1.10   0.272    -.0359961
.1278439
_cons |  -1.271098   1.134072    -1.12   0.262    -3.493839
.9516428
-------------+----------------------------------------------------------
------
h2           |
x5 |  -.0239751   .0509927    -0.47   0.638    -.1239191
.0759688
_cons |   -.241399   1.313751    -0.18   0.854    -2.816303
2.333505
-------------+----------------------------------------------------------
------
/athrho |   .5238399   .5659559     0.93   0.355    -.5854134
1.633093
-------------+----------------------------------------------------------
------
rho |   .4806582   .4352019                     -.5265889
.9265008
------------------------------------------------------------------------
------
Likelihood-ratio test of rho=0:     chi2(1) =  .984849    Prob > chi2 =
0.3210

. test [h1]x5=[h2]x5

( 1)  [h1]x5 - [h2]x5 = 0

chi2(  1) =    1.44
Prob > chi2 =    0.2298

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Sara Mottram
Sent: Wednesday, September 13, 2006 10:38 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Testing equality of coefficients in different logistic
models

I have an ordinal response with three levels and I am hoping eventually
to fit an ordinal regression model, possible a partial proportional odds
model using -gologit2-. However, to explore my data and get an idea of
where I may and may not have proportionality of odds, I have created two
dichotomies and would like to fit two binary logistic regression models,
testing for the equality of the slope coefficients, much as the
-autofit- option does in -gologit2-.
i.e. in the output below, is 1.86 equal to 1.96?

. logistic mstair_1 edu
------------------------------------------------------------------------
------
mstair_1 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
-------------+------
edu |   1.861951   .0870595    13.29   0.000     1.698903
2.040648
------------------------------------------------------------------------
------

. logistic mstair_2 edu
------------------------------------------------------------------------
------
mstair_2 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
-------------+------
edu |   1.960462   .1124576    11.74   0.000     1.751988
2.193743
------------------------------------------------------------------------
------

I suspect that there is an Stata command to carry out this test, but I
have been unable to find it, either in the manuals or in the FAQ. From
the manual, I get the impression that the Wald test performed by -test-
can compare coefficients within the same model or compare all of the
coefficients in two models?

I would also value opinions on whether there is any value in performing
two binary regressions, given that -gologit2- has an automatic fitting
procedure in -autofit-. (I am basing my analysis plan on a fairly out of
date paper, which suggests that binary regressions are the only way to
choose where non-proportionality is needed as there were no programs
able to do this at the time).

Best wishes
Sara

--
Sara Mottram
Research Assistant: Biostatistics
Primary Care Musculoskeletal Research Centre Primary Care Sciences Keele
University Staffordshire, ST5 5BG
Tel:  01782 584711
Fax:  01782 583911

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```

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