predict.pep: (Point) Prediction under PEP approach

In PEPBVS: Bayesian Variable Selection using Power-Expected-Posterior Prior

(Point) 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 pep.lm).
xnew	An optional data frame of numeric, the new data on the explanatory variables to be used for prediction. The data frame needs to contain information about all explanatory variables available in the full model; if not an error message is output. 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). Default value="BMA".
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 zero and one, 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 is equal to the initial data frame used for fitting, 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) and non–quantitative data in the new data frame xnew 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/21-BA1288")}

Fouskakis, D. and Ntzoufras, I. (2020) Bayesian Model Averaging Using Power–Expected–Posterior Priors. Econometrics, 8(2): 17. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/econometrics8020017")}

Examples

data(UScrime_data)
X <- UScrime_data[,-15]
set.seed(123)
res <- pep.lm(y~.,data=UScrime_data[1:45,],intrinsic=TRUE,
               algorithmic.choice="MC3",itermc3=4000)
resf <- predict(res)
resf2 <- predict(res,estimator="MPM")
resp <- predict(res,xnew=X[46:47,])

PEPBVS documentation built on April 3, 2025, 6:12 p.m.