BMA (version 3.12)

glib: Model uncertainty in generalized linear models using Bayes factors

Description

Function to evaluate Bayes factors and account for model uncertainty in generalized linear models.

Usage

glib(x, y, n = rep(1, nrow(x)), error = "poisson", link = "log", 
     scale = 1, models = NULL,  phi = c(1, 1.65, 5), psi = 1, nu = 0, 
     pmw = rep(1, nrow(models)), glimest = TRUE, glimvar = FALSE, 
     output.priorvar = FALSE, post.bymodel = TRUE, output.postvar = FALSE, 
     priormean = NULL, priorvar = NULL, nbest = 10, call = NULL, ...)

glib(g, scale = 1, phi = c(1, 1.65, 5), psi = 1, nu = 0, 
     glimest = TRUE, glimvar = FALSE, output.priorvar = F, 
     post.bymodel = TRUE, output.postvar = FALSE, priormean = NULL, 
     priorvar = NULL, call = NULL, ...)

as.bic.glm( g, phi.index=1)

Value

• glib returns an object of type glib, which is a list containing the following items:
• inputs
  a list echoing the inputs (x,y,n,error,link,models,phi,psi,nu)
• bf
  a list containing the model comparison results: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

synopsis

glib(x, ...)

item

• posterior
• glim.est
• posterior.bymodel
• prior
• models
• glm.out
• call

describe

• mean
  prior mean for the biggest model (this doesn't depend on phi)
• var
  similar to corresponding member of posterior.bymodel.

code

bic.glm

Details

Function to evaluate Bayes factors and account for model uncertainty in generalized linear models. This also calculates posterior distributions from a set of reference proper priors. as.bic.glm creates a 'bic.glm' object from a 'glib' object.

References

Raftery, A.E. (1988). Approximate Bayes factors for generalized linear models. Technical Report no. 121, Department of Statistics, University of Washington. 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 of this was issued as Working Paper 94-12, Center for Studies in Demography and Ecology, University of Washington, and this is available as a Postscript file at http://www.stat.washington.edu/tech.reports/bic.ps. Raftery, A.E. (1996). Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika (83: 251-266). An earlier version of this was issued as Technical Report no. 255, Department of Statistics, University of Washington, and is available as a Postscript file at http://www.stat.washington.edu/tech.reports/tr255.ps.

See Also

bic.glm, summary.glib

Examples

### Finney data
library(forward)
data(vaso)
x<- vaso[,1:2]
y<- vaso[,3]
n<- rep(1,times=length(y))

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

finney.glib <- glib (x,y,n, error="binomial", link="logit", models=finney.models, 
   glimvar=TRUE, output.priorvar=TRUE, output.postvar=TRUE)
summary(finney.glib)

finney.bic.glm<- as.bic.glm(finney.glib)
plot(finney.bic.glm,mfrow=c(2,1))

### 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))

glib.yates <- glib (x,y,n,models=models,glimvar=TRUE,output.priorvar=TRUE,
   output.postvar=TRUE) 
summary(glib.yates)

### logistic regression with no models specified
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)

glib.birthwt<- glib(x,y, error="binomial", link = "logit")
summary(glib.birthwt)

glm.birthwt<- as.bic.glm(glib.birthwt)

imageplot.bma(glm.birthwt)

plot(glm.birthwt)