Evaluate Log Likelihood for non-homothetic Logit Model
llnhlogit evaluates log-likelihood for the Non-homothetic Logit model.
llnhlogit(theta, choice, lnprices, Xexpend)
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 |
Non-homothetic logit model, Pr(i) = exp(tau v_i) / sum_j exp(tau v_j)
v_i = alpha_i - e^{kappaStar_i}u^i - lnp_i
tau is the scale parameter of extreme value error distribution.
u^i solves u^i = psi_i(u^i)E/p_i.
ln(psi_i(U)) = alpha_i - e^{kappaStar_i}U.
ln(E) = gamma'Xexpend.
Structure of theta vector:
alpha: p x 1 vector of utility intercepts.
kappaStar: p x 1 vector of utility rotation parms expressed on natural log scale.
gamma: k x 1 – expenditure variable coefs.
tau: 1 x 1 – logit scale parameter.
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 Chapter 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1
N=1000; p=3; k=1 theta = c(rep(1,p), seq(from=-1,to=1,length=p), rep(2,k), 0.5) lnprices = matrix(runif(N*p), ncol=p) Xexpend = matrix(runif(N*k), ncol=k) simdata = simnhlogit(theta, lnprices, Xexpend) ## evaluate likelihood at true theta llstar = llnhlogit(theta, simdata$y, simdata$lnprices, simdata$Xexpend)
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