predict.mnp {MNP}R Documentation

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

  ## S3 method for class 'mnp':
  predict(object, newdata = NULL, newdraw = NULL, moredraw = 1,
          type = c("prob", "choice", "order", "latent"), verbose = FALSE, ...)

Arguments

object An output object from mnp.
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 newdata has multiple rows. The default is the original data frame used for fitting the model.
newdraw An optional matrix of MCMC draws to be used for posterior predictions. The default is the original MCMC draws stored in object.
moredraw The number of additional draws of latent variables for each of MCMC draws. Given a particular MCMC draw of coefficients and covariance matrix, the specified number of latent variables will be sampled from the multivariate normal distribution. This will be particularly useful calculating the uncertainty of predicted probabilities. The default is 1.
type The type of posterior predictions required. There are four options: type = "prob" returns the predictive probabilities of being the most preferred choice among the choice set. type = "choice" returns the Monte Carlo sample of the most preferred choice, type = "order" returns the Monte Carlo sample of the ordered preferences, and type = "latent" returns the Monte Carlo sample of the predictive values of the latent variable. The default is to return all four types of posterior predictions.
verbose logical. If TRUE, helpful messages along with a progress report on the Monte Carlo sampling from the posterior predictive distributions are printed on the screen. The default is FALSE.
... 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 vector-valued 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 containing at least one of the following elements:

o A four dimensional array of the Monte Carlo sample from the posterior predictive distribution of the ordered preferences. The first dimension corresponds to the alternatives in the choice set, the second dimension corresponds to the rows of newdata (or the original data set if newdata is left unspecified), the third dimension indexes the Monte Carlo sample, and the fourth dimension is the number of additional draws given by moredraw.
p A four 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 newdata (or the original data set if newdata is left unspecified), the second dimension corresponds to the alternatives in the choice set, and the third diemsion represents the number of additional draws given by moredraw.
y A three dimensional array of the Monte Carlo sample from the posterior predictive distribution of the most preferred choice. The first dimension correspond to the rows of newdata (or the original data set if newdata is left unspecified), the second dimension indexes the Monte Carlo sample, and the third dimension represents the number of additional draws given by moredraw.
w A four dimensional array of the Monte Carlo sample from the posterior predictive distribution of the latent variable. The first dimension corresponds to the alternatives in the choice set, the second dimension corresponds to the rows of newdata (or the original data set if newdata is left unspecified), the third dimension indexes the Monte Carlo sample, and the four dimension represents the number of additional draws given by moredraw.

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


[Package MNP version 2.4-2 Index]