Re: [R] permutation test for linear models with continuous covariates

From: Tim Hesterberg <timh_at_insightful.com>
Date: Tue 13 Dec 2005 - 06:52:24 EST

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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