getModel: Compute the regression coefficients for both stages

In qLearn: Estimation and inference for Q-learning

Description

getModel computes the regression coefficients for both stages. For stage 1 regression, peudo-outcomes are constructed based on stage 2 coefficients. Additionally it outputs the standard outputs of the lm function; however, the inference for stage 1 parameters based on these outputs is invalid due to non-regularity. Example could be found under qLearn.

Usage

getModel(s2Formula,s1Formula,completeData,
s2Treat,interact,s2Indicator,...)

Arguments

s2Formula	stage 2 regression formula
s1Formula	Stage 1 regression formula
completeData	data frame containing all the variables
s2Treat	character string: name of the stage 2 treatment variable
interact	character vector: names of variables that interact with s2_treat
s2Indicator	character string: names of the stage 2 treatment indicator variable
...	other arguments of the lm function

Value

A list containing:

s2Model	stage2 regression model
s1Model	stage1 regression model
pHat	estimated non-regularity level

Author(s)

Jingyi Xin [e-mail], Bibhas Chakraborty [e-mail], and Eric B.Laber [e-mail]

References

Chakraborty, B., and Laber, E.B. (2012). Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme. Submitted.

See Also

qLearn

Examples

set.seed(100)
# Simple Simulation on 1000 subjects
sim<-matrix(0,nrow=1000,ncol=7)
colnames(sim)<-c("H1","A1","Y1","H2","A2","Y2","IS2")
sim<-as.data.frame(sim)

# Randomly generate stage 1 covariates and stage 1 and 2 treatments
sim[,c("H1","A1","A2")]<-2*rbinom(1000*3,1,0.5)-1

# Generate stage 2 covariates based on H1 and T1
expit<-exp(0.5*sim$H1+0.5*sim$A1)/(1+exp(0.5*sim$H1+0.5*sim$A1))
sim$H2<-2*rbinom(1000,1,expit)-1

# Assume stage 1 outcome Y1 is 0
# Generate stage 2 outcome Y2 
sim$Y2<-0.5*sim$A2+0.5*sim$A2*sim$A1-0.5*sim$A1+rnorm(1000)

# Randomly assign 500 subjects to S2
sim[sample(1000,500),"IS2"]<-1 
sim[sim$IS2==0,c("A2","Y2")]<-NA

# Define models for both stages
s2Formula<-Y2~H1*A1+A1*A2+A2:H2
s1Formula<-Y1~H1*A1

## Fit model for both stages
getModel(s2Formula,s1Formula,sim,s2Treat="A2",interact=c("A1","H2"),
s2Indicator="IS2")

Example output

$s2Model

Call:
lm(formula = s2Formula, data = s2_data)

Coefficients:
(Intercept)           H1           A1           A2        H1:A1        A1:A2  
   0.009318    -0.065960    -0.494234     0.508544     0.020874     0.528056  
      A2:H2  
  -0.011565  


$s1Model

Call:
lm(formula = s1Formula, data = peudo_data)

Coefficients:
(Intercept)           H1           A1        H1:A1  
    0.53400     -0.06590      0.01458      0.01816  


$pHat
[1] 0.492

qLearn documentation built on May 2, 2019, 9:18 a.m.