llnhlogit: Evaluate Log Likelihood for non-homothetic Logit Model
Description
llmnp evaluates log-likelihood for the Non-homothetic Logit model.
Usage
llnhlogit(theta, choice, lnprices, Xexpend)
Arguments
theta
parameter vector (see details section)
choice
n x 1 vector of choice (1, ..., p)
lnprices
n x p array of log-prices
Xexpend
n x d array of vars predicting expenditure
Value
value of log-likelihood (sum of log prob of observed multinomial outcomes).
concept
multinomial logit
non-homothetic utility
Warning
This routine is a utility routine that does not check the
input arguments for proper dimensions and type.
Details
Non-homothetic logit model with: $ln(psi_i(U)) = alpha_i - e^{k_i}U$
Structure of theta vector
alpha: (p x 1) vector of utility intercepts.
k: (p x 1) vector of utility rotation parms.
gamma: (k x 1) -- expenditure variable coefs.
tau: (1 x 1) -- logit scale parameter.
References
For further discussion, see Bayesian Statistics and Marketing
by Allenby, McCulloch, and Rossi,Chapter 4.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html