[R] lmer- why do AIC, BIC, loglik change?

[Deepayan Sarkar]

On 18 Oct 2006 16:21:11 -0400, Darren M. Ward
<Darren.M.Ward at dartmouth.edu> wrote:
> Hi all,
>
> I am having issues comparing models with lmer.  As an example, when
>  I run the code below the model summaries (AIC, BIC, loglik) differ between
> the summary() and anova() commands.  Can anyone clear up what's wrong?

'summary' uses REML or ML depending on what 'method' was used, whereas
'anova' always uses ML (presumably at the parameter values that
maximize the REML if method="REML"). With 'method="ML"' in the lmer
calls, you should see the same in both.

-Deepayan

> Thank you!
>
> Darren Ward
>
> library(lme4)
> data(sleepstudy)
> fm1<-lmer(Reaction ~ Days + (1|Subject), sleepstudy)
> summary(fm1)
> fm2<-lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
> summary(fm2)
> anova(fm1, fm2)
>
> Sample output:
>
> > summary(fm1)
> Linear mixed-effects model fit by REML
> Formula: Reaction ~ Days + (1 | Subject)
>    Data: sleepstudy
>   AIC  BIC logLik MLdeviance REMLdeviance
>  1792 1802 -893.2       1794         1786
>
> > summary(fm2)
> Linear mixed-effects model fit by REML
> Formula: Reaction ~ Days + (Days | Subject)
>    Data: sleepstudy
>   AIC  BIC logLik MLdeviance REMLdeviance
>  1754 1770 -871.8       1752         1744
>
> > anova(fm1, fm2)
> Data: sleepstudy
> Models:
> fm1: Reaction ~ Days + (1 | Subject)
> fm2: Reaction ~ Days + (Days | Subject)
>     Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
> fm1  3 1800.10 1809.68 -897.05
> fm2  5 1761.98 1777.95 -875.99 42.115      2  7.158e-10 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> > sessionInfo()
> R version 2.4.0 (2006-10-03)
> i386-pc-mingw32
>
> locale:
> LC_COLLATE=English_United States.1252;LC_CTYPE=English_United States.1252;LC_MONETARY=English_United States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252
>
> attached base packages:
> [1] "methods"   "stats"     "graphics"  "grDevices" "utils"     "datasets"
> [7] "base"
>
> other attached packages:
>      vegan       lme4     Matrix    lattice
>    "1.8-3" "0.9975-6" "0.9975-3"   "0.14-9"
>
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> and provide commented, minimal, self-contained, reproducible code.
>


-- 
http://www.stat.wisc.edu/~deepayan/