# psiITR_VS: psi-Learning in individulized treatment rule in the linear... In mylzwq/psi-learning-for-ITR: An Implementation of psiLearn on Individualized Treatment Rule

## Description

Given the tunning parameters return the psiLearning model to estimate the optimal ITR with variable selection

## Usage

 1 psiITR_VS(X,A,R,w0=NULL,tau=0.1,kappa=0.2,lambda=0.8,maxit=100,tol=1e-4,tau2=0.2,res=FALSE) 

## Arguments

 X n by p input matrix. A a vector of n entries coded 1 and -1 for the treatment assignments. R a vector of outcome variable, larger is more desirable. w0 Inital estimate for the coefficients from psi_Init or can be provided by the user. tau tuning parameter for the loss function in psi-Learn kappa tunning parameter to control the complexity of the decision function in the ridge penaly lambda tunning parameter to control the complexity of the decision function in the TLP penalty maxit maximum iterations allowed tol tolerance error bound tau2 tunning parameter to control the margin used in TLP penalty res Whether to estimate the residual as the outcome for interaction effect, default is FALSE

## Value

It returns the estimated coefficients in the decision funcion and the fitted value

 w the coefficent for the decision function, if in the linear case it is p-dimension and if in the rbf kernel case, it is n-dimension. bias the intercept in both the linear case and the kernel case. fit a vector of estimated values for \hat{f(x)} in training data, in the linear case it is fit=bias+X*w and in the kernel case fit=bias+K(X,X)w.

## Author(s)

MingyangLiu <[email protected]>

psi_Init
 1 2 3 4 5 6 7 8  n=100;p=5 X=replicate(p,runif(n, min = -1, max = 1)) A=2*rbinom(n, 1, 0.5)-1 T=cbind(rep(1,n,1),X)%*%c(1,2,1,0.5,rep(0,1,p-3)) T0=(cbind(rep(1,n,1),X)%*%c(0.54,-1.8,-1.8,rep(0,1,p-2)))*A R=as.vector(rnorm(n,mean=0,sd=1)+T+T0) w0.Linear=psi_Init(X,A,R,kernel='linear') psi_Linear<-psiITR_VS(X,A,R,w0.Linear,tau=0.1,kappa=0.3,lambda=1,maxit=100,tol=1e-4,tau2=0.2)