madr {madr}

Calculate model averaged double robust estimate

Description

This function estimates a model averaged double robust estimate.

Usage

madr(Y, X, U, W = NULL, M = 1000, cut = 0.95, enumerate = F,
  tau = NULL, two.stage = NULL)

Arguments

Y

vector of the outcome

X

vector of the treatment (0/1)

U

matrix of covariates to be considered for inclusion/exclusion

W

matrix of covariates that will be included in all models (optional)

M

the number of MCMC iteration

cut

cumulative probability of models to be retained for improved computational efficiency (1 retains all visited models)

enumerate

indicator if all possible models should be enumerated (default: FALSE)

tau

scalar value for the prior model dependence (1 is an independent prior; defaults to 0)

two.stage

indicator if the two-stage procedure for calculating the model weights should be used (defaults to TRUE)

Value

A list. The list contains the following named components:

madr

the model averaged double robust estimate

weight.ps

a vector that contains the inclusion probability of each covariate in the propensity score model

weight.om

a vector that contains the inclusion probability of each covariate in the outcome model

Examples

set.seed(122)
## generate data
n = 100 # number of observations
k = 4   # number of covariates
U = matrix(rnorm(n*k),n,k)
colnames(U) = paste0("U",1:k)
A = rbinom(n,1,expit(-1+.5*rowSums(U)))
Y = rnorm(n,1+A+.25*rowSums(U))

## A is confounded -- true effect is 1
lm(Y~A)

## fit ma-dr -- can enumerate models if k isnt too big
res = madr(Y=Y,X=A,U=U,enumerate=TRUE,tau=1,two.stage=FALSE) # independent prior
res

res = madr(Y=Y,X=A,U=U,enumerate=TRUE,tau=0,two.stage=TRUE) # tau=0 and using two-stage weights
res

## no need to refit madr each time when enumerating -- use summarize and specify different taus
summary(res,tau=1,two.stage=FALSE) # independent prior
summary(res,tau=0,two.stage=FALSE)
summary(res,tau=0,two.stage=TRUE) # two-stage procedure for calculating weights

## use mcmc instead of enumerating (the default)
madr(Y=Y,X=A,U=U,M=1000,cut=1) #should approximate tau=0 and two.stage=TRUE