[R] Likelihood Function for Multinomial Logistic Regression and its partial derivatives

[markleeds at verizon.net]

   Hi: John Fox's CAR book has some very nice examples of how the multinomial
   likelihood  is  estimated  computationally speaking. But you mentioned
   multilevel earlier which sounds more complex ?

   On Aug 2, 2009, nikolay12 <nikolay12 at gmail.com> wrote:

     Thanks a lot. The info about computing the gradient will be helpful.
     I admit that I am somewhat confused about the likelihood function itself.
     It
     is often said that you need to set a reference category. However, I found
     two different implementations in Matlab for which setting the reference
     category  is  not  really  obvious. Thus I wanted to find a single,
     indisputable
     implementation of the likelihood function for multinomous logistic
     regression in R. Can't believe there is no such available.
     Nick
     Ravi Varadhan wrote:
     >
     > Hi,
     >
     >  Providing  the  gradient  function  is  generally a good idea in
     optimization;
     > however, it is not necessary. Almost all optimization routines will
     > compute this using a simple finite-difference approximation, if they are
     > not user-specified. If your function is very complicated, then you are
     > more likely to make a mistake in computing analytic gradient, although
     > many optimization routines also provide a check to see if the gradient
     is
     > correctly specified or not. But you can do this yourself using the
     `grad'
     > function in "numDeriv" package.
     >
     > Hope this is helpful,
     > Ravi.
     >
     > ____________________________________________________________________
     >
     > Ravi Varadhan, Ph.D.
     > Assistant Professor,
     > Division of Geriatric Medicine and Gerontology
     > School of Medicine
     > Johns Hopkins University
     >
     > Ph. (410) 502-2619
     > email: [1]rvaradhan at jhmi.edu
     >
     >
     > ----- Original Message -----
     > From: nikolay12 <[2]nikolay12 at gmail.com>
     > Date: Sunday, August 2, 2009 3:04 am
     > Subject: [R] Likelihood Function for Multinomial Logistic Regression and
     > its partial derivatives
     > To: [3]r-help at r-project.org
     >
     >
     >> Hi,
     >>
     >> I would like to apply the L-BFGS optimization algorithm to compute
     >> the MLE
     >> of a multilevel multinomial Logistic Regression.
     >>
     >> The likelihood formula for this model has as one of the summands the
     >> formula
     >> for computing the likelihood of an ordinary (single-level)
     >> multinomial logit
     >> regression. So I would basically need the R implementation for this
     >> formula.
     >> The L-BFGS algorithm also requires computing the partial derivatives
     >> of that
     >> formula in respect to all parameters. I would appreciate if you can
     >> point me
     >> to existing implementations that can do the above.
     >>
     >> Nick
     >>
     >> PS. The long story for the above:
     >>
     >> My data is as follows:
     >>
     >> - a vector of observed values (lenght = D) of the dependent multinomial
     >> variable each element belonging to one of N levels of that variable
     >>
     >> - a matrix of corresponding observed values (O x P) of the independent
     >> variables (P in total, most of them are binary but also a few are
     >> integer-valued)
     >>
     >> - a vector of current estimates (or starting values) for the Beta
     >> coefficients of the independent variables (length = P).
     >>
     >> This data is available for 4 different pools. The partially-pooled
     model
     >> that I want to compute has as a likelihood function a sum of several
     >> elements, one being the classical likelihood function of a
     >> multinomial logit
     >> regression for each of the 4 pools.
     >>
     >> This is the same model as in Finkel and Manning "Hierarchical Bayesian
     >> Domain Adaptation" (2009).
     >>
     >> --
     >> View this message in context:
     >> Sent from the R help mailing list archive at Nabble.com.
     >>
     >> ______________________________________________
     >> [4]R-help at r-project.org mailing list
     >>
     >> PLEASE do read the posting guide
     >> and provide commented, minimal, self-contained, reproducible code.
     >
     > ______________________________________________
     > [5]R-help at r-project.org mailing list
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     > PLEASE do read the posting guide
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     > and provide commented, minimal, self-contained, reproducible code.
     >
     >
     --
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     ession-and-its-partial-derivatives-tp24772731p24781298.html
     Sent from the R help mailing list archive at Nabble.com.
     ______________________________________________
     [9]R-help at r-project.org mailing list
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     and provide commented, minimal, self-contained, reproducible code.

References

   1. mailto:rvaradhan at jhmi.edu
   2. mailto:nikolay12 at gmail.com
   3. mailto:r-help at r-project.org
   4. mailto:R-help at r-project.org
   5. mailto:R-help at r-project.org
   6. https://stat.ethz.ch/mailman/listinfo/r-help
   7. http://www.R-project.org/posting-guide.html
   8. http://www.nabble.com/Likelihood-Function-for-Multinomial-Logistic-Regression-and-its-partial-derivatives-tp24772731p24781298.html
   9. mailto:R-help at r-project.org
  10. https://stat.ethz.ch/mailman/listinfo/r-help
  11. http://www.R-project.org/posting-guide.html