llmnl: Evaluate Log Likelihood for Multinomial Logit Model
Description
llmnl evaluates log-likelihood for the multinomial logit model.
Usage
llmnl(y, X, beta)
Arguments
y
n x 1 vector of obs on y (1,..., p)
X
n*p x k Design matrix (use createX to make)
beta
k x 1 coefficient vector
Value
value of log-likelihood (sum of log prob of observed multinomial outcomes).
concept
multinomial logit
likelihood
Warning
This routine is a utility routine that does not check the
input arguments for proper dimensions and type.
Details
Let $mu_i=X_i \beta$, then $Pr(y_i=j) = exp(mu_{i,j})/\sum_kexp(mu_{i,k})$.
$X_i$ is the submatrix of X corresponding to the
ith observation. X has n*p rows.
Use createX to create X.
References
For further discussion, see Bayesian Statistics and Marketing
by Allenby, McCulloch, and Rossi.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html