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Re: st: Brant's Test for Parallel Lines


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Brant's Test for Parallel Lines
Date   Fri, 14 Oct 2011 17:03:42 -0400

At 04:36 PM 10/14/2011, Stephen Clark wrote:
Hello,

I have an ordered logit model that uses a large amount of data, 2.5 million
cases. Brant's test for parallel lines is significant (p>chi2 = 0.00) which
suggest that the model I am using is inappropriate. However, I have found
various references that suggest the test is pessimistic with very large
samples - highlighting small differences that are not actually critical. I
cannot get access to Brant original paper so I would welcome some advice as
to whether this is likely to be the case here. Is there a better test
available for large samples?

Probably the same can be said of most statistical tests -- if you have 2.5 million cases, even substantively trivial deviations from the null will be statistically significant.

You might consider using a BIC test instead, which is possible using the -gologit2- program available from SSC. Do something like

use "http://www.stata-press.com/data/r12/nhanes2f";, clear
gologit2 health female black rural, pl sto(ologit)
gologit2 health female black rural, npl sto(gologit)
lrtest ologit gologit, stats

The last command yields

Likelihood-ratio test                                 LR chi2(9)  =     56.11
(Assumption: ologit nested in gologit)                Prob > chi2 =    0.0000

-----------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
      ologit |  10335    -15764.4   -15614.23      7     31242.46    31293.16
     gologit |  10335    -15764.4   -15586.17     16     31204.35    31320.24
-----------------------------------------------------------------------------
               Note:  N=Obs used in calculating BIC; see [R] BIC note

Based on a brant test (or the very similar chi-square test reported above) you would conclude the assumptions are violated. But based on the BIC test, you would stick with the ordered logit model.

The -gamma- option on gologit2 also lets you see how big the deviations from proportionality are, which you might look at as a way of assessing how substantively important they are.


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Richard Williams, Notre Dame Dept of Sociology
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