[R] logistic discrimination: which chance performance??

Hello,
I am using logistic discriminant analysis to check whether a known
classification Yobs can be predicted by few continuous variables X.

What I do is to predict class probabilities with multinom() in nnet(),
obtaining a predicted classification Ypred and then compute the percentage
P(obs) of objects classified the same in Yobs and Ypred.

My problem now is to figure out whether P(obs) is significantly higher
than
chance.

I opted for a crude permutation approach: compute P(perm) over 10000
random
permutations of Yobs (i.e., refit the multinom() model 10000 times
randomly
permuting Yobs) and consider P(obs) as significantly higher than chance if
higher than the 95th percentile of the P(perm) distribution.

Now, the problem is that the mode of P(perm) is always really close to
P(obs), e.g., if P(obs)=1 (perfect discrimination) also the most likely
P(perm) value is 1!!!

I figured out that this is due to the fact that, with my data, randomly
permuted classifications are highly likely to strongly agree with the
observed classification Yobs, but, probably since my machine learning
background is almost 0, I am kind of lost about how to proceed at this
point.

I would greatly appreciate a comment on this.

Thanks
Bruno

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bruno L. Giordano, Ph.D.
CIRMMT
Schulich School of Music, McGill University
555 Sherbrooke Street West
Montr?al, QC H3A 1E3
Canada
http://www.music.mcgill.ca/~bruno/

______________________________________________
R-help at stat.math.ethz.ch 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.

Bruno L. Giordano wrote:
Well,
If posting a possible solution to one's own problem is not part of the
netiquette of this list please correct me.

Following Titus et al. (1984) one might use Cohen's kappa to have a
chance-corrected measure of agreement between the original and reproduced
classification:

Kappa() in library vcd
kappa2() in library irr
ckappa() in library psy
cohen.kappa() in library concord......

Bruno

Kimberly Titus; James A. Mosher; Byron K. Williams (1984), Chance-corrected
Classification for Use in Discriminant Analysis: Ecological Applications,
American Midland Naturalist, 111(1),1-7.


----- Original Message -----
From: "Bruno L. Giordano" <[email protected]>
To: <[email protected]>
Sent: Thursday, August 10, 2006 6:18 PM
Subject: [R] logistic discrimination: which chance performance??

______________________________________________
R-help at stat.math.ethz.ch 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.