Thank you for your reply, the only one I have got so far.
"Donald F. Burrill" wrote:
>
> Looks to me like a simple typo. The null hypothesis is
> H0: beta1 = beta2 = 0
> and I would attribute the "+" sign to a typing error ("+" is a shifted
> "=" on most keyboards).
You may be right here. This problem is found in a survival analysis
text. The text does have a few obvious typos. Hopefully this is just
another instance.
> While the _interpretation_ of non-zero estimates of the betas
> (should H0 be rejected) depends on the specific choice of
> parameterization for the three levels, all of the choices that spring to
> mind would have this null. It corresponds to the standard null
> hypothesis in an ANOVA with a 3-level factor:
> H0: mu_A = mu_B = mu_C, with 2 degrees of freedom.
Agree. Now I am interested in my second question. That is, if I do
want to test that a null hypothesis H0: beta1=0 or beta2=0,
which, in my understanding, is different from H0: beta1=0 and beta2=0,
I suppose the test for the former should be different from the
test for the latter. Is this correct?
> On Sun, 5 Mar 2000, Paul Y. Peng wrote:
>
> > Suppose that I have a factor with three levels A, B, and C. If it
> > is used in a GLM model as a covariate, I will have two parameter
> > beta1 and beta2 (assuming they are for level B and C). To test a
> > statement "Any of the last two levels (either level B or level C)
> > has a different effect on the response variable than level A," a text
> > book says that the null hypothesis should be H0: beta1 + beta2 = 0.
> > However, I cannot figure out why this is the null hypothesis. I
> > thought the hypotheses should be H0: beta1=0 or beta2=0 vs
> > Ha: beta1!=0 and beta2!=0. If they are correct, how should I test
> > them using say Wald's test or the likelihood ratio test? Thanks
> > for any hints.
>
> Why not the standard F test, comparing the residual SS for a model that
> includes the factor to the residual SS for a model that does not include
> the factor?
I should say the original question is from a survival model
rather than a GLM (I mentioned GLM because I believe a GLM may be
more popular than a survival model). In survival models, we
usually use Wald's test or LRT.
Thanks.
Paul.
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