R help - Oct 2009 - Bootstrapping confidence intervals

Hello,
 
We are a group of PhD students working in the field of toxicology. Several
of us have small data sets with N=10-15. Our research is mainly about the
association between an exposure and an effect, so preferrably we would like
to use linear regression models. However, most of the time our data do not
fulfill the model assumptions for linear models ( no normality of y-varible
achieved even after log transformation). We have been told that we can use
bootstrapping to derive a confidence interval for the original parameter
estimate ( Beta 1)  from the linear regression model and if the confidence
interval do not include 0, we can "trust" the result from the original
linear model ( of couse only if a scatter plot of the variables looks ok).
What is your opinion about this method? Is that ok?  I have problems
understanding how it is possible to resample several times from an already
poor distribution ( that do not fulfill the model assumptions for linear
models) to achieve a confidence interval that "validates" the use of
these
linear models? I would really appriciate a simple explanation about this!
 
Many thanks,
 
Charlotta Rylander

	[[alternative HTML version deleted]]

John Fox has a nice explanation here:
http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-bootstrapping.pdf

-Ista

On Wed, Oct 21, 2009 at 6:38 AM, Charlotta Rylander <zcr at nilu.no>
wrote:
> Hello,
>
> We are a group of PhD students working in the field of toxicology. Several
> of us have small data sets with N=10-15. Our research is mainly about the
> association between an exposure and an effect, so preferrably we would like
> to use linear regression models. However, most of the time our data do not
> fulfill the model assumptions for linear models ( no normality of y-varible
> achieved even after log transformation). We have been told that we can use
> bootstrapping to derive a confidence interval for the original parameter
> estimate ( Beta 1) ?from the linear regression model and if the confidence
> interval do not include 0, we can "trust" the result from the
original
> linear model ( of couse only if a scatter plot of the variables looks ok).
> What is your opinion about this method? Is that ok? ?I have problems
> understanding how it is possible to resample several times from an already
> poor distribution ( that do not fulfill the model assumptions for linear
> models) to achieve a confidence interval that "validates" the use
of these
> linear models? I would really appriciate a simple explanation about this!
>
> Many thanks,
>
> Charlotta Rylander
>
> ? ? ? ?[[alternative HTML version deleted]]
>
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>


-- 
Ista Zahn
Graduate student
University of Rochester
Department of Clinical and Social Psychology
http://yourpsyche.org