R help - Apr 2011 - logistic regression: wls and unbalanced samples

Greetings from Rio de Janeiro, Brazil.

I am looking for advice / references on binary logistic regression
with weighted least squares (using lrm & weights), on the following
context:

1) unbalanced sample (n0=10000, n1=700);
2) sampling weights used to rebalance the sample (w0=1, w1=14.29); e
3) after modelling, adjust the intercept in order to reflect the
expected % of 1?s in the population (e.g., circa 7%, as opposed to
50%).

I have identified references that deal with the last point, but no
conclusive article or book dealing with this specific use of weights
in unbalaced samples.

The area under the ROC is about 0.70, and the estimated probabilities
are close to the frequencies of 1?s in different ranges, which looks
satisfactory. Hosmer & Lemeshow?s test is not significant, as
expected.

Can someone comment on the adopted strategy, or suggest some specific
bibliography that might address the issue of weights and unbalanced
samples in logistic regression?

Thanks in advance,

Andr? Guimar?es

On Apr 27, 2011, at 00:22 , Andre Guimaraes wrote:
> Greetings from Rio de Janeiro, Brazil.
> 
> I am looking for advice / references on binary logistic regression
> with weighted least squares (using lrm & weights), on the following
> context:
> 
> 1) unbalanced sample (n0=10000, n1=700);
> 2) sampling weights used to rebalance the sample (w0=1, w1=14.29); e
> 3) after modelling, adjust the intercept in order to reflect the
> expected % of 1?s in the population (e.g., circa 7%, as opposed to
> 50%).
??

If the proportion of 1 in the population is about 7%, how exactly is the sample
"unbalanced". I don't see a reason to use weights at all if the
sample is representative of the population. The opposite situation, where the
sample is balanced (e.g. case-control), the population not, and you are
interested in the population values, _that_ might require weighting, with some
care because case weighting and sample weighting are two different things so the
s.e. will be wrong. That sort of stuff handled by the survey package.

However what you seem to be doing is to create results for an artificial 50/50
population, then project back to the population you were sampling from all
along. I don't think this makes sense at all.

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com