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LRT between GLMM and GLM to test a Single Random Intercept

2 messages · Juho Kristian Ruohonen, Thierry Onkelinx

#
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.
#
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 at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op wo 12 dec. 2018 om 06:37 schreef Juho Kristian Ruohonen <
juho.kristian.ruohonen at gmail.com>: