llnhlogit {bayesm} R Documentation

## Evaluate Log Likelihood for non-homothetic Logit Model

### Description

`llnhlogit` 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

### Details

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

Value of log-likelihood (sum of log prob of observed multinomial outcomes).

### Warning

This routine is a utility routine that does not check the input arguments for proper dimensions and type.

### Author(s)

Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.

### References

For further discussion, see Chapter 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1

`simnhlogit`

### Examples

```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)
```

[Package bayesm version 3.1-4 Index]