[R-sig-ME] Poisson mixed models with glmer and glmmPQL

[Antonio.Gasparrini at lshtm.ac.uk]

Dear R user,
 
I'm running an analysis on the trend of rates of acute myocardial infarction in 20 regions.
I want to specify both the national and the region-specific trends with a polynomial function. The latter are included as random effects in a model with region as grouping factor.
I tried to use both 'glmmPQL' (package MASS) and 'glmer' (package lme4), the former being more flexible in the choice of var-covar structure, the second known as more robust.
 
Here you can find the code (stdpop in the standardized population size, seasonality is modelled with harmonic functions of month):
 
pql.model <- glmmPQL(outcome ~ offset(log(stdpop)) + poly(time,3) + 
 harmonic(month,3,12), random=list(region=pdSymm(~poly(time,3))), family=poisson, data)
 
glmer.model <- glmer(outcome ~ offset(log(stdpop)) + poly(time,3) + 
 harmonic(mm,3,12) + (poly(time,3)|region), family=poisson, data)
 
I have 2 questions:
 
1) If a specify the pql.model with pdSymm as above, or with a simple argument 'random=~poly(time,3)|region', I got different results. Very small changes, but not exactly the same anyway. I also realized the latter simpler formula included here use a log-Cholesky parametrization, while the former does not. I had some convergence problem with the simpler formula, not with the pdSymm specification. Can someone give me some explanation/suggestion?
 
2) More importantly, the pql.model returns a value of sigma (pql.model$sigma) higher than 1. I interpreted it as a within-group error parameter which can explain some overdispersion in the data. Conversely, the glmer.model gives sigma=1 ( attributes(summary(glmerpoly3))$sigma ), although the estimates being practically identical to pql.model. Do you think the glmer.model included a within-group parameter as well, or not?
 
Thanks for your help

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
Skype contact: a.gasparrini
http://www.lshtm.ac.uk/people/gasparrini.antonio ( http://www.lshtm.ac.uk/pehru/ )