| Type: | Package |
| Title: | Bayesian Treed Regression Model for Personalized Prediction and Precision Diagnostics |
| Version: | 0.2.0 |
| Date: | 2025-05-26 |
| Description: | Generalization of the Bayesian classification and regression tree (CART) model that partitions subjects into terminal nodes and tailors regression model to each terminal node. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | R (≥ 4.5.0), pROC, arm, stats, graphics, MASS |
| NeedsCompilation: | no |
| Packaged: | 2025-05-26 22:15:32 UTC; ychung36 |
| Author: | Yunro Chung  [aut,
cre],
Yaliang Zhang [aut] |
| Maintainer: | Yunro Chung <yunro.chung@asu.edu> |
| Repository: | CRAN |
| Date/Publication: | 2025-05-26 22:30:02 UTC |
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)
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). |
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.
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 |
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. |
Author(s)
Yunro Chung [aut, cre], Yaliang Zhang [aut]
References
Yaliang Zhang and Yunro Chung, Bayesian treed model (in preperation)
Examples
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*(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*(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)