[R] AICs from lmer different with summary and anova

[Jonathan Williams]

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.

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