On Mon, 11 Oct 2004 10:09:03 -0500, Richard Williams
<[email protected]> wrote:
> At 10:37 AM 10/11/2004 -0400, Stas Kolenikov wrote:
> >Also, I've seen people deriving F-statistics for testing an increase
> >in R2 as you add variables to the model. So it is the R2 that is the
> >"first principle" for them. The distinction between "measures" and
>
> If by that you mean researchers are primarily interested in the R^2, I
> wouldn't agree (at least not always). If I have X1, X2, and X3 in the
> (constrained) model, and I then add X4, X5, and X6 to the (unconstrained)
> model, I'm likely interested in testing the hypothesis
>
> H0: B4 = B5 = B6 = 0
> HA: At least one of the above betas does not equal 0.
Of course there are multiple ways of testing this hypothesis, either
Wald way by forming the vector of hyptheses and deriving covariance
matrix for them; or by likelihood ratio way which would be the
difference of sum of squares (if you don't believe the likelihood, you
can still use sum of squares in model-free way, but the results will
only have asymptotic sense then). The score test should also be
feasible. The three are equivalent in linear regression, but different
in nonlinear models, and there are models where one of them is easy to
do (usually the Wald test), while others may be prohibitively
difficult to implement, so the equivalence is quite limited.
The point I was trying to make is that I found it amusing to call this
a test on R2 increase, thus concentrating on R2 as the primary outcome
of the regression. Of course you can derive the F-test from R2, but
that is doing some extra work and going back to the original
statistics that are more natural to the regression, namely the sums of
squares. That of course varies by discipline; this particular one was
in business research methods that seem to stem from psychology.
--
Stas Kolenikov
http://stas.kolenikov.name
*
* 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/
