Skip to content

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

3 messages · Leo Gürtler, Daniel Malter, Andrew Robinson

Leo Gürtler
# 
Dear R-List,

I am interested in the Bayesian view on parameter estimation for
multilevel models and ordinary regression models. 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.

However, p(data_or_extreme|H0) is not really interesting for social
science research questions (psychology). Much more interesting is
p(H0|data). Is there a way or formula to calculate these probabilities
of the H0 (or another hypothesis) from lm-/lmer objects in R?

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.

The frequentist literature - of course - does not cover that topic.

Thanks a lot,
best,

leo g?rtler
Daniel Malter
# 
This is very opaque to me. But if H0 is a null hypothesis (i.e. a hypothesis
about one or several coefficients in your model), then you can test linear
or nonlinear restrictions of the coefficients. Because your coefficients are
derived using your data, it appears to me you get something like a
p(H0|data).


-------------------------
cuncta stricte discussurus
-------------------------

-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von Leo G?rtler
Gesendet: Thursday, December 25, 2008 1:52 PM
An: r-help at stat.math.ethz.ch
Betreff: [R] p(H0|data) for lm/lmer-objects R

Dear R-List,

I am interested in the Bayesian view on parameter estimation for multilevel
models and ordinary regression models. 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.

However, p(data_or_extreme|H0) is not really interesting for social science
research questions (psychology). Much more interesting is p(H0|data). Is
there a way or formula to calculate these probabilities of the H0 (or
another hypothesis) from lm-/lmer objects in R?

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.

The frequentist literature - of course - does not cover that topic.

Thanks a lot,
best,

leo g?rtler

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Andrew Robinson
# 
Dear Leo,
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.
I don't think that the last comment is necessarily relevant nor is it
necessarily true.
That's fine, but first you have to believe that the statement has
meaning.
See the books above.  Note that in order to do so, you will need to
nominate a prior distribution of some kind.
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