bicreg {BMA}R Documentation

Bayesian Model Averaging for linear regression models.

Description

Bayesian Model Averaging accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to approximate posterior model probability.

Usage

bicreg(x, y, wt = rep(1, length(y)), strict = FALSE, OR = 20, 
       maxCol = 31, drop.factor.levels = TRUE, nbest = 150)

Arguments

x

a matrix of independent variables

y

a vector of values for the dependent variable

wt

a vector of weights for regression

strict

logical. FALSE returns all models whose posterior model probability is within a factor of 1/OR of that of the best model. TRUE returns a more parsimonious set of models, where any model with a more likely submodel is eliminated.

OR

a number specifying the maximum ratio for excluding models in Occam's window

maxCol

a number specifying the maximum number of columns in the design matrix (including the intercept) to be kept.

drop.factor.levels

logical. Indicates whether factor levels can be individually dropped in the stepwise procedure to reduce the number of columns in the design matrix, or if a factor can be dropped only in its entirety.

nbest

a value specifying the number of models of each size returned to bic.glm by the leaps algorithm. The default is 150 (replacing the original default of 10).

Details

Bayesian Model Averaging accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to the approximate posterior model probabilities.

Value

bicreg returns an object of class bicreg

The function 'summary' is used to print a summary of the results. The function 'plot' is used to plot posterior distributions for the coefficients.

An object of class bicreg is a list containing at least the following components:

postprob

the posterior probabilities of the models selected

namesx

the names of the variables

label

labels identifying the models selected

r2

R2 values for the models

bic

values of BIC for the models

size

the number of independent variables in each of the models

which

a logical matrix with one row per model and one column per variable indicating whether that variable is in the model

probne0

the posterior probability that each variable is non-zero (in percent)

postmean

the posterior mean of each coefficient (from model averaging)

postsd

the posterior standard deviation of each coefficient (from model averaging)

condpostmean

the posterior mean of each coefficient conditional on the variable being included in the model

condpostsd

the posterior standard deviation of each coefficient conditional on the variable being included in the model

ols

matrix with one row per model and one column per variable giving the OLS estimate of each coefficient for each model

se

matrix with one row per model and one column per variable giving the standard error of each coefficient for each model

reduced

a logical indicating whether any variables were dropped before model averaging

dropped

a vector containing the names of those variables dropped before model averaging

residvar

residual variance for each model

call

the matched call that created the bicreg object

Author(s)

Original Splus code developed by Adrian Raftery (raftery@AT@stat.washington.edu) and revised by Chris T. Volinsky. Translation to R by Ian Painter.

References

Raftery, Adrian E. (1995). Bayesian model selection in social research (with Discussion). Sociological Methodology 1995 (Peter V. Marsden, ed.), pp. 111-196, Cambridge, Mass.: Blackwells.

See Also

summary.bicreg, print.bicreg, plot.bicreg

Examples

library(MASS)
data(UScrime)
x<- UScrime[,-16]
y<- log(UScrime[,16])
x[,-2]<- log(x[,-2])
lma<- bicreg(x, y, strict = FALSE, OR = 20) 
summary(lma)
plot(lma)

imageplot.bma(lma)


[Package BMA version 3.18.15 Index]