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: rvarad...@jhmi.edu ----- Original Message ----- From: nikolay12 <nikola...@gmail.com> Date: Sunday, August 2, 2009 3:04 am Subject: [R] Likelihood Function for Multinomial Logistic Regression and its partial derivatives To: r-help@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. > > ______________________________________________ > R-help@r-project.org mailing list > > PLEASE do read the posting guide > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
