When I simulate variance at only a single level in a nested analysis using lme (all levels are random effects), the results confuse me. Instead of lme reporting high variance in only that simulated level, substantial variance (>10% of simulated level) often appears in other levels -- in some configurations, as often as 50% of the time. Usually this spurious variance shows up in levels of nesting above the level with high simulated variance.
Am I doing something wrong or should I expect such 'over-detection'? I was expecting near zero variance in those other levels except say, 5% of the time.
Here's some example code with variance simulated in level 2 and spurious variance appearing frequently in level 1:
library(nlme) # 4 level nesting simVar <- c(0,1,0,.1) # first is level one, last becomes error nAtLevel <- c(5,5,5,5) # number of replicates at each level
F1V <- F2V <- F3V <- residV <- numeric(0)
for (rep in 1:100){
F1f <- F2f <- F3f <- value <- numeric(0)
mn <- numeric(length(nAtLevel))
# data generator
for (F1 in 1:nAtLevel[1]) {
mn[1] <- rnorm(1,sd=simVar[1]) # set mean for level 1
for (F2 in 1:nAtLevel[2]) {
mn[2] <- rnorm(1,sd=simVar[2]) # set mean for level 2
for (F3 in 1:nAtLevel[3]) {
mn[3] <- rnorm(1,sd=simVar[3]) # set mean for level 3
for (F4 in 1:nAtLevel[4]) {
mn[4] <- rnorm(1,sd=simVar[4]) #set mean for lowest level
value <- c(value, sum(mn))
F1f <- c(F1f,F1)
F2f <- c(F2f,F2)
F3f <- c(F3f,F3)
}
}
}
} y.lme <- lme(value ~ 1,random = ~ 1 | as.factor(F1f)/
as.factor(F2f)/
as.factor(F3f))
v <- as.numeric(VarCorr(y.lme)[,2])
v <- as.numeric(na.omit(v))
F1V <- c(F1V,v[1])
F2V <- c(F2V,v[2])
F3V <- c(F3V,v[3])
residV <- c(residV,y.lme$sigma)
}
var.df <- data.frame(F1V,F2V,F3V,residV)
par(mfrow=c(2,2))
hist(var.df$F1V,main='Level 1 StdDev')
hist(var.df$F2V,main='Level 2 StdDev')
hist(var.df$F3V,main='Level 3 StdDev')
hist(var.df$residV,main='Residual StdDev')
txt <- 'Simulated stddev:'
for (i in 1:length(simVar)) {
txt <- paste(txt,' level ',i,'=',simVar[i],',',sep='')}
mtext(txt, outer=T,line=-1,side=3)
Summary plots for several sample sizes is at: http://david.science.oregonstate.edu/~allisong/R/sampSize.pdf
Thanks for any suggestions! Gary
-- Gary Allison Department of Evolution, Ecology and Organismal Biology Ohio State University
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