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Different variance estimates from lmer and lmer2

2 messages · Jonathan Bartlett, Douglas Bates

#
Dear all

For some mixed models, I get different variance estimates if I use lmer
compared to using lmer2. Is there a reason why the two commands are
giving quite different estimates?

The analysis below is from page 168 of "Extending the linear model with
R" by Faraway, using the dataframe irrigation from the faraway package.
Strangely, the results using lmer2 agree with the book, whereas lmer
gives slightly different estimates.

I have am running R 2.5.0 with lme4 version 0.99875-0 on WinXP.

lmod <- lmer(yield ~ irrigation * variety + (1|field),data=irrigation)
Linear mixed-effects model fit by REML 
Formula: yield ~ irrigation * variety + (1 | field) 
   Data: irrigation 
  AIC   BIC logLik MLdeviance REMLdeviance
 63.4 70.35  -22.7      68.62         45.4
Random effects:
 Groups   Name        Variance Std.Dev.
 field    (Intercept) 15.5182  3.9393  
 Residual              2.1919  1.4805  
number of obs: 16, groups: field, 8

....
(1|field),data=irrigation)
Linear mixed-effects model fit by REML 
Formula: yield ~ irrigation * variety + (1 | field) 
   Data: irrigation 
  AIC   BIC logLik MLdeviance REMLdeviance
 63.4 70.35 -22.70      68.61        45.39
Random effects:
 Groups   Name        Variance Std.Dev.
 field    (Intercept) 16.1991  4.0248  
 Residual              2.1076  1.4518  
Number of obs: 16, groups: field, 8

lmer2, the book and Stata's xtmixed give the estimate of the random
intercept SD as 4.02, whereas lmer gives it as 3.94.

My apologies if the reason for such differences is down to a mistake on
my part - I was unable to find any postings on the list regarding this
issue.

Many thanks
Jonathan
London School of Hygiene and Tropical Medicine
www.lshtm.ac.uk
#
On 5/22/07, Jonathan Bartlett <Jonathan.Bartlett at lshtm.ac.uk> wrote:

            
These differences are just reflecting different parameterizations and
different convergence criteria for lmer and lmer2.  Notice that the
REML deviance for the model fit by lmer2 is slightly smaller than that
fit by lmer (45.39 vs 45.4).  If you add the optional argument control
= list(msVerbose = 1) to the call to lmer and to lmer2 you will see
that lmer2 takes more iterations and, as shown above, produces a
slightly better criterion for the fit.

Having said all this, I would note that a difference of 0.01 in the
deviance is not going to be in any way significant.  Essentially what
all this is indicating is that the estimates of the variance
components are not very precisely determined.

It was probably after Julian fitted the models for his book that I
made the change in lmer to loosen the convergence criterion in lmer
somewhat.  In retrospect that may not have been a good idea.