estimation.pep: Model averaged estimates

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

Model averaged estimates

Description

Simulates values from the (joint) posterior distribution of the beta coefficients under Bayesian model averaging.

Usage

estimation.pep(
  object,
  ssize = 10000,
  estimator = "BMA",
  n.models = NULL,
  cumul.prob = 0.99
)

Arguments

object	An object of class pep (e.g., output of pep.lm).
ssize	Positive integer, the number of values to be simulated from the (joint) posterior distribution of the beta coefficients. Default value=10000.
estimator	A character, the type of estimation. 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 where the average 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 computing the average. Relevant for estimator="BMA". Default value=0.99.

Details

For the computations, Equation 10 of Garcia–Donato and Forte (2018) is used. That (simplified) formula arises when changing the prior on the model parameters to the reference prior. This change of prior is justified in Garcia–Donato and Forte (2018). The resulting formula is a mixture distribution and the simulation is implemented as follows: firstly the model (component) based on its posterior probability is chosen and subsequently the values of the beta coefficients included in the chosen model are drawn from the corresponding multivariate Student distribution, while the values of the beta coefficents outside the chosen model are set to zero.

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 summation 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 estimation.

Value

estimation.pep returns a matrix (of dimension ssize \times \, (p+1)) — where the rows correspond to the simulations and the columns to the beta coefficients (including the intercept) — containing the simulated data.

References

Garcia–Donato, G. and Forte, A. (2018) Bayesian Testing, Variable Selection and Model Averaging in Linear Models using R with BayesVarSel. The R Journal, 10(1): 155–174. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/RJ-2018-021")}

Examples

data(UScrime_data)
res <- pep.lm(y~.,data=UScrime_data)
set.seed(123)
estM1 <- estimation.pep(res,ssize=2000)
estM2 <- estimation.pep(res,ssize=2000,estimator="MPM")

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