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)
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