Jacknife and Regression Approaches to Missing Data Imputation.

Authors

  • Jumlong Vongprasert

Keywords:

Missing Data,, Imputation, Jacknife.

Abstract

Missing data imputation is an important task in cases where it is crucial to use all available data
and not discard records with missing values. The purpose of this work were first to develop the
Average of Jacknife Mean and Regression (AJRI) for missing data estimation and secondly to
compare its efficiency of estimation with another methods, namely; Mean Imputation ( MI)
Regression Imputation ( RI) Regime Switching Regression Imputation (RSRI) EM Algorithm
(EM) and Multiple Imputation (MUL) . By using simulation data, the comparisons were made
with the following conditions: ( i) Four sample size (100, 200 500 and 1,000) ( ii) three type of
missing data MCAR MAR and NMAR. The best imputation under MSE. The best imputation
under MSE of mean variance and correlation classified by sample sizes and by percentage of
missing data were obtained using RSRI EM and RI respectively, classified by missing data type
were obtained using RSRI for mean and EM for variance and correlation. The best imputation
under MSE of regression coefficient were obtained using EM and RSRI for model 1 and model
2 respectively. The best imputation under MSE of R2 were obtained using EM.

Author Biography

Jumlong Vongprasert

Applied Statistics Department, Ubon Ratchathani Rajabhat University

References

[1] Becker, W. E., and W. B. Walstad. Data loss from pretest to posttest as a sample selection problem. Review of Economics and Statistics. 1990; 72 (1): 184-188.

[2] Becker, W., & Powers, J. Student performance, attrition, and class size given missing student data. Economics of Education Review. 2001. 20, 377-388.

[3] Rubin, D.B. Multiple imputation for nonresponse in surveys, New York: John Wiley & Sons, Inc.; 1987.

[4] Chen, S. X., Leung, D. H. Y. and Qin, J. Improving semiparametric estimation by using surrogate data. Journal of Royal Statistical Society: Series B. 2008; 70: 803–823.

[5] Kott, P. S. and Chang, T. Using calibration weighting to adjust for nonignorable unit nonresponse. Journal of the American Statistical Association. 2010; 105, 1265–1275.

[6] Anderson, A.B., Basilevsky, A. & Hum, D. P. J. Missing data: A review of the literature. In P. H. Rossi, J. D. Wright, & A. B. Anderson (Eds.), Handbook of survey research (pp. 415-494). San Diego: Academic Press.; 1983.

[7] Kim, J.O. and Curry, J. The Treatment of Missing Data in Multivariate Analysis. Sociological Methods Research. 1977; 6:215-240.

[8] Cohen, J., & Cohen, P. Missing data. In J. Cohen & P. Cohen, Applied multiple regression: Correlation analysis for the behavioral sciences (pp. 275-300).; 1983.

[9] Little, R.J. and D.B. Rubin, Statistical Analysis with Missing Data. 2nd Edn., John Wiley and Sons, New York, ISBN: 978-0-471-18386-0, pp: 408. 2002.

[10] Im, Jongho. Some methods for handling missing data in surveys. PhD [Dissertations]. Iowa State University; 2015.

[11] Quenonuille, M. H. Notes on Bias in Estimation. Biometrika. 1956;43, 353-360.

[12] Yu, C. H., Resampling Methods: Concepts, Applications, and Justification, Practical Assessment, Research and Evaluation. 2003: 8(19).

[13] Sahinler S., & Topuz, D. Bootstrap and Jackknife Resampling Algorithms for Estimation of Regression Parameters. Journal of Applied Qualitative Methods. 2007;2(2) Summer, 188-199
.
[15] Little, R.J.A. Regression with missing X’s:a review, Journal of the American Statistical Association. 1992;87: 1227–1237.

[14] Draper, Norman R., & Smith, H.. Applied Regression Analysis. 3rd ed. John Willey & Sons, Inc., New York; 1998.

[16] Vongprasert, J. and B. Premanode, Missing data imputation using weighted of regime switching mean and regression. J. Math. Stat. 2014; 10: 255-261.

[17] Dempster, A.P.; Laird, N.M.; Rubin, D.B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B. 1977;39 (1): 1–38.

[18] Rubin, D.B. Multiple Imputation for Nonresponse in Surveys. New York: Wiley; 1987.

Downloads

Published

2019-01-17

How to Cite

Vongprasert, J. (2019). Jacknife and Regression Approaches to Missing Data Imputation. Journal of Applied Statistics and Information Technology, 3(1), 52–61. Retrieved from https://ph02.tci-thaijo.org/index.php/asit-journal/article/view/166906