BRegression {Baldur}R Documentation

Bayesian Linear Regression Model

Description

BRegression produces iid draws from the posterior density of a Bayesian Regression model with a multivariate normal prior for the regression coefficients and a separate independent Gamma prior for the data precision.

Usage

BRegression(y,X,mu,P,V0,n0,draws,Prec=FALSE,A=FALSE,maxiter=10000)

Arguments

y n*1 Matrix with observed data values.
X n*k Matrix with the values for the independent variables.
mu k*1 Prior mean vector.
P k*k Prior variance-covariance matrix (must be Positive Definite). If Prec=TRUE, this is instead treated as the prior precision matrix (inverse variance-covariance matrix).
V0 Prior point estimate for data variance.
n0 Number of prior "observations" for data variance.
draws Numeric variable containing number of desired draws from the posterior density. Non-integer values are rounded to the nearest integer.
Prec Optional logical argument with default Prec=FALSE. If argument is set to TRUE, the matrix P is treated as a prior precision matrix.
A Optional logical argument with default A=FALSE. If argument is set to TRUE, the function returns not only the simulated draws from the posterior density but also a vector with information related to the acceptance rate for the underlying accept/reject procedure (see below).
maxiter Maximum number of candidates to be used by accept/reject procedure before terminating.

Details

Makes use of the likelihood subgradient density accept/reject procedure of Nygren and Nygren (2006) in order to generate iid samples from the posterior density of a Bayesian Logit model with a multivariate normal prior.

author{ Kjell Nygren knygren@us.imshealth.com}

Value

If A=FALSE, a matrix beta. If A=TRUE, a list containing the matrix beta and a matrix Accept.:

beta draws*k matrix with the iid draws for the model parameters.
Accept draws*1 matrix with the number of candidates for each draw that were required before acceptance in the accept/reject procedure.

Author(s)

Kjell Nygren knygren@us.imshealth.com

Examples


# Bayesian Regression using Pearson's Height Data for Father-Son pairs

data(Height, package = "Baldur")

m<-1078
nvars<-2

y<-matrix(Height$Son,nrow=m,ncol=1)
X<-matrix(0,nrow=m,ncol=nvars)
mu<-matrix(0,nrow=nvars,ncol=1)
X[,1]<-1
X[,2]<-Height$Father[1:m]

P<-100*diag(nvars)
V0<-10
n0<-3

draws<-1000

set.seed(666)

system.time(out<-BRegression(y, X, mu, P, V0, n0, draws)) 

mean(out$beta[,1])
mean(out$beta[,2])

mean(out$Var)

sqrt(var(out$beta[,1]))
sqrt(var(out$beta[,2]))
sqrt(var(out$Var))
[Package Baldur version 0.0-0 Index]