waldtest and nested models - poolability (parameter stability)

Dear Achim,

Thanks a lot for the superquick reply!
Somehow with your suggestion I can get around the problem, but of course I 
run into other problems, such as this:

waldtest(inv.log.leva.base, inv.log.leva, test = "Chisq", vcov = sandwich)

Error in bread. %*% meat. : non-conformable arguments

Cheers
Roberto

----- Original Message ----- From: "Achim Zeileis" <Achim.Zeileis at uibk.ac.at>
To: "Patuelli Roberto" <roberto.patuelli at usi.ch>
Cc: <r-help at r-project.org>
Sent: Monday, December 06, 2010 9:38 PM
Subject: Re: [R] waldtest and nested models - poolability (parameter 
stability)


On Mon, 6 Dec 2010, Roberto Patuelli wrote:

Dear All,

I'm trying to use waldtest to test poolability (parameter stability) 
between
two logistic regressions. Because I need to use robust standard errors 
(using
sandwich), I cannot use anova. anova has no problems running the test, but
waldtest does, indipendently of specifying vcov or not. waldtest does not
appear to see that my models are nested.

Yes. Because waldtest() needs to figure out which contrasts to apply to
go from the unrestricted model to the restricted model. The current
implementation can only do so by looking at the names of the coefficients.
It assumes that unrestricted model has all coefficients from the
restricted model plus some more (which are set to zero under the null
hypothesis).

When you use interactions (as you do below), this only works if you use
the *-coding but not the /-coding.

In pseudo code:

fm0  <- glm(y ~ x, family = binomial)
fm1a <- glm(y ~ a * x, family = binomial)
fm1b <- glm(y ~ a / x, family = binomial)

The restricted model is fm0 and the unrestricted model is fm1a/fm1b. Both
are equivalent in terms of fitted values. With waldtest() you can compare

 waldtest(fm0, fm1a)

but

 waldtest(fm0, fm1b)

fails because the models do not fulfill the restriction above. So, only
for the inference with waldtest() you need to compute fm1a as well. If
significant, you can go on and interpret fm1b.

Hope that helps,
Z

H0 in my case is the the vector of
regression parameters beta1 is the same as the vector of parameters beta2,
where beta1 and beta2 are computed for the two subgroups (divided according
to a factor).

I was wondering if anyone can help me making waldtest recognize the 
nesting.

Here's the lines I run:
(BTW, I try to use robust standard errors because what I normally use
(glm.binomial.disp) to correct for overdispersion does not converge for the
unpooled model. But this is another story....)

# poolability for leva.fin03.d
# pooled model
inv.log.leva.base = glm(mix.au.bin ~ cat.gap.tot + leva.fin03.d + ... +
sud0nord1, data = inv.sub.au, family = binomial, maxit = 1000) # I deleted
almost all variables to make the line more readable

# overdispersed pooled model - NOT THE PROBLEM NOW
inv.log.leva.base.disp = glm.binomial.disp(inv.log.leva.base)

# unpooled model
inv.log.leva = glm(mix.au.bin ~ leva.fin03.d/(cat.gap.tot + ... + sud0nord1 
-
1), data = inv.sub.au, family = binomial, maxit = 1000) # again I deleted
most variables for readability

# overdispersed unpooled model - NOT CONVERGING :(
inv.log.leva.disp = glm.binomial.disp(inv.log.leva, maxit = 10000)

# inv.log.leva.disp not converging, so I resort to using waldtest with
sandwich, BUT IT DOES NOT SEE THE NESTING!
waldtest(inv.log.leva.base, inv.log.leva, test = "Chisq", vcov = sandwich)

# anova would work but its results are not reliable because of the
overdispersion - basically without correcting for overdispersion almost 
every
variable is highly significant
anova(inv.log.leva.base, inv.log.leva, test = "Chisq")


Thanks everyone!
Best regards,
Roberto Patuelli

********************
Roberto Patuelli, Ph.D.
Istituto Ricerche Economiche (IRE) (Institute for Economic Research)
Universit? della Svizzera Italiana (University of Lugano)