References

The canonical citation list. Each entry notes where longmi relies on it. longmi implements established missing-data theory; it does not introduce a new proof of multiple imputation.

Missing-data foundations

  • Rubin DB. Inference and Missing Data. Biometrika. 1976;63(3):581–592. doi:10.1093/biomet/63.3.581. — Proposition 1 (ignorability under MAR); assumptions A2–A3.
  • Little RJA, Rubin DB. Statistical Analysis with Missing Data. 3rd ed. Hoboken: Wiley; 2019. doi:10.1002/9781119482260. — General reference for mechanisms and taxonomy (MCAR, MAR, MNAR).

Multiple imputation and posterior-predictive draws

  • Rubin DB. Multiple Imputations in Sample Surveys — A Phenomenological Bayesian Approach to Nonresponse. Proceedings of the Survey Research Methods Section, American Statistical Association. 1978:20–34. — Origin of the MI construction (Proposition 2).
  • Rubin DB. Multiple Imputation for Nonresponse in Surveys. New York: Wiley; 1987. doi:10.1002/9780470316696. — Combining rules, proper imputation, large-sample parameter draws (Propositions 2–3; the NB backend's declared approximation cites sec. 4.3).
  • Rubin DB. Multiple Imputation After 18+ Years. Journal of the American Statistical Association. 1996;91(434):473–489. doi:10.1080/01621459.1996.10476908. — Retrospective and defense of the framework.
  • Tanner MA, Wong WH. The Calculation of Posterior Distributions by Data Augmentation. Journal of the American Statistical Association. 1987;82(398):528–540. doi:10.1080/01621459.1987.10478458. — The data-augmentation scheme behind the joint Gaussian backend.
  • Schafer JL. Analysis of Incomplete Multivariate Data. New York: Chapman & Hall/CRC; 1997. — The NORM algorithm the joint Gaussian backend implements (with regressors).
  • White IR, Royston P, Wood AM. Multiple Imputation Using Chained Equations: Issues and Guidance for Practice. Statistics in Medicine. 2011;30(4):377–399. doi:10.1002/sim.4067. — Practical guidance informing the reporting checklist and choice of M.
  • Carpenter JR, Bartlett JW, Morris TP, Wood AM, Quartagno M, Kenward MG. Multiple Imputation and its Application. 2nd ed. Chichester: Wiley;
  • doi:10.1002/9781119756118. — Modern book-length treatment, including sensitivity analysis.

Combining rules and degrees of freedom

  • Barnard J, Rubin DB. Small-Sample Degrees of Freedom With Multiple Imputation. Biometrika. 1999;86(4):948–955. doi:10.1093/biomet/86.4.948. — The pool_rubin degrees-of-freedom rule (algorithm).

Large-sample theory, congeniality, estimating equations

  • Wang N, Robins JM. Large-Sample Theory for Parametric Multiple Imputation Procedures. Biometrika. 1998;85(4):935–948. doi:10.1093/biomet/85.4.935. — Proposition 3's asymptotics.
  • Meng XL. Multiple-Imputation Inferences With Uncongenial Sources of Input. Statistical Science. 1994;9(4):538–573. doi:10.1214/ss/1177010269. — Congeniality (A8; Proposition 4).
  • Robins JM, Wang N. Inference for Imputation Estimators. Biometrika. 2000;87(1):113–124. doi:10.1093/biomet/87.1.113. — Variance under incompatibility (Proposition 4).
  • Yang S, Kim JK. A Note on Multiple Imputation for Method of Moments Estimation. Biometrika. 2016;103(1):244–251. doi:10.1093/biomet/asv073. — Rubin-variance bias for method-of-moments analyses (Proposition 4).

GEE and marginal models

  • Liang KY, Zeger SL. Longitudinal Data Analysis Using Generalized Linear Models. Biometrika. 1986;73(1):13–22. doi:10.1093/biomet/73.1.13. — The GEE estimator behind StatsmodelsGEE.
  • Zeger SL, Liang KY, Albert PS. Models for Longitudinal Data: A Generalized Estimating Equation Approach. Biometrics. 1988;44(4):1049–1060. doi:10.2307/2531734. — Marginal vs subject-specific (conditional) estimands; the attenuation the NB simulation's truth calibration accounts for.

MI with GEE in longitudinal research

  • Beunckens C, Sotto C, Molenberghs G. A Simulation Study Comparing Weighted Estimating Equations With Multiple Imputation Based Estimating Equations for Longitudinal Binary Data. Computational Statistics & Data Analysis. 2008;52(3):1533–1548. doi:10.1016/j.csda.2007.04.020.
  • Lipsitz SR, Fitzmaurice GM, Weiss RD. Using Multiple Imputation With GEE With Non-monotone Missing Longitudinal Binary Outcomes. Psychometrika. 2020;85(4):890–904. doi:10.1007/s11336-020-09729-y.

Inverse probability weighting (the complementary approach)

  • Robins JM, Rotnitzky A, Zhao LP. Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data. Journal of the American Statistical Association. 1995;90(429):106–121. doi:10.1080/01621459.1995.10476493. — IPW-GEE, the response-model counterpart planned for the epil example's comparison arm.

Robust inference under uncongeniality

  • Bartlett JW, Hughes RA. Bootstrap Inference for Multiple Imputation Under Uncongeniality and Misspecification. Statistical Methods in Medical Research. 2020;29(12):3533–3546. doi:10.1177/0962280220932189. — Bootstrap-then-impute, the planned 0.2 pooling mode.

MNAR sensitivity analysis

  • Cro S, Morris TP, Kenward MG, Carpenter JR. Sensitivity Analysis for Clinical Trials With Missing Continuous Outcome Data Using Controlled Multiple Imputation: A Practical Guide. Statistics in Medicine. 2020;39(21):2815–2842. doi:10.1002/sim.8569. — Delta adjustment as controlled MI (how-to).

Numerical methods

  • Liu Q, Pierce DA. A Note on Gauss–Hermite Quadrature. Biometrika. 1994;81(3):624–629. doi:10.1093/biomet/81.3.624. — The quadrature integrating the NB backend's random intercept.

Evaluating statistical methods by simulation

  • Morris TP, White IR, Crowther MJ. Using Simulation Studies to Evaluate Statistical Methods. Statistics in Medicine. 2019;38(11):2074–2102. doi:10.1002/sim.8086. — The framework behind the simulation harness's performance measures and Monte Carlo standard errors.

Applied tutorial and validation oracles

  • Wijesuriya R, et al. Multiple Imputation for Longitudinal Data: A Tutorial. Statistics in Medicine. 2024. doi:10.1002/sim.10274. — The external methodological oracle (simulated CATS parity).
  • Thall PF, Vail SC. Some Covariance Models for Longitudinal Count Data With Overdispersion. Biometrics. 1990;46(3):657–671. doi:10.2307/2532086. — Source of the epil seizure-count data.
  • Venables WN, Ripley BD. Modern Applied Statistics with S. 4th ed. New York: Springer; 2002. doi:10.1007/978-0-387-21706-2. — The MASS package distributing epil.

Software validated against or built upon

  • van Buuren S, Groothuis-Oudshoorn K. mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software. 2011;45(3):1–67. doi:10.18637/jss.v045.i03. — pool_rubin is verified bit-compatible with mice::pool.scalar.
  • Halekoh U, Højsgaard S, Yan J. The R Package geepack for Generalized Estimating Equations. Journal of Statistical Software. 2006;15(2):1–11. doi:10.18637/jss.v015.i02. — The R side of the epil GEE cross-implementation comparison.
  • Seabold S, Perktold J. statsmodels: Econometric and Statistical Modeling with Python. Proceedings of the 9th Python in Science Conference. 2010:92–96. doi:10.25080/Majora-92bf1922-011. — The GEE/GLM engines wrapped by the analysis adapters.