# [R-sig-ME] binomial fixed-effect p-values by simulation

Ben Bolker bolker at ufl.edu
Mon Aug 25 15:56:50 CEST 2008

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My guess, based on Littell et al 2003, would be that
something like  p %*% V^{-1} %*% p would give you a
quadratic form that would be chi-squared distributed with
rank(V) df, or (with an estimated scale parameter) F-distributed
with (rank(V), n-whatever) df -- or at least nominally
so, and if you're going to simulate anyway you're going
to find out how it's _really_ distributed ...

[I have a glmer fit named "zz", and a factor named "status"
that I want to test all levels == 0 simultaneously]

params <- grep("^status",names(fixef(zz)))
fixef(zz)[params] %*% solve(vcov(zz)[params,params]) %*% fixef(zz)[params]

cheers
Ben

Daniel Ezra Johnson wrote:
> Sorry if this has been covered elsewhere, but if my interest is in
> testing a single fixed effect _term_ (all coefficients at once) is
> there an appropriate statistic to simulate for a binomial model?
>
> In other words, if I fit a linear model "glmodel" I can simulate one
> of the F-statistics from anova(glmodel). If there's only one
> coefficient for the term then F = t^2...
>
> If I have a "glmmodel" I can do anova(glmmodel) but I wanted to make
> sure the F-statistic reported there was a sensible thing to look at
> since it wasn't quite the square of the z-statistic in the simple
> case.
>
> Maybe it doesn't have an F-distribution but it would still work well
> as a single-number stand-in for the 'size of a fixed effect' in a
> simulation...
>
> Thanks,
> D

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