[R] loglikelihood and lmer

Marco Geraci marcodoc75 at yahoo.com
Fri Mar 31 21:56:31 CEST 2006

Dear R users,
I am estimating Poisson mixed models using glmmPQL
(MASS) and lmer (lme4). We know that glmmPQL do not
provide the correct loglikelihood for such models (it
gives the loglike of a 'pseudo' or working linear
mixed model). I would like to know how the loglike is
calculated by lmer.
A minor question is: why do glmmPQL and lmer give
different degrees-of-freedom for the same estimated
model? Does glmmPQL consider the scale parameter 'phi'
as a degree of freedom?

A toy example

m <- 5
n <- 100
N <- n*m
X <- cbind(1,runif(N))
Z <- kronecker(diag(n),rep(1,m))
z <- rpois(N, exp(X%*%matrix(c(1,2)) +
id <- rep(1:n,each=m)
fit.glmm <- glmmPQL(z ~ X-1, random = ~1|id,
fit.lmer <- lmer(z ~ X-1 + (1|id),

> logLik(fit.glmm)
'log Lik.' -386.4373 (df=4)
> logLik(fit.lmer)
'log Lik.' -458.1203 (df=3)


> sessionInfo()
R version 2.2.1, 2005-12-20, i386-pc-mingw32 

attached base packages:
[1] "methods"   "stats"     "graphics"  "grDevices"
[6] "datasets"  "base"     

other attached packages:
   mvtnorm    SemiPar    cluster       lme4    lattice
   "0.7-2"    "1.0-1"   "1.10.4"  "0.995-2"  "0.12-11"
      nlme       MASS 
"3.1-68.1"   "7.2-24" 

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