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`

`\sim`

`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,\ldots,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.

### See Also

### Examples

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

*bayesm*version 3.1-6 Index]