Estimation under not Missing at Random Nonresponse

Methods to estimate finite-population parameters under nonresponse that is not missing at random (NMAR, nonignorable). Incorporates auxiliary information and user-specified response models, and supports independent samples and complex survey designs via objects from the 'survey' package. Provides diagnostics and optional variance estimates. For methodological background see Qin, Leung and Shao (2002) and Riddles, Kim and Im (2016) .

NMAR

NMAR provides estimators for finite-population means when outcomes are subject to nonignorable nonresponse (Not Missing at Random, NMAR). It supports iid data.frame inputs and complex survey designs via survey.design objects from the survey package, and exposes a unified interface through nmar().

Methods

NMAR currently provides the following engines:

el_engine(): empirical likelihood (Qin, Leung and Shao, 2002).
exptilt_engine(): exponential tilting (Riddles, Kim and Im, 2016).
exptilt_nonparam_engine(): nonparametric exponential tilting for aggregated categorical data (Riddles, Kim and Im, 2016, Appendix 2).

References:

Qin, J., Leung, D., and Shao, J. (2002). Estimation with survey data under nonignorable nonresponse or informative sampling. Journal of the American Statistical Association, 97(457), 193-200. https://doi.org/10.1198/016214502753479338
Riddles, M. K., Kim, J. K., and Im, J. (2016). A propensity-score-adjustment method for nonignorable nonresponse. Journal of Survey Statistics and Methodology, 4(2), 215-245. https://doi.org/10.1093/jssam/smv047

See browseVignettes("NMAR") and the package website for worked examples and engine-specific assumptions: https://ncn-foreigners.ue.poznan.pl/NMAR/.

Installation

Install the CRAN release:

install.packages("NMAR")

Install the development version from GitHub:

# install.packages("pak")
pak::pak("ncn-foreigners/NMAR")

Or with remotes:

# install.packages("remotes")
remotes::install_github("ncn-foreigners/NMAR")

To build vignettes locally:

remotes::install_github("ncn-foreigners/NMAR", build_vignettes = TRUE)

Usage

Formula interface

nmar() uses a two-sided formula with the outcome on the left-hand side. In the common “missing values indicate nonresponse” workflow, nonrespondents are encoded as NA in the outcome.

Many engines support a partitioned right-hand side via | (e.g., y_miss ~ block1_vars | block2_vars), but the interpretation of these blocks is engine-specific. See ?el_engine and ?exptilt_engine for details.

Example

suppressPackageStartupMessages(library(NMAR))

data("riddles_case1", package = "NMAR")

# Empirical likelihood (EL)
fit_el <- nmar(
  y ~ x,
  data = riddles_case1,
  engine = el_engine(variance_method = "none")
)
summary(fit_el)
#> NMAR Model Summary
#> =================
#> y mean: -1.001986
#> Converged: TRUE 
#> Variance method: none 
#> Variance notes: Variance skipped (variance_method='none') 
#> Total units: 500 
#> Respondents: 368 
#> Call: nmar(y ~ x, data = <data.frame: N=500>, engine = empirical_likelihood)
#> 
#> Missingness-model coefficients:
#>              Estimate
#> (Intercept)  0.860555
#> y           -0.175376

# Exponential tilting (ET)
fit_et <- nmar(
  y ~ x,
  data = riddles_case1,
  engine = exptilt_engine(y_dens = "normal", family = "logit", variance_method = "none")
)
summary(fit_et)
#> NMAR Model Summary (Exponential tilting)
#> =================================
#> y mean: -1.004076
#> Converged: TRUE 
#> Variance method: none 
#> Call: nmar(y ~ x, data = <data.frame: N=?>, engine = exponential_tilting)
#> 
#> Response-model (theta) coefficients:
#>   (Intercept)          : 0.864241
#>   y                    : -0.169948

Result objects returned by nmar() support methods such as summary(), weights(), se(), and confint(), and tidy() / glance() via the generics package.

Survey designs

if (requireNamespace("survey", quietly = TRUE)) {
  suppressPackageStartupMessages(library(survey))
  set.seed(1)
  d <- riddles_case1
  d$w <- runif(nrow(d), 0.5, 2)
  des <- survey::svydesign(ids = ~1, weights = ~w, data = d)

  fit_svy <- nmar(y ~ x, data = des, engine = el_engine(variance_method = "none"))
  summary(fit_svy)
}
#> NMAR Model Summary
#> =================
#> y mean: -1.005961
#> Converged: TRUE 
#> Variance method: none 
#> Variance notes: Variance skipped (variance_method='none') 
#> Total units: 621.7412 
#> Respondents: 368 
#> Call: nmar(y ~ x, data = <survey.design: N=621.741>, engine = empirical_likelihood)
#> 
#> Missingness-model coefficients:
#>              Estimate
#> (Intercept)  0.893453
#> y           -0.129256