[R] logistic regression: wls and unbalanced samples

[Andre Guimaraes]

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
<ripley at 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=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.
>
> 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.mes at cbs.dk  Priv: PDalgd at gmail.com
>>
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>
> --
> Brian D. Ripley,                  ripley at 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