miceMNAR (version 1.0.2)

mice.impute.hecknorm2step: Imputation by Heckman's model for continuous Missing Not At Random ouctome using a two-step estimator

Description

Imputes univariate continuous Missing Not At Random (MNAR) outcome using Heckman's model with a two-step estimator.

Usage

mice.impute.hecknorm2step(y, ry, x, JointModelEq, control, ...)

Arguments

y

Incomplete data vector of length n.

ry

Vector of missing data pattern of length n (FALSE=missing, TRUE=observed).

x

Matrix (n x p) of complete covariates.

JointModelEq

Output JointModelEq provided by MNARargument() function.

control

Output control provided by MNARargument() function.

…

Other named arguments.

Value

A vector of length nmis with imputations.

Details

Imputation of continuous MNAR outcome using two-step Heckman's model (Galimard, 2016). This imputation model requires to define a selection and an outcome equation. The imputation algorithm consists of the following steps:

1. Compute Inverse Mill's Ratio (IMR) from the selection equation probit model

2. Include IMR as predictor in the imputation model

3. Draw imputation parameters using approximate proper imputation for the linear model and adding the Heckman variance correction as detailed in Galimard et al (2016)

4. Draw imputed values from their predictive distribution

References

Galimard, J.-E., Chevret, S., Protopopescu, C., and Resche-Rigon, M. (2016) A multiple imputation approach for MNAR mechanisms compatible with Heckman's model. Statistics In Medicine, 35: 2907-2920. doi:10.1002/sim.6902.

See Also

miceMNAR

Examples

# NOT RUN {
require("GJRM")
require(mvtnorm)
require(sampleSelection)

# Generation of a simulated dataset with MNAR mechanism on a continuous outcome

X1 <- rnorm(500,0,1)
X2 <- rbinom(500,1,0.5)
X3 <- rnorm(500,1,0.5)
  
errors <- rmvnorm(500,mean=c(0,0),sigma=matrix(c(1,0.3,0.3,1),nrow=2,byrow=TRUE))

Y <- X1+X2+errors[,1]
Ry <- ifelse(0.66+1*X1-0.5*X2+X3+errors[,2]>0,1,0)

Y[Ry==0] <- NA
  
simul_data <- data.frame(Y,X1,X2,X3)

JointModelEq <- generate_JointModelEq(data=simul_data,varMNAR = "Y")

JointModelEq[,"Y_var_sel"] <- c(0,1,1,1)
JointModelEq[,"Y_var_out"] <- c(0,1,1,0)

arg <- MNARargument(data=simul_data,varMNAR="Y",JointModelEq=JointModelEq)
arg$method["Y"] <- "hecknorm2step"

# }
# NOT RUN {
imputation3 <- mice(data = arg$data_mod,
                 method = arg$method,
                 predictorMatrix = arg$predictorMatrix,
                 JointModelEq=arg$JointModelEq,
                 control=arg$control,
                 maxit=1,m=5)

analysis3 <- with(imputation3,lm(Y~X1+X2+X3))
result3 <- pool(analysis3)
summary(result3)
# }