Many thanks for your messages.
I will take a look at the survey package.
I was concerned with the issues raised by Cramer (1999) in Predictive
performance of the binary logit model in unbalanced samples.
In this particular case, misclassification costs are much higher for
the smaller group (defaults) than for the larger group (non-defaults).
However, I have no specific guidelines for how much higher. If I
understood correctly, using sampling weights would help improve
accuracy on the smaller group and, at least, I would be able to
explain the rationale for the different weights.
To cite properly, I was referring to lrm in the Design package
(Harrel, 2008). Sorry to have intruded the list with such question,
but - once again - thank you for your answers.
On Wed, Apr 27, 2011 at 7:29 AM, Prof Brian Ripley
rip...@stats.ox.ac.uk wrote:
On Wed, 27 Apr 2011, peter dalgaard wrote:
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=1, 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.
There are circumstances where it might. It is quite common in pattern
recognition for the proportions in the training set to not reflect the
population. And if the misclassification costs are asymmetric, you may want
to weight the fit.
The case I encountered was SGA births. By definition there are about 10%
'successes', but false negatives are far more important than false positives
(or one would simply predict all births as normal). This means that you
want accurate estimation of probabilities in the right tail of the
population distribution, and plug-in estimation of logistic regression is
biased. One of many ways to reduce that bias is to re-weight the training
set so the estimated probabilities of marginal cases are in the middle of
the range.
Note that logistic regression is not normally fitted by 'weighted least
squares' (not even by 'lrm' from some unstated package).
This is not a list for tutorials in advanced statistics, but one reference
is my Pattern Recognition and Neural Networks book.
--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd@cbs.dk Priv: pda...@gmail.com
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--
Brian D. Ripley, rip...@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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