At 16:22 15/04/2009, Jonathan Williams wrote:
Dear R Helpers,
I have noticed that when I use lmer to analyse data, the summary function
gives different values for the AIC, BIC and log-likelihood compared with the
anova function.
I do not think I have seen a reply to this.
What happens if you fit the models originally using ML rather than REML?
Here is a sample program
#make some data
set.seed(1);
datx=data.frame(array(runif(720),c(240,3),dimnames=list(NULL,c('x1','x2','y'
))))
id=rep(1:120,2); datx=cbind(id,datx)
#give x1 a slight relation with y (only necessary to make the random effects
non-zero in this artificial example)
datx$x1=(datx$y*0.1)+datx$x1
library(lme4)
#fit the data
fit0=lmer(y~x1+x2+(1|id), data=datx); print(summary(fit0),corr=F)
fit1=lmer(y~x1+x2+(1+x1|id), data=datx); print(summary(fit1),corr=F)
#compare the models
anova(fit0,fit1)
Now, look at the output, below. You can see that the AIC from
"print(summary(fit0))" is 87.34, but the AIC for fit0 in "anova(fit0,fit1)"
is 73.965. There are similar changes for the values of BIC and logLik.
Am I doing something wrong, here? If not, which are the real AIC and logLik
values for the different models?
Thanks for your help,
Jonathan Williams
Output:-
> fit0=lmer(y~x1+x2+(1|id), data=datx); print(summary(fit0),corr=F)
Linear mixed model fit by REML
Formula: y ~ x1 + x2 + (1 | id)
Data: datx
AIC BIC logLik deviance REMLdev
87.34 104.7 -38.67 63.96 77.34
Random effects:
Groups Name Variance Std.Dev.
id (Intercept) 0.016314 0.12773
Residual 0.062786 0.25057
Number of obs: 240, groups: id, 120
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.50376 0.05219 9.652
x1 0.08979 0.06614 1.358
x2 -0.06650 0.06056 -1.098
> fit1=lmer(y~x1+x2+(1+x1|id), data=datx); print(summary(fit1),corr=F)
Linear mixed model fit by REML
Formula: y ~ x1 + x2 + (1 + x1 | id)
Data: datx
AIC BIC logLik deviance REMLdev
90.56 114.9 -38.28 63.18 76.56
Random effects:
Groups Name Variance Std.Dev. Corr
id (Intercept) 0.0076708 0.087583
x1 0.0056777 0.075351 1.000
Residual 0.0618464 0.248689
Number of obs: 240, groups: id, 120
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.50078 0.05092 9.835
x1 0.09236 0.06612 1.397
x2 -0.06515 0.06044 -1.078
> anova(fit0,fit1)
Data: datx
Models:
fit0: y ~ x1 + x2 + (1 | id)
fit1: y ~ x1 + x2 + (1 + x1 | id)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
fit0 5 73.965 91.368 -31.982
fit1 7 77.181 101.545 -31.590 0.7839 2 0.6757
Michael Dewey
http://www.aghmed.fsnet.co.uk
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