anova - aov() error term in R: what's the difference bw Error(id) and Error(id/timevar) specification? -
what difference between aov(depvar~timevar+error(id)) , aov(depvar~timevar+error(id/timevar)) formula specifications? these 2 variants produce different results.
the same question once asked here: https://stats.stackexchange.com/questions/60108/how-to-write-the-error-term-in-repeated-measures-anova-in-r however, i'd repeat more appropriate example.
here example created:
var=rep(na,180) id=rep(1:20,each=180/20) group=rep(rep(1:2,each=9),180/(9*2)) time1=rep(rep(1:3,each=3),180/(3*3)) time2=rep(c(8,15,20),180/3) var[group==1&time1==1&time2==8]=runif(10,105,115) var[group==2&time1==1&time2==8]=runif(10,105,115) var[group==1&time1==1&time2==15]=runif(10,95,105) var[group==2&time1==1&time2==15]=runif(10,95,105) var[group==1&time1==1&time2==20]=runif(10,85,95) var[group==2&time1==1&time2==20]=runif(10,85,95) var[group==1&time1==2&time2==8]=runif(10,95,105) var[group==2&time1==2&time2==8]=runif(10,95,105) var[group==1&time1==2&time2==15]=runif(10,85,95) var[group==2&time1==2&time2==15]=runif(10,75,85) var[group==1&time1==2&time2==20]=runif(10,75,85) var[group==2&time1==2&time2==20]=runif(10,65,75) var[group==1&time1==3&time2==8]=runif(10,95,105) var[group==2&time1==3&time2==8]=runif(10,95,105) var[group==1&time1==3&time2==15]=runif(10,85,95) var[group==2&time1==3&time2==15]=runif(10,75,85) var[group==1&time1==3&time2==20]=runif(10,75,85) var[group==2&time1==3&time2==20]=runif(10,65,75) df=data.frame(id,var,group,time1,time2) df$id=factor(df$id) df$group=factor(df$group) df$time1=factor(df$time1) df$time2=factor(df$time2) performing aov() on gets different results depending on error() term specification:
just 1 time term:
> summary(aov(var~time1+error(id),data=df)) error: id df sum sq mean sq f value pr(>f) residuals 19 958.4 50.44 error: within df sum sq mean sq f value pr(>f) time1 2 7538 3769 30.41 6.72e-12 *** residuals 158 19584 124 > summary(aov(var~time1+error(id/time1),data=df)) error: id df sum sq mean sq f value pr(>f) residuals 19 958.4 50.44 error: id:time1 df sum sq mean sq f value pr(>f) time1 2 7538 3769 211.5 <2e-16 *** residuals 38 677 18 --- signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 error: within df sum sq mean sq f value pr(>f) residuals 120 18907 157.6 or both time terms (don't type output here sake of space, may check on own):
summary(aov(var~group*time1*time2+error(id/(group*time1*time2)),data=df)) summary(aov(var~group*time1*time2+error(id),data=df)) why happen? variant correct?
here's blog post that'll break down each means under "random effects in classical anova" section.
from blog, here's summary "dividing" in error term means.
aov(y ~ error(a), data=d) # lone random effect aov(y ~ b + error(a/b), data=d) # random, b fixed, b nested within aov(y ~ (b*x) + error(a/(b*x)), data=d) # b , x interact within levels of so question,
aov(depvar~timevar+error(id/timevar)) means have random effect id fix timevar timevar nested within id levels versus
aov(depvar~timevar+error(id)) which taking id random effects no constraint on other variables.
source: http://conjugateprior.org/2013/01/formulae-in-r-anova/
this might prove useful well, code going on analysis of variance has recommendations on learning anova.
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