bayesm (version 3.1-6)

llmnp: 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)

Value

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

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

Warning

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

Author

Peter Rossi, Anderson School, UCLA, .

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 \(j=p\), \(e < - mu\).

References

For further discussion, see Chapters 2 and 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

createX, rmnpGibbs

Examples

if (FALSE) ll=llmnp(beta,Sigma,X,y,r)