micemd (version 1.10.0)

mice.impute.2l.2stage.heckman: Imputation based on Heckman model for multilevel data.

Description

Imputes both outcome or predictor incomplete variables that follow an indirectly non-ignorable Missing Not at Random (MNAR) mechanism, i.e., the likelihood of a missing value in the incomplete variable depends on other unobserved variable(s) that are also correlated with the incomplete variable. This imputation is based on Heckman's selection model and is suitable for multilevel databases, such as individual participant data, with both systematic or sporadic missing data.

Usage

mice.impute.2l.2stage.heckman(y, ry, x, wy = NULL, type,
pmm = FALSE, ypmm = NULL, meta_method = "reml", pred_std = FALSE,...)

Value

Vector with imputed data, of type binary or continuous type

Arguments

y

Vector to be imputed

ry

A logical vector of length length(y) indicating the subset y[ry] of elements in y to which the imputation model is fitted. The ry generally distinguishes the observed (TRUE) and missing values (FALSE) in y.

x

A numeric design matrix with length(y) rows with predictors for y. Matrix x may have no missing values.

wy

A logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created.

type

Type of the variable in the prediction model, which can be one of the following: No predictor (0), Cluster variable (-2), Predictor in both the outcome and selection equation (2), Predictor only in the selection equation (-3), Predictor only in the outcome equation (-4). In this method all predictors are considered random variables that also included the fixed effect.

pmm

A logical value that specifies whether the predictive mean matching method is applied.(default = "FALSE"). This method is only applicable to missing continuous variables.

ypmm

A continuous vector of donor values for y used in the predictive mean matching method. if ypmm is not provided, the observable values of y are used as donors.

meta_method

A character value that indicates the method for estimating meta_analysis random effects: "ml" (maximum likelihood), "reml" (restricted maximum likelihood) or "mm" (method of moments).

pred_std

A logical value that indicates whether internally standardize the set of predictor variables (default = FALSE).

...

Other named arguments. Not used.

Author

Julius Center Methods Group UMC, 2022

Details

This function imputes systematically and sporadically missing binary and continuous univariate variables that follow an MNAR mechanism according to the Heckman selection model. It is specifically designed for clustered datasets. The imputation method employs a two-stage approach in which the Heckman model parameters at the cluster level are estimated using the copula method.

References

Munoz J,Hufstedler H,Gustafson P, Barnighausen T, De Jong V, Debray T. Dealing with missing data using the Heckman selection model: methods primer for epidemiologists.IJE,December 2022. tools:::Rd_expr_doi("10.1093/ije/dyac237").

Munoz J, Egger M, Efthimiou O, Audigier V, De Jong V, Debray T. Multiple imputation of incomplete multilevel data using Heckman selection models, Jan 2023, tools:::Rd_expr_doi("10.48550/arXiv.2301.05043").

See Also

mice

Examples

require(mice)
require(nlme)
require(broom.mixed)
require(parallel)

# Load dataset
data(Obesity) 

# Define imputation methods for each incomplete variables
meth <- find.defaultMethod(Obesity, ind.clust = 1)

# Modify some of the proposed imputation methods
# Deterministic imputation
meth["BMI"] <- "~ I(Weight / (Height)^2)" 
meth["Age"] <- "2l.2stage.pmm" 

# Set method, here Weight variable is assumed an MNAR variable
# Weight imputed with the Heckman method
meth["Weight"] <- "2l.2stage.heckman" 

# Set type of predictor variable, 
# All covariates are included in both outcome and selection equation
ini <- mice(Obesity, maxit = 0)
pred <- ini$pred
pred[,"Time"] <- 0
pred[,"Cluster"] <- -2
pred[pred == 1] <- 2

# Time was used as exclusion restriction variable 
pred["Weight","Time"]  <- -3  
# Deterministic imputation, to avoid circular predictions
pred[c("Height", "Weight"), "BMI"] <- 0 

# Imputation of continuous variables (time consumming)

# nnodes <- detectCores()
# imp <- mice.par(Obesity, meth = meth, pred = pred, m=10, seed = 123,
#                 nnodes = nnodes)
# summary(complete(imp,"long")$Weight)

# Imputation of continuous variables using the predictor mean matching method.
# Imputed values fall within the range of observable variables.

# imp_pmm <- mice.par(Obesity, meth = meth, pred = pred, m = 10,
#                     seed = 123, pmm=TRUE, nnodes = nnodes) 
# summary(complete(imp_pmm,"long")$Weight)

# Fit the model

# model_MNAR <- with(imp,lme( BMI ~ Age + FamOb + Gender,random=~1+Age|Cluster))
# model_MNAR_pmm <- with(imp_pmm,lme( BMI ~ Age + FamOb + Gender,random=~1+Age|Cluster))

# summary(pool(model_MNAR))
# summary(pool(model_MNAR_pmm))