Posterior Prediction under the Bayesian Multinomial Probit Models

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Description

Obtains posterior predictions under a fitted (Bayesian) multinomial probit model. predict method for class mnp.

Usage

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  ## S3 method for class 'mnp'
predict(object, newdata = NULL, newdraw = NULL, n.draws = 1,
          type = c("prob", "choice", "order"), 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.

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 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, and type = "order" returns the Monte Carlo sample of the ordered preferences,

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 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 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 dimension indexes the Monte Carlo sample. If n.draws is greater than 1, then each entry will be an average over these additional draws.

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 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 dimension (if it exists) indexes the Monte Carlo sample. If n.draws is greater than 1, then the third diemsion exists and indexes the Monte Carlo sample.

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 newdata (or the original data set if newdata is left unspecified), and the second dimension indexes the Monte Carlo sample. n.draws will be set to 1 when computing this quantity of interest.

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