When analysing mixed-effects data using lmer() I find that using anova(type='marginal') and anova(type='III') give different results. Why the discrepancy?
The results from anova(type='marginal') are identical to those I get from using car:Anova(type='III') on the same model and to using both anova(type='marginal') and car:Anova(type='III') on the same data fitted using lme().
library(lme4)
library(nlme)
library(car)
# Some data
group<-as.factor(c(rep('A',32),rep('B',32)))
time<-as.factor(rep(c(rep('t1',16),rep('t2',16)),2))
cond<-as.factor(rep(c(rep('c1',8),rep('c2',8)),4))
subject<-as.factor(rep(c(rep(1:8,2),rep(9:16,2)),2))
set.seed(1)
dv<-c(rnorm(16, mean=3),rnorm(16, mean=1),rnorm(16, mean=0),rnorm(16, mean=3))
data<-data.frame(dv,group,time,cond, subject)
# Model using both lme() and lmer()
model_lme<-lme(dv~group*time*cond, random=~1|subject, data = data, method='ML')
model_lmer<-lmer(dv~group*time*cond+ (1|subject), data = data, REML=FALSE)
# Investigate output of same model with lme() og lmer()
'lme() anova(type=marginal):'
anova(model_lme, type='marginal')
'lme() car::Anova(type=III):'
Anova(model_lme,type='III')
'lmer() anova(type=III):'
anova(model_lmer, type='III')
'lmer() anova(type=marginal):'
anova(model_lmer, type='marginal')
'lmer() car::Anova(type=III):'
Anova(model_lmer,type='III')