From: John Fox <jfox_at_mcmaster.ca>

Date: Tue, 22 May 2007 09:11:54 -0400

John Fox, Professor

Department of Sociology

McMaster University

Hamilton, Ontario

Canada L8S 4M4

905-525-9140x23604

http://socserv.mcmaster.ca/jfox

R-help_at_stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 22 May 2007 - 13:16:52 GMT

Date: Tue, 22 May 2007 09:11:54 -0400

Dear Wolfgang,

I agree that it's preferable to compute the two-sided p-value without assuming symmetry. Another, equivalent, way of thinking about this is to use t^2 for the two-sided test in place of t.

BTW, the formula used in my appendix (for the one-sided p-value) is from Davison and Hinkley, I believe, and differs trivially from the one in Efron and Tibshirani.

Regards,

John

John Fox, Professor

Department of Sociology

McMaster University

Hamilton, Ontario

Canada L8S 4M4

905-525-9140x23604

http://socserv.mcmaster.ca/jfox

> -----Original Message-----

*> From: r-help-bounces_at_stat.math.ethz.ch
**> [mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of
**> Viechtbauer Wolfgang (STAT)
**> Sent: Monday, May 21, 2007 10:41 AM
**> To: r-help_at_stat.math.ethz.ch
**> Subject: [R] Boostrap p-value in regression [indirectly related to R]
**>
**> Hello All,
**>
**> Despite my preference for reporting confidence intervals, I
**> need to obtain a p-value for a hypothesis test in the context
**> of regression using bootstrapping. I have read John Fox's
**> chapter on bootstrapping regression models and have consulted
**> Efron & Tibshirani's "An Introduction to the Bootstrap" but I
**> just wanted to ask the experts here for some feedback to make
**> sure that I am not doing something wrong.
**>
**> Let's take a simplified example where the model includes one
**> independent variable and the idea is to test H0: beta1 = 0
**> versus Ha: beta1 != 0.
**>
**> ########################################################
**>
**> ### generate some sample data
**>
**> n <- 50
**> xi <- runif(n, min=1, max=5)
**> yi <- 0 + 0.2 * xi + rnorm(n, mean=0, sd=1)
**>
**> ### fit simple regression model
**>
**> mod <- lm(yi ~ xi)
**> summary(mod)
**> b1 <- coef(mod)[2]
**> t1 <- coef(mod)[2] / coef(summary(mod))[2,2]
**>
**> ### 1000 bootstrap replications using (X,Y)-pair resampling
**>
**> t1.star <- rep(NA,1000)
**>
**> for (i in 1:1000) {
**>
**> ids <- sample(1:n, replace=TRUE)
**> newyi <- yi[ids]
**> newxi <- xi[ids]
**> mod <- lm(newyi ~ newxi)
**> t1.star[i] <- ( coef(mod)[2] - b1) / coef(summary(mod))[2,2]
**>
**> }
**>
**> ### get bootstrap p-value
**>
**> hist(t1.star, nclass=40)
**> abline(v=t1, lwd=3)
**> abline(v=-1*t1, lwd=3)
**> 2 * mean( t1.star > abs(t1) )
**>
**> ########################################################
**>
**> As suggested in the chapter on bootstrapping regression
**> models by John Fox, the bootstrap p-value is 2 times the
**> proportion of bootstrap t-values (with b1 subtracted so that
**> we get the distribution under H0) larger than the absolute
**> value of the actual t-value observed in the data.
**>
**> Doesn't this assume that the bootstrap sampling distribution
**> is symmetric? And if yes, would it then not be more reasonable to
**> calculate:
**>
**> mean( abs(t1.star) > abs(t1) )
**>
**> or in words: the number of bootstrap t-values that are more
**> extreme on either side of the bootstrap distribution than the
**> actual t-value observed?
**>
**> Any suggestions or comments would be appreciated!
**>
**> --
**> Wolfgang Viechtbauer
**> Department of Methodology and Statistics University of
**> Maastricht, The Netherlands http://www.wvbauer.com
**>
**> ______________________________________________
**> R-help_at_stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide
**> http://www.R-project.org/posting-guide.html
**> and provide commented, minimal, self-contained, reproducible code.
*

>

R-help_at_stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 22 May 2007 - 13:16:52 GMT

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