llmnp {bayesm} | R Documentation |
llmnp
evaluates the log-likelihood for the multinomial probit model.
llmnp(beta, Sigma, X, y, r)
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 |
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 of log-likelihood (sum of log prob of observed multinomial outcomes)
This routine is a utility routine that does not check the input arguments for proper dimensions and type.
Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.
For further discussion, see Chapters 2 and 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
## Not run: ll=llmnp(beta,Sigma,X,y,r)