[R] evaluation methods for logistic regression with proportion data

From: ahimsa campos arceiz <ahimsa_at_camposarceiz.com>
Date: Mon 26 Dec 2005 - 21:28:50 EST


Dear list-members,

I have made a logistic regression analysis of the spatial distribution of an ecological phenomenon (wildlife-caused crop damage). I divided the region into 5x5 km grids, and in each grid I have performed a number of questionnaires to asses the presence of crop damage in particular houses. As a result, my dependent variable is not a simple presence/ absence data but a proportion of positive responses (n of positive responses/ n of questionnaires) per grid.

I used glm to fit a suitable model (all the variable and model selection process is ok).

The problem comes once that I get the final model. Since my observed data has no real positive or negative (but proportion of positives) I cannot calculate specifity or sensitivity, and therefore (I think that) cannot use statistics like kappa or area under the curve ROC to evaluate the performance of my model.

Can anybody suggest a suitable method to evaluate the performance of this kind of "proportion data" model that can be implemented in R? Does any body know any alternative as elegant as the AUC ROC for this case?

Besides the internal evaluation, I am planning to use bootstrap resampling in order to produce "pseudo-independent" data to evaluate the performance of the model.

An example of how do my data look like:

       observed   predicted
         0.200   0.4079725
         0.556   0.5987730
         0.500   0.9140571
         0.857   0.8878290
         0.875   0.7845368
         1.000   0.8575587
         1.000   0.9406087
         0.778   0.5861066
         0.600   0.6204616
         1.000   0.8585725
         0.000   0.2949169
         0.100   0.1291246
         0.444   0.7627612

observed = proportion of positive responses to crop damage questionnaires in a 25 km2 grid
predicted = values produced by the final glm(binomial) model on the same dataset as used to develop the model

Thanks a lot in advance for any suggestion

Ahimsa

Ahimsa Campos Arceiz
The University Museum,
The University of Tokyo

Hongo 7-3-1, Bunkyo-ku,
Tokyo 113-0033
phone +81-(0)3-5841-2824
cell +81-(0)80-5402-7702 
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