[R] p(H0|data) for lm/lmer-objects R

[Andrew Robinson]

Dear Leo,

> Dear R-List,
> 
> I am interested in the Bayesian view on parameter estimation for multilevel
> models and ordinary regression models. 

You might find Gelman & Hill's recent book to be good reading, and
there is a book in the Use-R series that focuses on using R to perform
Bayesian analyses.  

> AFAIU traditional frequentist p-values they give information about
> p(data_or_extreme|H0).  AFAIU it further, p-values in the Fisherian
> sense are also no alpha/type I errors and therefor give no
> information about future replications.

I don't think that the last comment is necessarily relevant nor is it
necessarily true.

> However, p(data_or_extreme|H0) is not really interesting for social science
> research questions (psychology). Much more interesting is
> p(H0|data). 

That's fine, but first you have to believe that the statement has
meaning.

> Is there a way or formula to calculate these probabilities of the H0
> (or another hypothesis) from lm-/lmer objects in R?

See the books above.  Note that in order to do so, you will need to
nominate a prior distribution of some kind.

> Yes I know that multi-level modeling as well as regression can be done in a
> purely Bayesian way. However, I am not capable of Bayesian statistics,
> therefor I ask that question. I am starting to learn it a little bit.

No offense, but it sounds to me like you want to have the Bayesian
omelette without breaking the Bayesian eggs ;).  Certain kinds of
multi-level models are mathematically identical to certain kinds of
Empirical Bayes models, but that does not make them Bayesian (despite
what some people say).  I caution against your implied goal of
obtaining Bayesian statistics without performing a Bayesian analysis.
 
Good luck,

Andrew

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/