Multiple Imputation of Turnover in EDINET Data: Toward the Improvement of Imputation for the Economic Census

Transcription

1 ultiple Imputation of Turnover in EDINET Data: Toward the Improvement of Imputation for the Economic Census UNECE Work Session on Statistical Data Editing, WP.35 Oslo, Norway, 25 September 2012 National Statistics Center (Japan) asayoshi Takahashi Takayuki Ito Notes: The views and opinions expressed in this presentation are the authors own, not necessarily those of the institution.

2 Introduction Economic Census for Business Activity ultiple Imputation EB Algorithm R Package Amelia EDINET Data Diagnostics of ultiple Imputation 1

3 ultiple Imputation via EB Algorithm 2

4 R Package Amelia II Amelia I (2001) General-purpose multiple imputation software Developed by Harvard University Professor Gary King and his colleagues Amelia II (2011) Need to apply multiple imputation to a gigantic dataset Implemented with the new EB Algorithm Can handle 240 variables and 32,000 observations, i.e., 7.68 million variableobservations. 3

5 Descriptions of EDINET Dataset EDINET = Electronic Disclosure for Investors NETwork aintained by the Financial Services Agency of the Japanese Government No missing values in the EDINET turnover data Can artificially create missing values in this dataset. Can compare the true and the imputed values. 4

6 Results of ultiple Imputation and Single Imputation: Sector Sector ultiple Imputation Single Imputation Total E (n = 1222, manufacturing) 66.7% 33.3% 100 % I (n = 571, retailing) 50.0% 50.0 % 100 % D (n = 158, construction) 10.0% 90.0 % 100 % G (n = 276, communication) 85.7% 14.3 % 100 % L (n = 191, service) 92.3% 7.7 % 100 % Total 62.5% 37.5 % 100 % 5

7 Results of ultiple Imputation and Single Imputation: issing Pattern issing Pattern ultiple Imputation Single Imputation Total Completely Random 75.0% 25.0 % 100 % Worker Size Small 75.0% 25.0 % 100 % Worker Size edium 90.0% 10.0 % 100 % Worker Size Large 66.7% 33.3 % 100 % Worker Size Large and Small 50.0% 50.0 % 100 % Systematic Sampling 20.0% 80.0 % 100 % Total 62.5% 37.5 % 100 % 6

8 Results of ultiple Imputation and Single Imputation: odel odel ultiple Imputation Single Imputation Total 1 st Order Polynomial 64.7% 35.3 % 100 % Natural Log 60.9% 39.1 % 100 % Total 62.5% 37.5 % 100 % 7

9 Results of ultiple Imputation and Single Imputation: issing Rate issing Rate ultiple Imputation Single Imputation Total 30% 55.0 % 45.0 % 100 % 40% 69.2% 30.8 % 100 % 50% 71.4% 28.6 % 100 % Total 62.5% 37.5 % 100 % 8

10 Results of ultiple Imputation and Single Imputation: Standard Deviation (CAR) Standard Deviation Difference: Truth & Imputation True Value ultiple Imputation Single Imputation Notes: Sector E, Natural Log, issing Rate = 50% 9

11 Scatterplots (CAR) True Scatterplot CAR issing Rate 50% Single Imputation ultiple Imputation (m = 10) 10

12 Results of ultiple Imputation and Single Imputation: Standard Deviation (AR) Standard Deviation Difference: Truth & Imputation True Value ultiple Imputation Single Imputation Notes: Sector E, Natural Log, issing Rate = 50% 11

13 Scatterplots (AR: Worker = Small) True Scatterplot AR issing Rate 50% Single Imputation ultiple Imputation (m = 10) 12

14 ultiple Imputation Diagnostics Amelia II supplies the following four diagnostic functions for multiple imputation. Comparing Densities function issingness ap function Overimpute function Overdispersed Starting Values function 13

15 ultiple Imputation Diagnostics 1a (CAR) 14

16 ultiple Imputation Diagnostics 1b (CAR) 15

17 ultiple Imputation Diagnostics 2a (AR) 16

18 ultiple Imputation Diagnostics 2b (AR) 17

19 Conclusions and Future Research Fit of multiple imputation Efficiency of multiple imputation Usefulness of R package Amelia II Diagnostic methods in multiple imputation Impact of outliers on multiple imputation 18

20 References 1 Abayomi, Kobi, Andrew Gelman, and arc Levy. (2008). Diagnostics for ultivariate Imputations, Applied Statistics vol.57, no.3: Congdon, Peter. (2006). Bayesian Statistical odelling, Second Edition. West Sussex: John Wiley & Sons Ltd. DeGroot, orris H. and ark J. Schervish. (2002). Probability and Statistics. Boston: Addison- Wesley. Drechsler, Jörg. (2009). Far From Normal - ultiple Imputation of issing Values in a German Establishment Survey, Work Session on Statistical Data Editing, Conference of European Statisticians, Neuchâtel, Switzerland, 5-7 October Financial Services Agency, the Japanese Government. (2011). EDINET-Electronic Disclosure for Investors NETwork, (Accessed on April 13, 2012), Gelman, Andrew, and Jennifer Hill. (2006). Data Analysis Using Regression and ultilevel/hierarchical odels. New York: Cambridge University Press. Gill, Jeff. (2008). Bayesian ethods A Social Sciences Approach, Second Edition. London: Chapman & Hall/CRC. Honaker, James and Gary King. (2010). What to do About issing Values in Time Series Cross- Section Data, American Journal of Political Science vol.54, no.2: Honaker, James, Gary King, and atthew Blackwell. (2011). Amelia II: A Program for issing Data, Journal of Statistical Software vol.45, no.7. 19

21 References 2 Honaker, James, Gary King, and atthew Blackwell. (2012a). Amelia II: A Program for issing Data Version (Accessed on April 9, 2012), Honaker, James, Gary King, and atthew Blackwell. (2012b). Package Amelia Version (Accessed on April 4, 2012), Imai, Kosuke, Gary King, and Olivia Lau. (2008). Toward A Common Framework for Statistical Analysis and Development, Journal of Computational and Graphical Statistics vol.17, no.4: King, Gary, James Honaker, Anne Joseph, and Kenneth Scheve. (2001). Analyzing Incomplete Political Science Data: An Alternative Algorithm for ultiple Imputation, American Political Science Review vol.95, no.1: Little, Roderick J. A. and Donald B. Rubin. (2002). Statistical Analysis with issing Data, Second Edition. New Jersey: John Wiley & Sons. Rubin, Donald B. (1978). ultiple Imputations in Sample Surveys A Phenomenological Bayesian Approach to Nonresponse, Proceedings of the Survey Research ethods Section, American Statistical Association: Rubin, Donald B. (1987). ultiple Imputation for Nonresponse in Surveys. New York: John Wiley & Sons. Schafer, Joseph L. (1999). ultiple Imputation: A Primer, Statistical ethods in edical Research vol.8: Schmidt, Katrin. (2009). ultiple Imputation with Standard Software: First Application Experiences, Work Session on Statistical Data Editing, Conference of European Statisticians, Neuchâtel, Switzerland, 5-7 October

22 References 3 Shadish, William R., Thomas D. Cook, and Donald T. Campbell. (2002). Experimental and Quasi- Experimental Designs for Generalized Causal Inference. Boston: Houghton ifflin Company. Shao, Jun. (2002). Replication ethods for Variance Estimation in Complex Surveys with Imputed Data, in Survey Nonresponse edited by Robert. Groves, Don A. Dillman, John L. Eltinge, Roderick J. A. Little. New York: John Wiley & Sons, pp Shao, Jun and Dongsheng Tu. (1995). The Jackknife and Bootstrap. New York: Springer. Templ, atthias, Alexander Kowarik, and Peter Filzmoser. (2011). Imputation of Complex Data With R-Package VI: Traditional and New ethods Based on Robust Estimation, Work Session on Statistical Data Editing, Conference of European Statisticians, Ljubljana, Slovenia, 9-11 ay Waal, Ton de, Jeroen Pannekoek, and Sander Scholtus. (2011). Handbook of Statistical Data Editing and Imputation. Hoboken, NJ: John Wiley & Sons. Watanabe, ichiko, and Kazunori Yamaguchi. (2000). E Algorithm to Fukanzen Data no Shomondai (E Algorithm and the Problems of Incomplete Data). Tokyo: Taga Shuppan. Wooldridge, Jeffrey. (2002). Econometric Analysis of Cross Section and Panel Data. Cambridge, A: IT Press. Yucel, Recai. (2011). State of the ultiple Imputation Software, Journal of Statistical Software vol.45, no.1. 21

23 Thank you. 22

24 Appendix 1: ultiple Imputation Formula 23 m m 1 ˆ 1 v v T ~ 1 1 m v m v 1 1 m m v 1 2 ˆ 1 1 ~

25 Appendix 2: ultiple Imputation odel D ~ N (, ) p ~ D D ij i ~ ~, j i 24

26 Appendix 3: Distributions of I and SI 25

27 Appendix 4: Asymptotic Relative Efficiency ARE

28 Appendix 5: ARE (50% issingness) ARE