Posterior Prediction under the Bayesian Multinomial Probit Models
Description
Obtains posterior predictions under a fitted (Bayesian) multinomial
probit model. predict
method for class mnp
.
Usage
1 2 3 
Arguments
object 
An output object from 
newdata 
An optional data frame containing the values of the
predictor variables. Predictions for multiple values of the
predictor variables can be made simultaneously if 
newdraw 
An optional matrix of MCMC draws to be used for
posterior predictions. The default is the original MCMC draws stored
in 
n.draws 
The number of additional Monte Carlo draws given each
MCMC draw of coefficients and covariance matrix. The specified
number of latent variables will be sampled from the multivariate
normal distribution, and the quantities of interest will be
calculated by averaging over these draws. This will be
particularly useful calculating the uncertainty of predicted
probabilities. The default is 
type 
The type of posterior predictions required. There are
four options:

verbose 
logical. If 
... 
additional arguments passed to other methods. 
Details
The posterior predictive values are computed using the
Monte Carlo sample stored in the mnp
output (or other sample if
newdraw
is specified). Given each Monte Carlo sample of the
parameters and each vector of predictor variables, we sample the
vectorvalued latent variable from the appropriate multivariate Normal
distribution. Then, using the sampled predictive values of the latent
variable, we construct the most preferred choice as well as the
ordered preferences. Averaging over the Monte Carlo sample
of the preferred choice, we obtain the predictive probabilities of
each choice being most preferred given the values of the predictor
variables. Since the predictive values are computed via Monte Carlo
simulations, each run may produce somewhat different values. The
computation may be slow if predictions with many values of the
predictor variables are required and/or if a large Monte Carlo
sample of the model parameters is used. In either case, setting
verbose = TRUE
may be helpful in monitoring the progress of the
code.
Value
predict.mnp
yields a list of class
predict.mnp
containing at least one of the
following elements:
o 
A three dimensional array of the Monte Carlo sample from the
posterior predictive distribution of the ordered preferences. The
first dimension corresponds to the rows of 
p 
A two or three dimensional array of the posterior predictive
probabilities for each alternative in the choice set being most
preferred. The first demension corresponds to the rows of

y 
A matrix of the Monte Carlo sample from the
posterior predictive distribution of the most preferred choice. The
first dimension correspond to the rows of 
x 
A matrix of covariates used for prediction 
Author(s)
Kosuke Imai, Department of Politics, Princeton University kimai@Princeton.Edu
See Also
mnp
; MNP home page at
http://imai.princeton.edu/research/MNP.html