st: Re: Re: Testing joint hypothesis

["Dr. Stephen Owusu-Ansah" <sowusuansah@rgv.rr.com>]

Hi Kit:

A happy new year to you and everybody on the list. I have read Greene as 
you suggested. I have also read a couple of good intro econometrics 
textbooks, including Peter Kennedy's A Guide to Econometrics, and J. 
Scott Long's Regression Models for Categorical and Limited Dependent 
Variables (a section on these tests on pp. 87-98).

However, I am a bit confused as to when should one use Wald (W), 
Likelihood ratio (LR), and Langrange multiplier (LM) tests. My confusion 
stems from the fact that Stata manuals portray something different about 
these tests.

From those textbooks, any of those tests can be used for any model. 
Also, while the three tests (W, LR and LM) are asymptotically 
equivalent, their differences in terms of tests requirements are very 
clear in Greene. Thus, the LR test requires calculation of both 
constrained and unconstrained estimations. The W test requires only the 
unconstrained estimator, and the LM test requires only the constrained 
estimator.

But the Stata manuals tend to suggest that the LR test is for limited 
dependent models estimators such as logit and probit (see the "lrtest" 
command). Further, they say that the W test can be used for either 
linear and nonlinear models (see the "test" and "testnl" commands 
respectively) with any estimation commands except "anova" and "mlogit" 
or "mvreg" in certain instances.

The situation is worsen when I use the "cnsreg" command in conjunction 
with the "lrtest" command following a model estimation with the "reg" 
command. That is, using the syntax you suggested earlier as:

1. I use the "constr" to construct the joint null hypothesis
2. I use the "cnsreg" command to estimate the constrained model
3. I store the results in (2) above with the "est" command.
4. I use the "reg" command to estimate the unconstrained model
5. I use the "lrtest" command to test joint hypothesis
6. The test in (5) above produces a likelihood-ratio test statistic.

Implying that my estimation command was one for the limited dependent 
models such as logit and probit. But, in fact, I used the "reg" command.

Can you and any other person clarify for me? Thanks for your cooperation.

Stephen


Christopher F Baum wrote:

> On Dec 31, 2003, at 2:33 AM, Stephen wrote:
>
> > Would you consider a sample size of 168 small, and as such any
> > inferences drawn on the basis of LM or LLR instead of Wald
> > could be wrong?
> >
> > Stephen
>
> Generally I would not consider that to be too small, but the N alone 
> does not necessarily tell you that much...for instance consider a 
> characteristic shared by only 5% of the observations that is involved 
> with several coefficients, and you want to test for their joint 
> significance. That test might not have a great deal of power, which is 
> related to 0.05*168 = 8 observations, not 168.
>
> I'd suggest you read what Greene has to say about inference from these 
> three forms of the test statistic in small samples. Econometric 
> Analysis, 5th ed, section 17.5.
>
> Happy new year
> Kit
>
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