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Re: st: Exact logistic regression


From   Jhilbe@aol.com
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Exact logistic regression
Date   Mon, 13 Jun 2005 14:37:17 EDT

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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