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st: Re: Re: Testing joint hypothesis


From   "Dr. Stephen Owusu-Ansah" <[email protected]>
To   [email protected]
Subject   st: Re: Re: Testing joint hypothesis
Date   Sat, 03 Jan 2004 09:57:31 -0600

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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