predict.pep {PEPBVS}

Prediction under PEP approach

Description

Computes predicted or fitted values under the PEP approach. Predictions can be based on Bayesian model averaging, maximum a posteriori model or median probability model. For the Bayesian model averaging, a subset of the top models (either based on explicit number or on their cumulative probability) can be used for prediction.

Usage

## S3 method for class 'pep'
predict(
  object,
  xnew,
  estimator = "BMA",
  n.models = NULL,
  cumul.prob = 0.99,
  ...
)

Arguments

object

An object of class pep (e.g. output of full_enumeration_pep or mc3_pep).

xnew

A matrix of numeric (with p columns), the new data to be used for prediction. This matrix contains the values of the explanatory variables without an intercept column of 1's, i.e. the number of its columns coincides with the number of columns of object$x. If omitted, fitted values are computed.

estimator

A character, the type of prediction. One of "BMA" (Bayesian model averaging, default), "MAP" (maximum a posteriori model) or "MPM" (median probability model).

n.models

Positive integer, the number of (top) models that prediction is based on or NULL. Relevant for estimator="BMA". Default value=NULL.

cumul.prob

Numeric between 0 and 1, cumulative probability of top models to be used for prediction. Relevant for estimator="BMA". Default value=0.99.

...

Additional parameters to be passed, currently none.

Details

When xnew is missing or xnew=object$x then fitted values are computed (and returned).

For prediction, Equation 9 of Fouskakis and Ntzoufras (2020) is used.

The case of missing data (i.e. presence of NA’s) in the new data matrix is not currently supported.

Let k be the number of models with cumulative posterior probability up to the given value of cumul.prob. Then, for Bayesian model averaging the prediction is based on the top (k+1) models if they exist, otherwise on the top k models.

When both n.models and cumul.prob are provided - once specifying the number of models for the given cumulative probability as described above - the minimum between the two numbers is used for prediction.

Value

predict returns a vector with the predicted (or fitted) values for the different observations.

References

Fouskakis, D. and Ntzoufras, I. (2022) Power-Expected-Posterior Priors as Mixtures of g-Priors in Normal Linear Models. Bayesian Analysis, 17(4): 1073-1099. doi:10.1214/21-BA1288

Fouskakis, D. and Ntzoufras, I. (2020) Bayesian Model Averaging Using Power-Expected-Posterior Priors. Econometrics, 8(2): 17. doi:10.3390/econometrics8020017

Examples

data(UScrime_data)
y <- UScrime_data[,"y"]
X <- UScrime_data[,-15]
set.seed(123)
res <- mc3_pep(X[1:45,],y[1:45],intrinsic=TRUE,itermc3=4000)
resf <- predict(res)
resf2 <- predict(res,estimator="MPM")
resp <- predict(res,xnew=X[46:47,])