[R] Logistic regression coef. Was: If this is should be posted elsewhere, please advise

[Peter Dalgaard]

Well, in principle there are general stats lists and newsgroups, and
this is not specifically an R question. However, people around here
have been known to contribute information about statistical substance
from time to time. You're still not excused for not using a meaningful
subject line though...

roy wilson <rwilson+ at pitt.edu> writes:

> Hi,
> 
> I am puzzled by the relationship between the p-values asociated with
> the coefficients of a univariate logistic regression involving
> categorical variables and the p-value I get from Fisher's exact test
> of the associated 2 x 2 contingency table.
> 
> (1) The 2-sided p-value for the table is ~ 0.0015, whereas the p-value
> for the independent is 0.101 and the p-value for the intercept is
> ~0.56.

The immediate conjecture is that you have become yet another victim of
the Hauck-Donner effect (an exact reference was given a week or so
ago, so use the list archives). The Wald tests given by dividing
coefficients with their formal s.e. can be badly misleading if you are
far from satisfying the requirements for asymptotic theory. This is
especially bad in cases where the OR is 0 or infinite so that the
glm() fit is divergent. 

You might try drop1(yourfit,test="Chisq") and see if the likelihod
ratio test for the independent is not at least somewhat closer to the
Fisher test.

> 
> (2) I know the the coefficient for the independent is the ln(OR)
> (assuming I recall correctly). Most accounts I've seen ignore the
> intercept, say it's hard to interpret, or give an interpretation (with
> respect to the dataset as a single group) that I can't square with the
> interpretation of beta[1].

In R it is (normally) the log-odds of the baseline group. That is,
provided you are using treatment contrasts.

> Thanks for help for redirection.
> 
> 
> 
> -- 
> Roy Wilson
> Learning Research Development Center
> University of Pittsburgh
> webpage: www.pitt.edu/~rwilson
> email: rwilson at pitt.edu
> 
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-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907