[R] Logistic Regression with 9 classes

[Frank E Harrell Jr]

On Sun, 01 Dec 2002 19:43:22 -0600
Paul Johnson <pauljohn at ku.edu> wrote:

> Hope this helps:
> 
> Your approach depends on your statistical theory.
> 
> If the 9 categories are ordered, the ordinal logistic (or probit) model 
> is called for.  The first publication I know of that proposed it was R D 
> McKelvey and W Zavoina.   A statistical model for the analysis of 
> ordinal level dependent variables.Journal of Mathematical Sociology, 
> 4:103-120, 1975.

One small correction Paul.  An earlier paper developing the proportional odds model is

@ARTICLE{wal67,
  author = {Walker, S. H. and Duncan, D. B.},
  year = 1967,
  title = {Estimation of the probability of an event as a function of several
          independent variables},
  journal = Biometrika,
  volume = 54,
  pages = {167-178},
  annote = {logistic model; ordinal logistic model}
}

Frank

> 
> The idea is that the probability of falling into one category depends on
> z=XB+e,
> where e is either logistic or Normal, depending on your taste. THe 
> resulting estimates give you estimates of B as well as 8 "thresholds" 
> which divide the "z scale" into sections and relate to the predicted 
> outcome for the categories.
> 
> For that, the MASS packages has polr.
> 
> 
> If the 9 categories are unordered, then some other statistical model 
> altogether is needed. One I know of is often called a multinomial model, 
> where you set one category as the baseline and then estimate the impact 
> of the variables to differentiate them from the baseline.  For 9 
> cagegories, you'd end up with 8 models, of the sort
> 
> ln(Pj/P0) = Xbj, j=1,...8.
> 
> In MASS, the function multinom is for that purpose, but I have not tried it.
> 
> Luis Silva wrote:
> > Hello!
> > 
> > I need to classify a data set with 19 variables and 9 classes 
> > using Logistic Regression(on R).
> > I know that when we have only 2 classes we can use glm() to 
> > how can I do a classification task with Logistic Regression on 
> > a data set with 9 classes! 
> > Does anybody know how can I estimate these coefficients (of a 
> > model with 9 classes) on R?
> > 
> > Thank you!
> > Janete
> >
> 
> 
> -- 
> Paul E. Johnson                       email: pauljohn at ukans.edu
> Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
> University of Kansas                  Office: (785) 864-9086
> Lawrence, Kansas 66045                FAX: (785) 864-5700
> 
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-- 
Frank E Harrell Jr              Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine  http://hesweb1.med.virginia.edu/biostat