# st: -binreg-

 From Jay Kaufman To Stata Subject st: -binreg- Date Thu, 21 Nov 2002 13:28:10 -0500

```The -binreg- routine fits generalized linear models for the
binomial family.  It is presumably preferred over fitting the same
model in -glm-, not only for the convenience of not having to
specify the distributional family in the command line, but also
because in iteratively seeking the estimates it checks to make sure
that they are consistent with the range of allowable probabilities
(i.e. 0 to 1), as described on page 138 of the manual [Ref A-G].
So my question is, why does -binreg- appear to be so

Take a very simple model using the auto.dta.

. use "C:\Stata\auto.dta", clear
(1978 Automobile Data)

. binreg  foreign mpg, rr

Residual df  =        72                   No. of obs =        74
Pearson X2   =  73.88014                   Deviance   =  78.99933
Dispersion   =  1.026113                   Dispersion =  1.097213

----------------------------------------------------------------------
|                 EIM
foreign | Risk Ratio   Std. Err.    z    P>|z|    [95% Conf. Interval]
--------+-------------------------------------------------------------
mpg |   1.097213   .0109901   9.26   0.000    1.075883    1.118966
----------------------------------------------------------------------

. predict phat, mu

. sum phat

Variable |     Obs        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------
phat |      74    .3008965     .22691   .1072727   1.580984

Clearly a predicted probability > 1.5 is not a good estimate.  Did
I do something wrong?  Or did -binreg- do something wrong?  Or is
this simply another example of why linear models of the logit and
probit have dominated analysis of binary data for decades?

By the way, note that if I fit the exact same model using -glm-,
this same observation gets a predicted probability of 1.43, so
-binreg- actually seems to do worse.

--
Jay S. Kaufman, Ph.D
-----------------------------
email: Jay_Kaufman@unc.edu
-----------------------------
Department of Epidemiology
UNC School of Public Health
2104C McGavran-Greenberg Hall
Chapel Hill, NC 27599-7435
phone:  919-966-7435
fax:    919-966-2089
-----------------------------
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