BMA (version 3.12)

MC3.REG: Bayesian simultaneous variable selection and outlier identification

Description

Performs Bayesian simultaneous variable selection and outlier identification (SVO) via Markov chain Monte Carlo model composition (MC3).

Usage

MC3.REG(all.y, all.x, num.its, M0.var= , M0.out= , outs.list= , 
        outliers = TRUE, PI=.1*(length(all.y) <50) +="" .02*(length(all.y)="">= 50),  K=7, nu= , lambda= , phi= )

Value

• An object of class mc3. Print and summary methods exist for this class. Objects of class mc3 are a list consisting of at least
• post.prob
  The posterior probabilities of each model visited.
• variables
  An indicator matrix of the variables in each model.
• outliers
  An indicator matrix of the outliers in each model, if outliers were selected.
• visit.count
  The number of times each model was visited.
• outlier.numbers
  An index showing which outliers were eligable for selection.
• var.names
  The names of the variables.
• n.models
  The number of models visited.
• PI
  The value of PI used.
• K
  The value of K used.
• nu
  The value of nu used.
• lambda
  The value of lambda used.
• phi
  The value of phi used.
• call
  The function call.

Details

Performs Bayesian simultaneous variable and outlier selection using Monte Carlo Markov Chain Model Choice (MC3). Potential models are visited using a Metropolis-Hastings algorithm on the integrated likelihood. At the end of the chain exact posterior probabilities are calculated for each model visited.

References

Bayesian Model Averaging for Linear Regression Models Adrian E. Raftery, David Madigan, and Jennifer A. Hoeting (1997). Journal of the American Statistical Association, 92, 179-191. A Method for Simultaneous Variable and Transformation Selection in Linear Regression Jennifer Hoeting, Adrian E. Raftery and David Madigan (2002). Journal of Computational and Graphical Statistics 11 (485-507) A Method for Simultaneous Variable Selection and Outlier Identification in Linear Regression Jennifer Hoeting, Adrian E. Raftery and David Madigan (1996). Computational Statistics and Data Analysis, 22, 251-270 Earlier versions of these papers are available via the World Wide Web using the url: http://www.stat.colostate.edu/~jah/papers/

See Also

out.ltsreg as.data.frame.mc3

Examples

# Example 1:   Scottish hill racing data.

data(race)
b<- out.ltsreg(race[,-1], race[,1], 2)
races.run1<-MC3.REG(race[,1], race[,-1], num.its=20000, c(FALSE,TRUE), 
                    rep(TRUE,length(b)), b, PI = .1, K = 7, nu = .2, 
                    lambda = .1684, phi = 9.2)
races.run1
summary(races.run1)

# Example 2: Crime data
library(MASS)
data(UScrime)

y.crime.log<- log(UScrime$y)
x.crime.log<- UScrime[,-ncol(UScrime)]
x.crime.log[,-2]<- log(x.crime.log[,-2])
crime.run1<-MC3.REG(y.crime.log, x.crime.log, num.its=2000, 
                     rep(TRUE,15), outliers = FALSE)
crime.run1[1:25,]
summary(crime.run1)