permutation test for linear models with continuous covariates
What do you want to test? To test H0: Y is independent of all X's, you can permute Y. To test H0: a particular X does not contribute to predicting Y, conditional on the other X's you have to be careful. If you permute that X, the size is wrong; the type I error can be nearly 50%, because you've lost the correlation between that X and others. I don't know of a suitable permutation test in general for testing individual X's. S+Resample has a permutationTest() function that lets you specify which columns to permute. The Canty/Davison/Hinkley "boot" library (in R or S-PLUS) offers "permutation" as one of the options for sampling in the boot() function; to use this you would specify the Y variable as the data set and pass the X's separately to the statistic. Tim Hesterberg
Hi I was wondering if there is a permutation test available in R for linear models with continuous dependent covariates. I want to do a test like the one shown here. bmi<-rnorm(100,25) x<-c(rep(0,75),rep(1,25)) y<-rnorm(100)+bmi^(1/2)+rnorm(100,2)*x+bmi*x H0<-lm(y~1+x+bmi) H1<-lm(y~1+x+bmi+x*bmi) anova(H0,H1) summary(lm(y~1+x+bmi)) But I want to use permutation testing to avoid an inflated p-value due to a y that is not totally normal distributed and I do not want to log transform y. Thanks Anders
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