[R-sig-ME] LRT between GLMM and GLM to test a Single Random Intercept
Thierry Onkelinx
thierry@onkelinx @ending from inbo@be
Wed Dec 12 11:07:40 CET 2018
Dear Juho,
I'd take a step back and think on why you add the random intercept. Is it
clearly a part of the design? E.g. it takes repeated measures into account.
Then you need the term in the model, what ever the p-value. The variance of
the random effect indicates its importance.
Best regards,
ir. Thierry Onkelinx
Statisticus / Statistician
Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be
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<https://www.inbo.be>
Op wo 12 dec. 2018 om 06:37 schreef Juho Kristian Ruohonen <
juho.kristian.ruohonen using gmail.com>:
> My readers are likely to want to see a p-value on the only random effect
> (an intercept) in my logistic GLMM.
>
> Supposedly, if I fit the model using Laplace approximation, then the
> likelihood is comparable with that of the fixed-effects model, so the
> p-value from a LRT (divided by two) can be used. But I don't trust the
> Laplace approximation much. I'd rather use at least 10 quadrature points
> for improved accuracy. This also results in a more flattering (smaller)
> random-effect variance and hence a lower reported intraclass correlation.
> But if I use any more than 1 quadrature point, I can no longer report a
> p-value on the random effect because *anova()* refuses to compare the
> models, citing incomparable likelihood functions. I thought of calculating
> the log-likelihood of the GLMM manually using *dbinom()*, the data and the
> fitted values, but this thread
> <
> https://stats.stackexchange.com/questions/381085/calculating-log-likelihood-of-logistic-adaptive-quadrature-glmm-for-comparison-w
> >
> says I can't use the binomial PMF for that.
>
>
> Is there a way I can have my cake (many quadrature points) and eat it too
> (get a p-value for the random effect)? That parametric bootstrap procedure
> sounds neat, but I'd still be running into the same problem: the LRT
> calculated at each iteration compares a fixed and a mixed model, hence the
> likelihoods cannot be compared.
>
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