bayesm (version 1.1-2)

llmnp: Evaluate Log Likelihood for Multinomial Probit Model

Description

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

Usage

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

Arguments

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).

beta

k x 1 vector of coefficients

Sigma

(p-1) x (p-1) Covariance matrix of errors

r

number of draws used in GHK

Value

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

concept

• multinomial probit
• likelihood

Warning

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

Details

X is (p-1)*n x k matrix. Use createX with DIFF=TRUE to create X. Model for each obs: $w = Xbeta + e$. $e$ $\sim$ $N(0,Sigma)$. censoring mechanism: if $y=j (j max(w_{-j})$ 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 $j=p$, $e < - mu$.

References

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

See Also

createX, rmnpGibbs

Examples

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