On 1/29/2009 11:43 AM, Thomas Mang wrote: > Hi, > > Please apologize if my questions sounds somewhat 'stupid' to the trained > and experienced statisticians of you. Also I am not sure if I used all > terms correctly, if not then corrections are welcome. > > I have asked myself the following question regarding bootstrapping in > regression: > Say for whatever reason one does not want to take the p-values for > regression coefficients from the established test statistics > distributions (t-distr for individual coefficients, F-values for > whole-model-comparisons), but instead apply a more robust approach by > bootstrapping. > > In the simple linear regression case, one possibility is to randomly > rearrange the X/Y data pairs, estimate the model and take the > beta1-coefficient. Do this many many times, and so derive the null > distribution for beta1. Finally compare beta1 for the observed data > against this null-distribution. > > What I now wonder is how the situation looks like in the multiple > regression case. Assume there are two predictors, X1 and X2. Is it then > possible to do the same, but just only rearranging the values of one > predictor (the one of interest) at a time? Say I want again to test > beta1. Is it then valid to many times randomly rearrange the X1 data > (and keeping Y and X2 as observed), fit the model, take the beta1 > coefficient, and finally compare the beta1 of the observed data against > the distributions of these beta1s ? > For X2, do the same, randomly rearrange X2 all the time while keeping Y > and X1 as observed etc. > Is this valid ? > > Second, if this is valid for the 'normal', fixed-effects only > regression, is it also valid to derive null distributions for the > regression coefficients of the fixed effects in a mixed model this way? > Or does the quite different parameters estimation calculation forbid > this approach (Forbid in the sense of bogus outcome) ? > > Thanks, Thomas
Have a look at the following document by John Fox: http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-bootstrapping.pdf > ______________________________________________ > R-help@r-project.org 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. -- Chuck Cleland, Ph.D. NDRI, Inc. (www.ndri.org) 71 West 23rd Street, 8th floor New York, NY 10010 tel: (212) 845-4495 (Tu, Th) tel: (732) 512-0171 (M, W, F) fax: (917) 438-0894 ______________________________________________ R-help@r-project.org 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.
