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::survey.design, 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 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: -1.003974
#> Converged: TRUE 
#> Variance method: none 
#> Call: nmar(y ~ x, data = <data.frame: N=?>, engine = exponential_tilting)
#> 
#> Response-model (theta) coefficients:
#>   (Intercept)          : 0.864080
#>   y                    : -0.170216

Result objects returned by nmar() support methods such as summary(), weights(), se(), and confint(), and broom-style 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

Getting help

If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub

Citation

If you use NMAR in academic work, please cite the package and the relevant method paper(s):

citation("NMAR")

Authors and acknowledgments

Research grant: OPUS 20 #2020/39/B/HS4/00941

• Maciej Beręsewicz
• Igor Kołodziej
• Mateusz Iwaniuk