bootstrapping in regression

On Fri, 30 Jan 2009, Stephan Kolassa wrote:

Hi Thomas,

Thomas Mang schrieb:

I have a question here: I am not sure if I understand your 'fit  
the full
model ... to the permuted data set'. Am I correct to suppose that  
once the
residuals of the reduced-model fit have been permuted and added  
back to
the fitted values, the values obtained this way (fitted + permuted
residuals) now constitute the new y-values to which the full model  
is
fitted? Is that correct ?

It is. Look at section 2.2, "Permutation of Residuals under the  
Reduced Model" here:

Anderson, M. J. & Legendre, P. An empirical comparison of  
permutation methods for tests of partial regression coefficients in  
a linear model. Journal of Statistical Computation and Simulation,  
1999, 62, 271-303

Do you know if this procedure is also valid for a mixed-effects  
model ?

That's a good question... if you find out anything about this,  
please let me know.

There are various kinds of residuals in mixed effects models. But  
mostly they are not what you want.

What you need are the type of residuals used in the section on  
significance tests in Beran and Srivastava:


@article{beran1985bta,
 title={{BOOTSTRAP TESTS AND CONFIDENCE REGIONS FOR FUNCTIONS OF A  
COVARIANCE MATRIX1}},
 author={Beran, R. and Srivastava, M.S.},
 journal={The Annals of Statistics},
 volume={13},
 number={1},
 pages={95--115},
 year={1985}
}