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Re: st: multinomial logistic regression: adjacent logits


From   rgates@stata.com (Richard Gates)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: multinomial logistic regression: adjacent logits
Date   Thu, 29 Sep 2005 16:56:20 -0500

Yi-fu <yifuc@uga.edu> made the following query about adjacent logits:

>I want to run a four-category multinomial logistic model and I find the 
>comparison will be more interesting for me if I use adjacent logits.
>Does anyone know how to do multinomial logistic regression with adjacent 
>logits?
 

Constantine <C_Daskalakis@mail.jci.tju.edu> replied with the following:

> In an older version of Stata I did this through -mlogit- and using 
> -constraint- for the constraints b_j = (J-j)*b. I think this is still what 
> you need to do.
> 
> Example: Y is the outcome (let's say it takes on values 0, 1, and 2) and X 
> and Z are predictors.
> 
> . constraint define 1 [2]x =2*[1]x
> 
> . constraint define 2 [2]z =2*[1]z
> 
> . mlogit y x z, basecategory(0) constraint(1 2)
 
In Stata 9 we now have -slogit- for fitting just such a model.  For example

. webuse sysdsn3
(Health insurance data)

. slogit insure age male nonwhite site2 site3, dim(1) base(1) nolog

Stereotype logistic regression                    Number of obs   =        615
                                                  Wald chi2(5)    =      28.20
Log likelihood = -539.75205                       Prob > chi2     =     0.0000

 ( 1)  [phi1_2]_cons = 1
------------------------------------------------------------------------------
      insure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0108366   .0061918     1.75   0.080    -.0012992    .0229723
        male |  -.5032537   .2078171    -2.42   0.015    -.9105678   -.0959396
    nonwhite |  -.9480351   .2340604    -4.05   0.000    -1.406785    -.489285
       site2 |  -.2444316   .2246366    -1.09   0.277    -.6847113    .1958481
       site3 |    .556665   .2243799     2.48   0.013     .1168886    .9964415
-------------+----------------------------------------------------------------
     /phi1_1 |          0  (base outcome)
     /phi1_2 |          1          .        .       .            .           .
     /phi1_3 |   .0383539   .4079705     0.09   0.925    -.7612535    .8379613
-------------+----------------------------------------------------------------
     /theta1 |          0  (base outcome)
     /theta2 |    .187542   .3303847     0.57   0.570    -.4600001     .835084
     /theta3 |  -1.860134   .2158898    -8.62   0.000     -2.28327   -1.436997
------------------------------------------------------------------------------
(insure=Indemnity is the base outcome)

The phi's are the constant multipliers for the regression coefficients and
the theta's are the constants.  Here instead of fixing the mulitiplier to
2 we add it to the model as a parameter to be estimated. 

I believe this is what Yu-fu is looking for.

-Rich
rgates@stata.com
  
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