btrm (version 0.1.0)

btrm: Bayesian Treed Regression Model

Description

The treed regression model generalizes the Bayesian classification and regression tree (CART) model by partitioning subjects into terminal nodes and tailoring simple regression model to each terminal node.

Usage

btrm(y,x,z,ynew,xnew,znew,sparse,nwarm,niter,minsample,base,power)

Value

An object of class btrm, which is a list with the following components:

terminal

Node numbers in terminal nodes.

internal

Node numbers in internal nodes.

splitVariable

Variable (i.e., x[,u] if splitVariable[k]=u) used to split the internal node k.

cutoff

cutoff[k] is the cutoff value to split the internal node k.

marker

Marker (i.e., z[,v] if marker[t]=v) assigned to the terminal node t.

node.hat

Estimated node on the training set.

marker.hat

Estimated marker on the training set.

beta.hat

beta.hat[[t]] is estimated regression coefficients from the linear (or logistic) regression model at the terminal node t \(\in\) terminal.

y.hat

Estimated y (or probability) on the training set if y is continuous (or binary).

mse

Training MSE.

bs

Training Brier Score.

roc

Training ROC curve.

auc

Training AUC.

y.hat.new

Estimated y (or probability) on the test set if y is continuous (or binary).

node.hat.new

Estimated node on the test set.

marker.hat.new

Estimated marker on the test set.

mse.new

Test MSE.

bs.new

Test Brier Score.

roc.new

Test ROC curve.

auc.new

Test AUC.

Arguments

y

Response vector. If a factor codied as 0 or 1, classification is assumed. Otherwise, regression is assumed.

x

Data.frame or matrix of predictors that is used to estimate a tree structure.

z

Data.frame or matrix of predictors that is used in terminal node specific ML models. See the description below about the difference between x and z.

ynew

Response vector for the test set corresponding to y (default ynew=NULL).

xnew

Data.frame or matrix for the test set corresponding to x (default xnew=NULL).

znew

Data.frame or matrix for the test set corresponding to z (default znew=NULL).

sparse

Whether to perform variable and machine learning model selections based on a sparse Dirichlet prior rather than simply uniform (default sparse=TRUE).

nwarm

Number of warm-up (default nwarm=1000).

niter

Number of iteration (defaut niter=1000).

minsample

The number of minimum sample size per each node, i.e., length(y)>min_sample if y is continuous and min(length(y==1),length(y==0))>min_sample (default min_sample=20).

base

Base parameter for tree prior (default base=0.95).

power

Power parameter for tree prior (default power=0.8).

Author

Yunro Chung [aut, cre], Yaliang Zhang [aut]

Details

Ideally, there are two sets of predictors, x and z, e.g., demographic variables and biomarkers, where x is used to split trees, and z is assigned to each terminal node. However, if this is not possible, it allows us to use the same x and z in the btml function, e.g., btml(y=y, x=x, z=x, ...). For high-dimensional variables, increase nwarm=10000 and niter=10000, or more; and increase minsample.

Ideally, there are two sets of predictors, x and z, e.g., demographic variables and biomarkers, where x is used to split trees, and z is assigned to each terminal node. However, if this is not possible, it allows to use the same x and z in the btrm function, e.g., btrm(y=y, x=x, z=x, ...).

Regarding the node numbers, an internal node s has left and right child nodes 2*s and 2*s+1, respectively, where node 1 is a root node; nodes 2 and 3 are left and right child nodes of node 1; nodes 4 and 5 are left and right nodes of node 2; and so on.

References

Yaliang Zhang and Yunro Chung, Bayesian treed model (in preperation)

Examples

# \donttest{
set.seed(10)
###
#1. continuous y
###
n=200*2 #n=200 & 200 for training & test sets

x=matrix(rnorm(n*10),n,10) #10 predictors
z=matrix(rnorm(n*10),n,10) #10 biomarkers

xcut=median(x[,1])
subgr=1*(x[,1]=xcut) #2 subgroups

lp=rep(NA,n)
for(i in 1:n)
  lp[i]=1+3*z[i,subgr[i]]
y=lp+rnorm(n,0,1)

idx.nex=sample(1:n,n*1/2,replace=FALSE)
ynew=y[idx.nex]
xnew=x[idx.nex,]
znew=z[idx.nex,]

y=y[-idx.nex]
x=x[-idx.nex,]
z=z[-idx.nex,]

fit1=btrm(y,x,z,ynew=ynew,xnew=xnew,znew=znew)
print(fit1$mse.new)
plot(fit1$y.hat.new~ynew,ylab="Predicted y",xlab="ynew")

###
#2. binary y
###
x=matrix(rnorm(n*10),n,10) #10 predictors
z=matrix(rnorm(n*10),n,10) #10 biomarkers

xcut=median(x[,1])
subgr=1*(x[,1]=xcut) #2 subgroups

lp=rep(NA,n)
for(i in 1:n)
  lp[i]=1+3*z[i,subgr[i]]
prob=1/(1+exp(-lp))
y=rbinom(n,1,prob)
y=as.factor(y)

idx.nex=sample(1:n,n*1/2,replace=FALSE)
ynew=y[idx.nex]
xnew=x[idx.nex,]
znew=z[idx.nex,]

y=y[-idx.nex]
x=x[-idx.nex,]
z=z[-idx.nex,]

fit2=btrm(y,x,z,ynew=ynew,xnew=xnew,znew=znew)
print(fit2$auc.new)
plot(fit2$roc.new)
# }