[R] waldtest and nested models - poolability (parameter stability)

Achim Zeileis Achim.Zeileis at uibk.ac.at
Mon Dec 6 21:38:07 CET 2010

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 

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)


   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,

> 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 
> 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)
> Università della Svizzera Italiana (University of Lugano)
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