llmnp {bayesm} R Documentation

## Evaluate Log Likelihood for Multinomial Probit Model

### Description

`llmnp` evaluates the log-likelihood for the multinomial probit model.

### Usage

`llmnp(beta, Sigma, X, y, r)`

### Arguments

 `beta ` k x 1 vector of coefficients `Sigma` (p-1) x (p-1) covariance matrix of errors `X ` n*(p-1) x k array where X is from differenced system `y ` vector of n indicators of multinomial response (1, ..., p) `r ` number of draws used in GHK

### Details

X is (p-1)*n x k matrix. Use `createX` with `DIFF=TRUE` to create X.

Model for each obs: w = Xbeta + e with e ~ N(0,Sigma).

Censoring mechanism:
if y=j (j<p), w_j > max(w_{-j}) and w_j >0
if y=p, w < 0

To use GHK, we must transform so that these are rectangular regions e.g. if y=1, w_1 > 0 and w_1 - w_{-1} > 0.

Define A_j such that if j=1,…,p-1 then A_jw = A_jmu + A_je > 0 is equivalent to y=j. Thus, if y=j, we have A_je > -A_jmu. Lower truncation is -A_jmu and cov = A_jSigmat(A_j). For j=p, e < - mu.

### 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 Chapters 2 and 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1

`createX`, `rmnpGibbs`
```## Not run: ll=llmnp(beta,Sigma,X,y,r)