[R-sig-ME] Different variance estimates from lmer and lmer2

[Douglas Bates]

On 5/22/07, Jonathan Bartlett <Jonathan.Bartlett at lshtm.ac.uk> wrote:


> 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)
> > summary(lmod)
> 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
>
> ....
>
> > lmod <- lmer2(yield ~ irrigation * variety +
> (1|field),data=irrigation)
> > summary(lmod)
> 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

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.

> 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
>
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