R help - Nov 2005 - permutation test for linear models with continuous covariates

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

"anders superanders" <andersdetermigigen at hotmail.com> writes:
> 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.
Er, what would you permute? For an interaction test like this (notice
by the way that "*" in your model formula does not mean what you think
it does) I do not think a permutation test exists.  You could try
bootstrapping to get an improved approximation the distribution of the
interaction term.


-- 
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~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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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