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` | X is n*(p-1) x k array. X is from differenced system.
`y` | y is 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. 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, 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, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.

### References

For further discussion, see Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch, Chapters 2 and 4.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

### See Also

`createX`, `rmnpGibbs`

### Examples

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

[Package bayesm version 2.0-8 Index]