R help - Sep 2010 - lmer() vs. lme() gave different variance component estimates

Hi, I asked this on mixed model mailing list, but that list is not very active, 
so I'd like to try the general R mailing list. Sorry if anyone receives the 
double post.


Hi, I have a dataset of animals receiving some eye treatments. There are 8 

treatments, each animal's right and left eye was measured with some scores 
(ranging from 0 to 7) 4 times after treatment. So there are nesting groups eyes 
within animal. Dataset attached
>
dat<-read.table("dat.txt",sep='\t',header=T,row.names=1)
> dat$id<-factor(dat$id)
> str(dat)
'data.frame':   640 obs. of  5 variables:
$ score: int  0 2 0 7 4 7 0 2 0 7 ...
$ id   : Factor w/ 80 levels
"1","3","6","10",..: 7 48 66 54 18 26 38
52 39 63
...
$ rep  : int  1 1 1 1 1 1 1 1 1 1 ...
$ eye  : Factor w/ 2 levels "L","R": 2 2 2 2 2 2 2 2 2 2 ...
$ trt  : Factor w/ 8 levels
"A","B","C","Control",..: 1 1 1 1 1 1 1
1 1 1 ...

I fit a mixed model using both lmer() from lme4 package and lme() from nlme 
package:
> lmer(score~trt+(1|id/eye),dat)
Linear mixed model fit by REML 
Formula: score ~ trt + (1 | id/eye) 
   Data: dat 
   AIC   BIC logLik deviance REMLdev
446.7 495.8 -212.4    430.9   424.7
Random effects:
Groups   Name        Variance   Std.Dev.      
eye:id   (Intercept) 6.9208e+00 2.630742315798
id       (Intercept) 1.4471e-16 0.000000012030
Residual             1.8750e-02 0.136930641909
Number of obs: 640, groups: eye:id, 160; id, 80
> summary(lme(score~trt, random=(~1|id/eye), dat))
Linear mixed-effects model fit by REML
Data: dat 
       AIC      BIC    logLik
  425.1569 474.0947 -201.5785

Random effects:
Formula: ~1 | id
        (Intercept)
StdDev:    1.873576

Formula: ~1 | eye %in% id
        (Intercept)  Residual
StdDev:    1.896126 0.1369306

As you can see, the variance components estimates of random effects are quite 
different between the 2 model fits. From the data, I know that the variance 
component for "id" can't be near 0, which is what lmer() fit
produced, so I
think the lme() fit is correct while lmer() fit is off. This can also be seen 
from AIC, BIC etc. lme() fit has better values than lmer() fit. 


I guess this might be due to lmer() didn't converge very well, is there
anyway
to adjust to make lmer() converge better to get similar results as lme()?

Thanks

John


      
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On 09/17/2010 09:14 PM, array chip wrote:
> Hi, I asked this on mixed model mailing list, but that list is not very
active,
> so I'd like to try the general R mailing list. Sorry if anyone receives
the
> double post.
> 
> 
> Hi, I have a dataset of animals receiving some eye treatments. There are 8 
> 
> treatments, each animal's right and left eye was measured with some
scores
> (ranging from 0 to 7) 4 times after treatment. So there are nesting groups
eyes
> within animal. Dataset attached
> 
>>
dat<-read.table("dat.txt",sep='\t',header=T,row.names=1)
>> dat$id<-factor(dat$id)
>> str(dat)
> 'data.frame':   640 obs. of  5 variables:
> $ score: int  0 2 0 7 4 7 0 2 0 7 ...
> $ id   : Factor w/ 80 levels
"1","3","6","10",..: 7 48 66 54 18 26 38
52 39 63
> ...
> $ rep  : int  1 1 1 1 1 1 1 1 1 1 ...
> $ eye  : Factor w/ 2 levels "L","R": 2 2 2 2 2 2 2 2 2
2 ...
> $ trt  : Factor w/ 8 levels
"A","B","C","Control",..: 1 1 1 1 1 1 1
1 1 1 ...
> 
> I fit a mixed model using both lmer() from lme4 package and lme() from nlme
> package:
> 
>> lmer(score~trt+(1|id/eye),dat)
> 
> Linear mixed model fit by REML 
> Formula: score ~ trt + (1 | id/eye) 
>    Data: dat 
>    AIC   BIC logLik deviance REMLdev
> 446.7 495.8 -212.4    430.9   424.7
> Random effects:
> Groups   Name        Variance   Std.Dev.      
> eye:id   (Intercept) 6.9208e+00 2.630742315798
> id       (Intercept) 1.4471e-16 0.000000012030
> Residual             1.8750e-02 0.136930641909
> Number of obs: 640, groups: eye:id, 160; id, 80
> 
>> summary(lme(score~trt, random=(~1|id/eye), dat))
> 
> Linear mixed-effects model fit by REML
> Data: dat 
>        AIC      BIC    logLik
>   425.1569 474.0947 -201.5785
> 
> Random effects:
> Formula: ~1 | id
>         (Intercept)
> StdDev:    1.873576
> 
> Formula: ~1 | eye %in% id
>         (Intercept)  Residual
> StdDev:    1.896126 0.1369306
> 
> As you can see, the variance components estimates of random effects are
quite
> different between the 2 model fits. From the data, I know that the variance
> component for "id" can't be near 0, which is what lmer() fit
produced, so I
> think the lme() fit is correct while lmer() fit is off. This can also be
seen
> from AIC, BIC etc. lme() fit has better values than lmer() fit. 
> 
> 
> I guess this might be due to lmer() didn't converge very well, is there
anyway
> to adjust to make lmer() converge better to get similar results as lme()?
That's your guess... I'd be more careful about jumping to conclusions.
If this is a balanced data set, perhaps you could supply the result of

summary(aov(score~trt+Error(id/eye), data=dat))

The correct estimates should be computable from the ANOVA table.


-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com