On Jan 4, 2004, at 2:33 AM, Stephen wrote:
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.
Well, the lrtest command does likelihood ratio tests for a living-- so
if you run lrtest, that is the form of the test you have requested.
All three tests can be used on any sort of model, linear or nonlinear.
The reason why LR tests are common in a limited dep var estimation
context is that estimators like logit or probit are maximum likelihood
estimators, and it is trivial to calculate the likelihood of the
restricted (constant-only) model in order to compute a LR statistic
that is the equivalent of a regression "anova F" test.
Now linear regression is a ML estimator, also, but normally we do not
compute regression estimates that way; we use the method of moments (in
this case the principle of least squares) which leads to a linear
expression. Likewise, the expression for any linear hypothesis test on
the parameter vector is also linear, and can be computed via a few
steps of matrix algebra. One could do those tests (i.e. what is
computed by -test-) via a maximum likelihood approach, but it would be
more computational effort.
I don't understand your comment about mvreg and Wald tests. When one
does tests after mvreg, they are presented as F statistics which are
Wald test statistics (based on the unconstrained model), just as -test-
after a single-equation -regress-. Since ANOVA is just regression with
dummy variables as regressors, I suspect any tests in that context are
Wald tests as well.
Kit
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
