Tom Backer Johnsen wrote:
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.
There is a very basic difference between bootstrapping and random
permutations. What you are suggesting is to shuffle values between
cases or rows in the frame. That amounts to a variant of a permutation
test, not a bootstrap.
What you do in a bootstrap test is different, you regard your sample as
a population and then sample from that population (with replacement),
normally by extracting a large number of random samples of the same size
as the original sample and do the computations for whatever you are
interested in for each sample.
In other words, with bootstrapping, the pattern of values within each
case or row is unchanged, and you sample complete cases or rows. With a
permutation test you keep the original sample of cases or rows, but
shuffle the observations on the same variable between cases or rows.
Have a look at the 'boot' package.
Tom
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
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| Tom Backer Johnsen, Psychometrics Unit, Faculty of Psychology |
| University of Bergen, Christies gt. 12, N-5015 Bergen, NORWAY |
| Tel : +47-5558-9185 Fax : +47-5558-9879 |
| Email : bac...@psych.uib.no URL : http://www.galton.uib.no/ |
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