Imputation Methods for Longitudinal Data: A Comparative Study
International Journal of Statistical Distributions and Applications
Volume 3, Issue 4, December 2017, Pages: 72-80
Received: Mar. 5, 2017; Accepted: Mar. 28, 2017; Published: Nov. 10, 2017
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Ahmed Mahmoud Gad, Statistics Department, Faculty of Economics and Political Science, Cairo University, Cairo, Egypt
Rania Hassan Mohamed Abdelkhalek, Department Statistics, Mathematics and Insurance, Faculty of Commerce, Benha University, Benha, Egypt
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Longitudinal studies play an important role in scientific researches. The defining characteristic of the longitudinal studies is that observations are collected from each subject repeatedly over time, or under different conditions. Missing values are common in longitudinal studies. The presence of missing values is always a fundamental challenge since it produces potential bias, even in well controlled conditions. Three different missing data mechanisms are defined; missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Several imputation methods have been developed in literature to handle missing values in longitudinal data. The most commonly used imputation methods include complete case analysis (CCA), mean imputation (Mean), last observation carried forward (LOCF), hot deck (HOT), regression imputation (Regress), K-nearest neighbor (KNN), The expectation maximization (EM) algorithm, and multiple imputation (MI). In this article, a comparative study is conducted to investigate the efficiency of these eight imputation methods under different missing data mechanisms. The comparison is conducted through simulation study. It is concluded that the MI method is the most effective method as it has the least standard errors. The EM algorithm has the largest relative bias. The different methods are also compared via real data application.
Dropout Missing, Longitudinal Data, Missing Data, Multiple Imputations, Single Imputation
To cite this article
Ahmed Mahmoud Gad, Rania Hassan Mohamed Abdelkhalek, Imputation Methods for Longitudinal Data: A Comparative Study, International Journal of Statistical Distributions and Applications. Vol. 3, No. 4, 2017, pp. 72-80. doi: 10.11648/j.ijsd.20170304.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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