[R-sig-ME] lme4, glmmPQL and calculating QAICc

[Antonio.Gasparrini at lshtm.ac.uk]

Dear R users,
 
following the recent discussion on calculating QAICc in lme4, I report the weird results I got comparing glmer and glmmPQL.
 
I ran these models: 
 
pql.model <- glmmPQL(outcome ~ offset(log(pop)) + time + 
 harmonic(month,3,12), random=list(region=pdSymm(~time)), family=poisson, data)
 
glmer.model <- glmer(outcome ~ offset(log(pop)) + time + 
 harmonic(mm,3,12) + (time|region), family=poisson, data)
The first model with glmmPQL estimates a sigma (within-group error) anyway, both with poisson or quasipoisson family.
Its value is 1.40
The value of sigma^2 is equal to the overdispersion parameter of simpler glm-gam models (~1.96), which makes sense.
 
The second model with glmer doesn't estimate a sigma (correctly), but when the family is set to quasipoisson the estimated sigma [lme4:::sigma(glmer.model)] is 15.8, which is simply unbelievable. The standard errors are therefore incredibly huge.
 
I couldn't find a reason for that.
Any comment/suggestion is more than welcome.
Thanks

Antonio Gasparrini
Public and Environmental Health Research Unit (PEHRU)
London School of Hygiene & Tropical Medicine
Keppel Street, London WC1E 7HT, UK
Office: 0044 (0)20 79272406 - Mobile: 0044 (0)79 64925523