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).
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.
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?
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
