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

[nikolay12]

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).

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