Writing an exact logistic regression routine is extremely difficult.
Moreover, because the algorithms depend on solving a number of complex permutations,
unless the algorithms are extremely efficient, the solution of a logistic
regression model may take an inordinate amount of time.
Cytel's LogiXact is the only software I know of that handles exact logistic
regression. LogiXact estimates exact Poisson regression models as well. By
exact it is meant that exact p-values are calculated; they are not based on
asymptotic methods.
Even using LogiXact, which is state-of-the-art, only relatively small models
can be estimated. Fortunately LogiXact -- as does StatXact, it
nonoparametric statistics companion -- allows users to estimate p-values based on Monte
Carlo methods when the data is too complex for the exact procedures.
LogiXact is best used for models with few categorical predictors (2 to 4),
which are either binary or indicator variables or categorical variables
limited to 3 or perhaps 4 levels. Larger models usually have to be estimated using
Monte Carlo -- which typically results in p-values close to those produced by
exact methods.
Stata may someday offer a variety of nonparametric exact statistics -- I
certainly hope so (especially since SAS and SPSS have recently "borrowed"
Cytel's published code to offer exact statistics capabilities), or even exact
statsitics for normal or Gaussian based tests/models (T-tests, ANOVA, OLS), but I
suspect that due to the amount of processing involved that they won't deal
with exact logistic and poisson models very soon. And given the limitations of
LogXact for such models, I do not believe it would be a worthwhile enterprise
until computing power has greatly advanced. By the way, XPro is the only
software package that handles exact statististics for Gaussian-based models (as
above).
The American Statistician has published a number of reviews over teh past
two years of exact statistics software. A summary review of all packages is
planned for the November issue. For those interested in this area of statistics
I recommend taking a look at these articles.
Joe HIlbe
=============================================
Dear Listers,
I wonder if there is a way to estimate exact logistic regression by now.
I have found a discussion that took place about one year ago ("Cytel
Challenge")
where Joseph Hilbe mentioned that such a procedure is not yet available.
My analysis is dealing with a data set that does not behave very well -
data
are sparse, n is small and the sample distribution is skewed. I build
my inference by way of contingency tables, however I would like to
run a logit model (dep.var.: coded nominal 0/1, indep.vars.: ordered
categorical coded 1/2/3) to check strength and direction of association.
I do not trust the LR chi2 statistics and standard errors, as they
rely on asymptotic theory which I feel is inappropriate for my data set.
Any suggestions as to how Stata might implement exact logistic
regression for this case? I have though about running a GLM, however
I do not know if this is appropriate for small sample sizes.
Best regards,
Marcus
___________________________________
Marcus Matthias Keupp, Dipl.-Kfm.
Research Associate
University of St. Gallen
Institute of Technology Management
Dufourstrasse 40a
CH-9000 St. Gallen / Switzerland
Tel. +41 (0)71 224 7236
Fax +41 (0)71 224 7301
www.item.unisg.ch
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