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Intro

This code implements, the analysis with test-based Bayes factors (TBF) originally proposed by Johnson (2008) and Hu and Johnson (2009) later revisited by Held, Sabanés Bové, and Gravestock (2015),

This does not implement stochastic model space exploration and all possible models (2k, where k is the number of covariates) are visited.

Data

We consider the heart transplant survival dataset and two spurious uncorrelated variable. This is just one draw for the simulation study described in the paper.

rm(list=ls()) 
set.seed(17) 
library(compiler) 
library(mvtnorm) 
library(plyr) 
library(doParallel) 
source("library-bf-cens-conv-prior.R") 
source("library-bf-cens-conv-prior-2.R") 
library(survival) 
data(heart) 
jasa=jasa[jasa$transplant==1,] 
surv.time=jasa$fu.date-jasa$accept.dt
fecha.fin=as.Date(0, origin = "1974-04-01") 
cens.time=fecha.fin-jasa$accept.dt  
cens.time[jasa$fustat==0]=surv.time[jasa$fustat==0] 
dat.heart=data.frame(as.numeric(surv.time),as.numeric(jasa$fustat),as.numeric(cens.time),jasa$age,rnorm(nrow(jasa)),rnorm(nrow(jasa))) 
colnames(dat.heart)=c("survival","rel","cens","age","spur1","spur2") 
dat.heart=dat.heart[dat.heart$survival>0,] 
summary(dat.heart)

##     survival           rel              cens           age       
##  Min.   :   4.0   Min.   :0.0000   Min.   :  38   Min.   :19.55  
##  1st Qu.:  71.0   1st Qu.:0.0000   1st Qu.: 487   1st Qu.:42.50  
##  Median : 206.0   Median :1.0000   Median : 941   Median :47.99  
##  Mean   : 414.5   Mean   :0.6522   Mean   :1060   Mean   :46.03  
##  3rd Qu.: 619.0   3rd Qu.:1.0000   3rd Qu.:1676   3rd Qu.:52.03  
##  Max.   :1799.0   Max.   :1.0000   Max.   :2277   Max.   :64.41  
##      spur1             spur2         
##  Min.   :-3.5561   Min.   :-3.32032  
##  1st Qu.:-0.6166   1st Qu.:-0.64045  
##  Median : 0.1510   Median :-0.04963  
##  Mean   : 0.1375   Mean   :-0.14477  
##  3rd Qu.: 0.7721   3rd Qu.: 0.59098  
##  Max.   : 2.4423   Max.   : 2.10842

Analysis

Posterior inclusion probabilities based on TBF

The full matrix is

var.name=c("age","spur1","spur2") 
k=length(var.name)
n=nrow(dat.heart)
Xfull=dat.heart[,var.name]
Xfull=scale(Xfull)
colnames(Xfull)=var.name 
Xfull=as.data.frame(Xfull) 
mod.list=index.models(ncol(Xfull)) 
nmodels=length(mod.list)

These are the examined models:

llply(mod.list,function(x) colnames(Xfull)[x]) 

## [[1]]
## [1] "age"
## 
## [[2]]
## [1] "spur1"
## 
## [[3]]
## [1] "spur2"
## 
## [[4]]
## [1] "age"   "spur1"
## 
## [[5]]
## [1] "age"   "spur2"
## 
## [[6]]
## [1] "spur1" "spur2"
## 
## [[7]]
## [1] "age"   "spur1" "spur2"

These are the inclusion probabilities according to different versions of the TBF:

source("TBFfunctions.R")
ipTBF(Xfull, y=dat.heart$survival, delta=dat.heart$rel, g.param="EB")

##       age     spur1     spur2 
## 0.5989054 0.4894859 0.4864764

ipTBF(Xfull, y=dat.heart$survival, delta=dat.heart$rel, g.param="g=nu")

##       age     spur1     spur2 
## 0.3021753 0.1103147 0.1011396

ipTBF(Xfull, y=dat.heart$survival, delta=dat.heart$rel, g.param="g=n")

##        age      spur1      spur2 
## 0.25252193 0.08415812 0.07625103

ZSadapt.ipTBF(Xfull, y=dat.heart$survival, delta=dat.heart$rel) 

##       age     spur1     spur2 
## 0.2685626 0.1103536 0.1026478

References

Held, L., D. Sabanés Bové, and I Gravestock. 2015. “Approximate Bayesian Model Selection with the Deviance Statistic.” Statistical Science 30: 242–57.

Hu, J., and V.E. Johnson. 2009. “Bayesian Model Selection Using Test Statistics.” Journal of the Royal Statistical Society. Series B (Methodological) 71 (1): 143–58.

Johnson, V.E. 2008. “Properties of Bayes Factors Based on Test Statistics.” Scandinavian Journal of Statistics 35 (2): 354–68.