[R-sig-ME] Variance components in generalized mixed models

[Marco Chiarandini]

Dear list,

I have some problems with lmer of lme4.

Using the latest version 0.999375-27 I receive as 
messages the following:

 > lmer(quality~ 
1+(1|instance),data=OONR,family=Gamma())
Error in mer_finalize(ans) :
   General form of glmer_linkinv not yet written
 > lmer(quality~ 
1+(1|instance),data=OONR,family=Gamma(link="log"))
Error in if (any(sd < 0)) return("'sd' slot has 
negative entries") :
   missing value where TRUE/FALSE needed


Before I was using the version 0.99875-9 and there 
my problems were the following:

1) Fitting a generalized mixed model with random 
effects having Gamma distribution, one obtains an 
estmate for the variance of the random effects as 
if it were a standard linear model (ie, with 
errors normally distributed). What is the exact 
meaning of this estimated variance? In other 
terms, to which parameter of the Gamma 
distribution it corresponds? (see examples below 
for code and results)

2) In lmer the approximation method "PQL" is said 
to be the default. Nevertheless running the 
examples that follows one obtains very different 
results. Why is this happening?

 > lmer(quality~ 
1+(1|instance),data=OONR,family=Gamma(link="log"),method="PQL")
Generalized linear mixed model fit using PQL
Formula: quality ~ 1 + (1 | instance)
    Data: OONR
  Family: Gamma(log link)
  AIC  BIC logLik deviance
   72 74.8    -34       68
Random effects:
  Groups   Name        Variance Std.Dev.
  instance (Intercept) 4.45e-01 0.66708
  Residual             2.68e-05 0.00518
number of obs: 30, groups: instance, 6

Fixed effects:
             Estimate Std. Error t value
(Intercept)    2.111      0.272    7.75
 > lmer(quality~ 
1+(1|instance),data=OONR,family=Gamma(link="log"))
Generalized linear mixed model fit using Laplace
Formula: quality ~ 1 + (1 | instance)
    Data: OONR
  Family: Gamma(log link)
   AIC  BIC logLik deviance
  14.7 17.5  -5.33     10.7
Random effects:
  Groups   Name        Variance Std.Dev.
  instance (Intercept) 0.0415   0.204
  Residual             0.2005   0.448
number of obs: 30, groups: instance, 6

Fixed effects:
             Estimate Std. Error t value
(Intercept)    2.166      0.117    18.6
 >

 > sessionInfo()
R version 2.7.0 (2008-04-22)
i486-pc-linux-gnu

locale:
C


The data OONR are available at:
http://www.imada.sdu.dk/~marco/Mixed/OONR.Rdata


Thank you in advance for any help you may provide.

Best regards,
Marco


-- 
Marco Chiarandini
Department of Mathematics and Computer Science,
University of Southern Denmark
Campusvej 55, DK-5230 Odense M, Denmark
marco at imada.sdu.dk,  http://www.imada.sdu.dk/~marco
Phone: +45 6550 4031,  Fax: +45 6550 2325