BMA (version 3.12)

bic.glm: Bayesian Model Averaging for generalized linear 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

bic.glm(x, y, glm.family, wt = rep(1, nrow(x)), strict = FALSE, 
    prior.param = c(rep(0.5, ncol(x))), OR = 20, maxCol = 30, OR.fix = 2, 
    nbest = 150, dispersion = , factor.type = TRUE, 
    factor.prior.adjust = FALSE, occam.window = TRUE, ...)

bic.glm(f, data, glm.family, wt = rep(1, nrow(data)), strict = FALSE, 
    prior.param = c(rep(0.5, ncol(x))), OR = 20, maxCol = 30, OR.fix = 2, 
    nbest = 150, dispersion = , factor.type = TRUE, 
    factor.prior.adjust = FALSE, occam.window = TRUE, ...)

Value

• bic.glm returns an object of class bic.glm The function summary is used to print a summary of the results. The function plot is used to plot posterior distributions for the coefficients. The function imageplot generates an image of the models which were averaged over. An object of class bic.glm is a list containing at least the following components:
• postprob
  the posterior probabilities of the models selected
• deviance
  the estimated model deviances
• label
  labels identifying the models selected
• 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
• mle
  matrix with one row per model and one column per variable giving the maximum likelihood 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
• call
  the matched call that created the bma.lm object

synopsis

bic.glm(x, ...)

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 approximate posterior model probability.

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. An earlier version, issued as Working Paper 94-12, Center for Studies in Demography and Ecology, University of Washington (1994) is available as a Postscript file at http://www.stat.washington.edu/tech.reports/bic.ps

See Also

summary.bic.glm, print.bic.glm, plot.bic.glm

Examples

### logistic regression
library("MASS")
data(birthwt)
y<- birthwt$lo
x<- data.frame(birthwt[,-1])
x$race<- as.factor(x$race)
x$ht<- (x$ht>=1)+0
x<- x[,-9]
x$smoke <- as.factor(x$smoke)
x$ptl<- as.factor(x$ptl)
x$ht <- as.factor(x$ht)
x$ui <- as.factor(x$ui)

glm.out.FT<- bic.glm(x, y, strict = FALSE, OR = 20, glm.family="binomial", 
    factor.type=TRUE)
summary(glm.out.FT)
imageplot.bma(glm.out.FT)

glm.out.FF<- bic.glm(x, y, strict = FALSE, OR = 20, glm.family="binomial", 
    factor.type=FALSE)
summary(glm.out.FF)
imageplot.bma(glm.out.FF)

glm.out.TT<- bic.glm(x, y, strict = TRUE, OR = 20, glm.family="binomial", 
    factor.type=TRUE)
summary(glm.out.TT)
imageplot.bma(glm.out.TT)

glm.out.TF<- bic.glm(x, y, strict = TRUE, OR = 20, glm.family="binomial", 
    factor.type=FALSE)
summary(glm.out.TF)
imageplot.bma(glm.out.TF)



### Gamma family 
library(survival)
data(veteran)
surv.t<- veteran$time
x<- veteran[,-c(3,4)]
x$celltype<- factor(as.character(x$celltype))
sel<- veteran$status == 0
x<- x[!sel,]
surv.t<- surv.t[!sel]

glm.out.va<- bic.glm(x, y=surv.t, glm.family=Gamma(link="inverse"),
    factor.type=FALSE)
summary(glm.out.va)
imageplot.bma(glm.out.va)
plot(glm.out.va)



### Poisson family
### Yates (teeth) data. 

x<- rbind(
    c(0, 0, 0),
    c(0, 1, 0),
    c(1, 0, 0),
    c(1, 1, 1))

y<-c(4, 16, 1, 21)
n<-c(1,1,1,1)

models<- rbind(
    c(1, 1, 0),
    c(1, 1, 1))

glm.out.yates <- bic.glm(x,y,n, glm.family = poisson(), factor.type=FALSE) 
summary(glm.out.yates)

### Gaussian
library(MASS)
data(UScrime)
f<- formula(log(y) ~  log(M)+So+log(Ed)+log(Po1)+log(Po2)+log(LF)+log(M.F)+ 
   log(Pop)+log(NW)+log(U1)+log(U2)+log(GDP)+log(Ineq)+log(Prob)+log(Time) )
glm.out.crime<- bic.glm(f, data = UScrime, glm.family = gaussian()) 
summary(glm.out.crime)
# note the problems with the estimation of the posterior standard deviation 
# (compare with bicreg example)