Evaluate Log Likelihood for Multinomial Logit Model
llmnl evaluates log-likelihood for the multinomial logit model.
llmnl(beta, y, X)
beta |
k x 1 coefficient vector |
y |
n x 1 vector of obs on y (1,..., p) |
X |
n*p x k design matrix (use |
Let μ_i = X_i beta, then Pr(y_i=j) = exp(μ_{i,j}) / ∑_k exp(μ_{i,k}).
X_i is the submatrix of X corresponding to the
ith observation. X has n*p rows.
Use createX to create X.
Value of log-likelihood (sum of log prob of observed multinomial outcomes).
This routine is a utility routine that does not check the input arguments for proper dimensions and type.
Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.
For further discussion, see Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1
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