[R] bootstrapping in regression

[Chuck Cleland]

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

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-- 
Chuck Cleland, Ph.D.
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