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Re: st: Lrtest versus Test


From   Joseph Coveney <jcoveney@bigplanet.com>
From   Richard Williams wrote:
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Lrtest versus Test
Date   Mon, 22 Dec 2003 12:12:29 +0900

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A couple of questions about Lrtest:

* When using routines like Logistic Regression, LrTest is generally 
supposed to be better than Test.  In practice, does it tend to make much 
difference, other than in maybe borderline cases?  And if so, are there any 
particular sets of circumstances when Test would be especially flawed? Test 
is generally easier to use.

* If you use LrTest with OLS regression, does it produce equivalent results 
to Test?  It seems to give virtually identical results with some 1 d.f. 
tests I have tried, but I'm not sure about more complicated tests. For 
example, the docs show how to do chow tests with logistic regression and 
LrTest, so I'm wondering if the same thing works ok with OLS regression.

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With logistic regression, especially, I believe that the likelihood ratio test 
is generally preferred:  there is an uncommon set of circumstances with 
logistic regression that lead to a likelihood function that renders the Wald 
test wildly inaccurate.  It's known as the Hauck-Donner Phenomenon or Hauck-
Donner Effect. (google brings up information on it.)  If you'd like to see this 
phenomenon in action with Stata, you can find a description of an example of a 
dataset that displays this effect at 
www.math.yorku.ca/Who/Faculty/Monette/S-news/0034.html .

Another case where I've stumbled across a dataset for which the Wald test gives 
inaccurate results compared to -lrtest- is Alan Agresti's AZT and race dataset 
from Table 5.5 of his _An Introduction to Categorical Data Analysis_; the 
dataset and SAS code can be downloaded from 
www.stat.ufl.edu/~aa/intro-cda/appendix.html .  (The example is also used in 
his _Categorical Data Analysis_.)  If you're typically more involved with 
hypothesis testing than with prediction (where overfitting is a concern), you 
might typically fit a model with interaction terms unless a particular term is 
not scientifically warranted or not implied by the study's objective and 
design.  If you fit a full model to this dataset (AZT, race and AZT-by-race 
interaction), then the Wald tests for the main effects are inaccurate.  
-lrtest-, however, provides test statistics that are consistent among saturated 
and reduced models.

Joseph Coveney


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