A Multiple Imputation Framework for Massive Multivariate Data of Different Variable Types: A Monte-Carlo Technique

  • Hakan DemirtasEmail author
Part of the ICSA Book Series in Statistics book series (ICSABSS)


The purpose of this chapter is to build theoretical, algorithmic, and implementation-based components of a unified, general-purpose multiple imputation framework for intensive multivariate data sets that are collected via increasingly popular real-time data capture methods . Such data typically include all major types of variables that are incomplete due to planned missingness designs, which have been developed to reduce respondent burden and lower the cost associated with data collection. The imputation approach presented herein complements the methods available for incomplete data analysis via richer and more flexible modeling procedures, and can easily generalize to a variety of research areas that involve internet studies and processes that are designed to collect continuous streams of real-time data. Planned missingness designs are highly useful and will likely increase in popularity in the future. For this reason, the proposed multiple imputation framework represents an important and refined addition to the existing methods, and has potential to advance scientific knowledge and research in a meaningful way. Capability of accommodating many incomplete variables of different distributional nature, types, and dependence structures could be a contributing factor for better comprehending the operational characteristics of today’s massive data trends. It offers promising potential for building enhanced statistical computing infrastructure for education and research in the sense of providing principled, useful, general, and flexible set of computational tools for handling incomplete data.


Random Number Generation Count Variable Standard Normal Variable Threshold Concept Tetrachoric Correlation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Amatya, A., & Demirtas, H. (2015a). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85, 3129–3139.MathSciNetCrossRefGoogle Scholar
  2. Amatya, A., & Demirtas, H. (2015b). Concurrent generation of ordinal and normal data with given correlation matrix and marginal distributions, R package OrdNor.
  3. Amatya, A., & Demirtas, H. (2016a). Simultaneous generation of multivariate binary and normal variates, R package BinNor.
  4. Amatya, A., & Demirtas, H. (2016b). Generation of multivariate ordinal variates, R package MultiOrd.
  5. Amatya, A., & Demirtas, H. (2016c). Simultaneous generation of multivariate data with Poisson and normal marginals, R package PoisNor.
  6. Demirtas, H. (2004). Simulation-driven inferences for multiply imputed longitudinal datasets. Statistica Neerlandica, 58, 466–482.Google Scholar
  7. Demirtas, H. (2005). Multiple imputation under Bayesianly smoothed pattern-mixture models for non-ignorable drop-out. Statistics in Medicine, 24, 2345–2363.MathSciNetCrossRefGoogle Scholar
  8. Demirtas, H. (2006). A method for multivariate ordinal data generation given marginal distributions and correlations. Journal of Statistical Computation and Simulation, 76, 1017–1025.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Demirtas, H. (2007). Practical advice on how to impute continuous data when the ultimate interest centers on dichotomized outcomes through pre-specified thresholds. Communications in Statistics-Simulation and Computation, 36, 871–889.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Demirtas, H. (2008). On imputing continuous data when the eventual interest pertains to ordinalized outcomes via threshold concept. Computational Statistics and Data Analysis, 52, 2261–2271.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Demirtas, H. (2009). Rounding strategies for multiply imputed binary data. Biometrical Journal, 51, 677–688.MathSciNetCrossRefGoogle Scholar
  12. Demirtas, H. (2010). A distance-based rounding strategy for post-imputation ordinal data. Journal of Applied Statistics, 37, 489–500.MathSciNetCrossRefGoogle Scholar
  13. Demirtas, H. (2014). Joint generation of binary and nonnormal continuous data. Journal of Biometrics and Biostatistics, 5, 1–9.Google Scholar
  14. Demirtas, H. (2016). A note on the relationship between the phi coefficient and the tetrachoric correlation under nonnormal underlying distributions. American Statistician, 70, 143–148.MathSciNetCrossRefGoogle Scholar
  15. Demirtas, H. (2017a). Concurrent generation of binary and nonnormal continuous data through fifth order power polynomials, Communications in Statistics—Simulation and Computation, 46, 344–357.Google Scholar
  16. Demirtas, H. (2017b). On accurate and precise generation of generalized Poisson variates, Communications in Statistics—Simulation and Computation, 46, 489–499.Google Scholar
  17. Demirtas, H., Ahmadian, R., Atis, S., Can, F. E., & Ercan, I. (2016a). A nonnormal look at polychoric correlations: Modeling the change in correlations before and after discretization. Computational Statistics, 31, 1385–1401.CrossRefzbMATHGoogle Scholar
  18. Demirtas, H., Arguelles, L. M., Chung, H., & Hedeker, D. (2007). On the performance of bias-reduction techniques for variance estimation in approximate Bayesian bootstrap imputation. Computational Statistics and Data Analysis, 51, 4064–4068.MathSciNetCrossRefzbMATHGoogle Scholar
  19. Demirtas, H., & Doganay, B. (2012). Simultaneous generation of binary and normal data with specified marginal and association structures. Journal of Biopharmaceutical Statistics, 22, 223–236.MathSciNetCrossRefGoogle Scholar
  20. Demirtas, H., Freels, S. A., & Yucel, R. M. (2008). Plausibility of multivariate normality assumption when multiply imputing non-Gaussian continuous outcomes: A simulation assessment. Journal of Statistical Computation and Simulation, 78, 69–84.MathSciNetCrossRefzbMATHGoogle Scholar
  21. Demirtas, H., & Hedeker, D. (2007). Gaussianization-based quasi-imputation and expansion strategies for incomplete correlated binary responses. Statistics in Medicine, 26, 782–799.MathSciNetCrossRefGoogle Scholar
  22. Demirtas, H., & Hedeker, D. (2008a). Multiple imputation under power polynomials. Communications in Statistics–Simulation and Computation, 37, 1682–1695.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Demirtas, H., & Hedeker, D. (2008b). An imputation strategy for incomplete longitudinal ordinal data. Statistics in Medicine, 27, 4086–4093.MathSciNetCrossRefGoogle Scholar
  24. Demirtas, H., & Hedeker, D. (2008c). Imputing continuous data under some non-Gaussian distributions. Statistica Neerlandica, 62, 193–205.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Demirtas, H., & Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65, 104–109.MathSciNetCrossRefzbMATHGoogle Scholar
  26. Demirtas, H., & Hedeker, D. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Communications in Statistics- Simulation and Computation, 45, 2744–2751.MathSciNetCrossRefzbMATHGoogle Scholar
  27. Demirtas, H., Hedeker, D., & Mermelstein, J. M. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31, 3337–3346.MathSciNetCrossRefGoogle Scholar
  28. Demirtas, H., Hu, Y., & Allozi, R. (2016b). Data generation with Poisson, binary, ordinal and normal components, R package PoisBinOrdNor.
  29. Demirtas, H., Nordgren, R., & Allozi, R. (2016c). Generation of up to four different types of variables, R package PoisBinOrdNonNor.
  30. Demirtas, H., & Schafer, J. L. (2003). On the performance of random-coefficient pattern-mixture models for non-ignorable drop-out. Statistics in Medicine, 22, 2553–2575.CrossRefGoogle Scholar
  31. Demirtas, H., Shi, Y., & Allozi, R. (2016d). Simultaneous generation of count and continuous data, R package PoisNonNor.
  32. Demirtas, H., Wang, Y., & Allozi, R. (2016e). Concurrent generation of binary, ordinal and continuous data, R package BinOrdNonNor.
  33. Demirtas, H., & Yavuz, Y. (2015). Concurrent generation of ordinal and normal data. Journal of Biopharmaceutical Statistics, 25, 635–650.CrossRefGoogle Scholar
  34. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of Royal Statistical Society-Series B, 39, 1–38.MathSciNetzbMATHGoogle Scholar
  35. Emrich, J. L., & Piedmonte, M. R. (1991). A method for generating high-dimensional multivariate binary variates. The American Statistician, 45, 302–304.Google Scholar
  36. Ferrari, P. A., & Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47, 566–589.CrossRefGoogle Scholar
  37. Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521–532.CrossRefzbMATHGoogle Scholar
  38. Headrick, T. C. (2002). Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. Computational Statistics and Data Analysis, 40, 685–711.MathSciNetCrossRefzbMATHGoogle Scholar
  39. Headrick, T. C. (2010). Statistical simulation: Power method polynomials and other transformations. Boca Raton, FL: Chapman and Hall/CRC.zbMATHGoogle Scholar
  40. Hedeker, D., Demirtas, H., & Mermelstein, R. J. (2008). An application of a mixed-effects location scale model for analysis of ecological momentary mssessment (EMA) data. Biometrics, 6, 627–634.CrossRefzbMATHGoogle Scholar
  41. Hedeker, D., Demirtas, H., & Mermelstein, R. J. (2009). A mixed ordinal location scale model for analysis of ecological momentary assessment (EMA) data. Statistics and Its Interface, 2, 391–402.MathSciNetCrossRefzbMATHGoogle Scholar
  42. Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2012). Modeling between- and within-subject variance in ecological momentary assessment (EMA) data using mixed-effects location scale models. Statistics in Medicine, 31, 3328–3336.MathSciNetCrossRefGoogle Scholar
  43. Higham, N. J. (2002). Computing the nearest correlation matrix—a problem from finance. IMA Journal of Numerical Analysis, 22, 329–343.MathSciNetCrossRefzbMATHGoogle Scholar
  44. Inan, G., & Demirtas, H. (2016a). Data generation with binary and continuous non-normal components, R package BinNonNor.
  45. Inan, G., & Demirtas, H. (2016b). Data generation with Poisson, binary and ordinal components, R package PoisBinOrd.
  46. Inan, G., & Demirtas, H. (2016c). Data generation with Poisson, binary and continuous components, R package PoisBinNonNor.
  47. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York, NY: Wiley.zbMATHGoogle Scholar
  48. Nelsen, R. B. (2006). An introduction to copulas. Berlin, Germany: Springer.zbMATHGoogle Scholar
  49. Qaqish, B. F. (2003). A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations. Biometrika, 90, 455–463.MathSciNetCrossRefzbMATHGoogle Scholar
  50. Raghunathan, T. E., Lepkowski, J. M., van Hoewyk, J., & Solenberger, P. A. (2001). Multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodology, 27, 85–95.Google Scholar
  51. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.MathSciNetCrossRefzbMATHGoogle Scholar
  52. Rubin, D. B. (2004). Multiple imputation for nonresponse in surveys (2nd ed.). New York, NY: Wiley.zbMATHGoogle Scholar
  53. Schafer, J. L. (1997). Analysis of incomplete multivariate data. London, UK: Chapman and Hall.Google Scholar
  54. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of American Statistical Association, 82, 528–540.MathSciNetCrossRefzbMATHGoogle Scholar
  55. Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465–471.CrossRefzbMATHGoogle Scholar
  56. Van Buuren, S. (2012). Flexible imputation of missing data. Boca Raton, Florida: CRC Press.CrossRefzbMATHGoogle Scholar
  57. Walls, T. A., & Schafer, J. L. (2006). Models for intensive longitudinal data. New York, NY: Oxford University Press.CrossRefzbMATHGoogle Scholar
  58. Yahav, I., & Shmueli, G. (2012). On generating multivariate Poisson data in management science applications. Applied Stochastic Models in Business and Industry, 28, 91–102.MathSciNetCrossRefzbMATHGoogle Scholar
  59. Yucel, R. M., & Demirtas, H. (2010). Impact of non-normal random effects on inference by multiple imputation: A simulation assessment. Computational Statistics and Data Analysis, 54, 790–801.MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Division of Epidemiology and Biostatistics (MC923)University of Illinois at ChicagoChicagoUSA

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