A R function for the permutation test for onw-way nested design ANOVA.
This work is inspired by Dr. David C. Howell, University of Vermont. In Dr. Howell’s webpage “Permutation Tests for Factorial ANOVA Designs” (http://www.uvm.edu/~dhowell/StatPages/More_Stuff/Permutation%20Anova/PermTestsAnova.html [access on May 28, 2012]), he described the algorithm of permutation test for a one-way nested design ANOVA by using R language. I followed this algorithm and made a R function to do this test.
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| # Copyright 2012 Chen-Pan Liao | |
| # This program is free software: you can redistribute it and/or modify | |
| # it under the terms of the GNU General Public License as published by | |
| # the Free Software Foundation, either version 2 of the License, or | |
| # any later version. | |
| # | |
| # This program is distributed in the hope that it will be useful, | |
| # but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| # GNU General Public License for more details. | |
| # | |
| # You should have received a copy of the GNU General Public License | |
| # along with this program. If not, see <http://www.gnu.org/licenses/>. | |
| # Author: Chen-Pan Liao | |
| # Date: May 28, 2012 | |
| # | |
| # This work is inspirated by Dr. David C. Howell, University of Vermont. | |
| # See Dr. Howell's webpage to learn more: | |
| # http://www.uvm.edu/~dhowell/StatPages/More_Stuff/ | |
| # Permutation%20Anova/PermTestsAnova.html | |
| nestedPermutationAnova <- function( | |
| dv, # Dependent variable | |
| treatment, # Treatment | |
| subject, # Experimental unit | |
| nreps = 1999 # Number of permutation | |
| ) { | |
| # initiation | |
| dv <- as.numeric(dv) | |
| treatment <- as.factor(treatment) | |
| subject <- as.factor(subject) | |
| nreps <- as.integer(nreps) | |
| subject <- as.factor(paste(subject,treatment,sep="_in_")) | |
| # rename subject as "subject_in_treatment" | |
| treatment.name <- levels(treatment) | |
| subject.name <- levels(subject) | |
| treatment.n <- nlevels(treatment) | |
| subject.n <- nlevels(subject) | |
| f.treatment <- numeric(nreps) | |
| f.subject <- numeric(nreps); | |
| # original model | |
| model.0 <- summary(aov(dv ~ treatment / subject)) | |
| f.subject.0 <- model.0[[1]][1,4] | |
| f.treatment.0 <- model.0[[1]][1,3] / model.0[[1]][2,3] | |
| # permutation | |
| for (i in 1:nreps) { | |
| # permutation for effect of subject | |
| dv.subject <- NULL | |
| for (j in 1:treatment.n){ | |
| dv.subject <- c( | |
| dv.subject, | |
| sample(dv[ treatment == treatment.name[j] ]) | |
| ) | |
| } | |
| model <- summary(aov(dv.subject ~ treatment / subject)) | |
| f.subject[i] <- model[[1]][1,4] | |
| # permutation for effect of treatment | |
| dv.treatment <- NULL | |
| subject.name.reorder <- sample(subject.name) | |
| for (j in 1:subject.n){ | |
| dv.treatment <- c( | |
| dv.treatment, | |
| dv[ subject == subject.name.reorder[j] ] | |
| ) | |
| } | |
| model <- summary(aov(dv.treatment ~ treatment / subject)) | |
| f.treatment[i] <- model[[1]][1,3] / model[[1]][2,3] | |
| } | |
| # p-value | |
| p.treatment <- (sum(f.treatment >= f.treatment.0)+1) / (nreps+1) | |
| p.subject <- (sum(f.subject >= f.subject.0)+1) / (nreps+1) | |
| # plot | |
| par(mfrow = c(1,2)) | |
| hist(f.treatment, breaks=40, xlab="Sudo f-value for treatment", main="") | |
| abline(v=f.treatment.0, lty=2) | |
| hist(f.subject, breaks=40, xlab="Sudo f-value for subject", main="") | |
| abline(v=f.subject.0, lty=2) | |
| # return | |
| return ( | |
| list( | |
| p.treatment = p.treatment, | |
| p.subject = p.subject, | |
| nreps = nreps | |
| ) | |
| ) | |
| } |
Example
dat <- read.csv(textConnection("
trt , unit , obs
1 , 1 , 11
1 , 1 , 9
1 , 1 , 9
1 , 2 , 8
1 , 2 , 7
1 , 2 , 6
1 , 3 , 8
1 , 3 , 10
1 , 3 , 11
2 , 4 , 11
2 , 4 , 8
2 , 4 , 7
2 , 5 , 10
2 , 5 , 14
2 , 5 , 12
2 , 6 , 9
2 , 6 , 10
2 , 6 , 8
"))
## traditional nested ANOVA
mod.2 <- aov(
obs ~ factor(trt) + Error(factor(unit)),
data = dat
)
summary(mod.2) # alternative
## permutation nested ANOVA
nestedPermutationAnova(dat$obs, dat$trt, dat$unit, 499)
