glmmADMB: Generalized Linear Mixed Models using AD Model Builder

The "Laplace" method in lmer and the default method in glmm.admb,
which according to the documentation is the Laplace approximation,
produce essentially the same model fit.  One difference is the
reported value of the log-likelihood, which we should cross-check, and
another difference is in the execution time

Yes, glmmADMB has sqrt(2*pi) constants missing. Thanks for pointing that out.

Execution time: As pointed out by Roel de Jong, the underlying software AD Model Builder
does not use hand-coded derivatives for the Hessian involved in the Laplace approximation, 
but calculates these by automatic differentiation. There is a cost in terms of execution
speed, but on the other hand it is very quick to develop new models, as you do not
have to worry about derivatives. I hope to exploit this beyond standard GLMMs, and provide
other R packages.

Comparison of glmmADMB with lmer: I find that the two packages do not give the same
result on one of the standard datasets in the literature (Lesaffre et. al., Appl. Statist. (2001) 50, Part3, pp 325-335).
The full set of R commands used to download data and fit the model is given at the end of this email.

fit_lmer_lapl <- lmer(y~ treat + time  + (1|subject),data=lesaffre,family=binomial,method="Laplace")

Warning message:
optim or nlminb returned message ERROR: ABNORMAL_TERMINATION_IN_LNSRCH 
 in: LMEopt(x = mer, value = cv) 

PART OF OUTPUT:

Fixed effects:
             Estimate Std. Error  z value Pr(>|z|)    
(Intercept) -0.626214   0.264996  -2.3631  0.01812 *  
treat       -0.304660   0.360866  -0.8442  0.39853    
time        -0.346605   0.026666 -12.9979  < 2e-16 ***

The corresponding estimates with glmmADMB is:

fit_glmmADMB <- glmm.admb(y~ treat + time,random=~1,group="subject",data=lesaffre,family="binomial",link="logit")

PART OF OUTPUT:

Fixed effects:
  Log-likelihood: -359.649 
  Formula: y ~ treat + time 
(Intercept)       treat        time 
   -2.33210    -0.68795    -0.46134 


So, the estimates of the fixed effects differ. lmer() does infact produces a warning, and it appears that
it method="Laplace" and method="PQL" produce the same results.


Best regards,

hans


# Load data
source("http://www.mi.uib.no/~skaug/cash/lesaffre_dat.s")

# Run lmer
library(lme4)
fit_lmer <- lmer(y~ treat + time + (1|subject),data=lesaffre,family=binomial)
fit_lmer_lapl <- lmer(y~ treat + time  + (1|subject),data=lesaffre,family=binomial,method="Laplace")


# Run glmmADMB
library(glmmADMB)
example(glmm.admb)	# Must be run once in each new directory (this feature will be removed in future version of glmmADMB).
fit_glmmADMB <- glmm.admb(y~ treat + time,random=~1,group="subject",data=lesaffre,family="binomial",link="logit")