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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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