Random Effects in Designed Experiments
The rats example, studied by aov with an Error term on p. 476, can be repeated as a linear mixed-effects model. This example works much better with lmer than with lme.
dd<-read.table("c:\\temp\\rats.txt",h=T) attach(dd) names(dd) [1] "Glycogen" "Treatment" "Rat" "Liver" Treatment<-factor(Treatment) Liver<-factor(Liver) Rat<-factor(Rat)
There is a single fixed effect (Treatment), and pseudoreplication enters the dataframe because each rat's liver is cut into three pieces and each separate liver bit produces two readings.
The rats are numbered 1 and 2 within each treatment, so we need Treatment as the largest scale of the random effects.
model<-lmer(Glycogen~Treatment+(1|Treatment/Rat/Liver)) summary(model) Linear mixed-effects model fit by REML Formula: Glycogen ~ Treatment + (1 | Treatment/Rat/Liver) AIC BIC logLik MLdeviance REMLdeviance 231.6 241.1 -109.8 234.9 219.6 Random effects: Groups Name Variance Std.Dev. Liver:(Rat:Treatment) (Intercept) 14.1617 3.7632 Rat:Treatment (Intercept) 36.0843 6.0070 Treatment (Intercept) 4.7039 2.1689 Residual 21.1678 4.6008 number of obs: 36, groups: Liver:(Rat:Treatment), 18; Rat:Treatment, 6; Treatment, 3
Fixed effects: Estimate Std. Error t value (Intercept) 140.500 5.184 27.104 Treatment2 10.500 7.331 1.432 Treatment3 -5.333 7.331 -0.728 Correlation of Fixed Effects: (Intr) Trtmn2 Treatment2 -0.707 ...
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