臺灣博碩士論文加值系統

本文討論台灣社會變遷調查中的顯著因子與比較不同估計方法對於處理缺失資料問題的差異，尤其是在高維度資料下所顯現出的優劣。隨著Wang et al. (2007)的研究，可以證明有母數與無母數的擴張反機率加權估計式至少會等效或好於完整資料分析法、多重插補法或有母數與無母數的反機率加權估計法。研究資料為兩份來自於2004年台灣社會變遷調查中包含著受訪者基本資料的問卷。在宗教文化的問卷中，我們討論宗教對於慈善態度、行為與價值取向的影響。而公民權的部分，經由政治參與和文化轉變的台灣社會變遷過程，思考國人對於公民權的發展趨勢。研究結果最後建議宗教信仰為影響捐款傾向的重要因子，而在公民權的議題中，的確存在較複雜的關係。

In this paper, we discuss significant factors and differences arisen from applying various methods of estimation to solve the problems with missing data, especially for the high dimensionality in Taiwan Social Change Survey (TSCS). Following the study of Wang et al. (2007), we show the parametric and nonparametric augmented inverse probability weighted (AIPW) estimator to be at least equal to or better than other methods, like complete case (CC) analysis, multiple imputation (MI), parametric and nonparametric inverse probability weighted (IPW) estimator. Two questionnaires from TSCS in 2004, both involving interviewees' basic materials. In religion and culture, the impact of religion toward charitable attitude, behavior and value orientation is discussed. As to the latter one, we consider the development of the trend of citizenship in Taiwan social changes through political participation and culture transition. Finally, the results suggest that religion be the most important factor affecting the inclination toward donation, and there exists more complicated relation on citizenship issue.

Contents
1 Introduction 1
1.1 Research Background 1
1.2 Defining Concepts 2
1.2.1 Missing data mechanism 2
1.2.2 Characterized by the conditional distribution 2
1.3 Literature Review 3
1.4 Research Purpose 4
1.5 Research Value 4
1.6 Overview 4
2 Methods 6
2.1 Research Design 6
2.2 Descriptive Statistics of data sets 7
2.2.1 Data of religion and culture 7
2.2.2 Data of citizenship 7
2.3 Statistical analysis 9
2.3.1 Complete case (CC) analysis 9
2.3.2 Multiple imputation (MI)10
2.3.3 Inverse probability weighted (IPW) estimator 12
2.3.4 Nonparametric inverse probability weighted (IPW) estimator 14
2.3.5 Augmented inverse probability weighted (AIPW) estimator 15
2.3.6 Nonparametric augmented inverse probability weighted (AIPW) estimator 17
3 Analysis of data 18
3.1 Questionnaire of religion and culture 19
3.1.1 CC analysis 20
3.1.2 MI 20
3.1.3 IPW estimator 21
3.1.4 Nonparametric IPW estimator 21
3.1.5 AIPW estimator 22
3.1.6 Nonparametric AIPW estimator 23
3.1.7 Comparison of parametric and nonparametric AIPW estimators of Wang with Lei's nonparametric 23
3.1.8 Research results 24
3.2 Questionnaire of citizenship 26
3.2.1 CC analysis 27
3.2.2 MI 27
3.2.3 IPW estimator 27
3.2.4 Nonparametric IPW estimator 28
3.2.5 AIPW estimator 28
3.2.6 Nonparametric AIPW estimator 28
3.2.7 Comparison of parametric and nonparametric AIPW
estimators of Wang with Lei's nonparametric 29
3.2.8 Research results 29
4 Conclusion 32
References 34
Appendix A: Outcomes on religion and culture 36
Appendix B: Outcomes on parametric and nonparametric (Lei and Wang) AIPW estimators 38
Appendix C: Outcomes on citizenship 43
Appendix D: Outcomes on the ratios of standard errors 47
List of Figures
2.1 Diagram of MI with m imputations 11
List of Tables
2.1 Definition of variables in religion and culture 8
2.2 Frequency of variables in religion and culture 9
2.3 Definition of variables in citizenship 10
2.4 Frequency of variables in citizenship (after the deleting process) 11
2.5 Imputation methods in PROC MI for SAS 12
3.1 Result of CC analysis in religion and culture 20
3.2 Result of MI in religion and culture 21
3.3 Result of IPW in religion and culture 22
3.4 Result of nonparametric IPW in religion and culture 22
3.5 Result of AIPW estimator in religion and culture 23
3.6 Result of nonparametric AIPW estimator in religion and culture 24
A.1 Comparison of analyses by CC, MI, (non)parametric IPW and AIPW estimator in logistic regression for religion and culture 37
B.2 Comparison of analyses by parametric and nonparametric (Lei and Wang) AIPW estimator in logistic regression for religion and culture 39
B.3 Comparison of analyses by parametric and nonparametric (Lei and Wang) AIPW estimator in multinomial logistic regression for citizenship (strong defense power) 40
B.4 Comparison of analyses by parametric and nonparametric(Lei and Wang) AIPW estimator in multinomial logistic regression for citizenship (voice for work) 41
B.5 Comparison of analyses by parametric and nonparametric (Lei and Wang) AIPW estimator in multinomial logistic regression for citizenship (enhancement of our city and country) 42
C.6 Comparison of analyses by CC, MI, (non)parametric IPW and AIPW estimator in multinomial logistic regression for citizenship (strong defense power) 44
C.7 Comparison of analyses by CC, MI, (non)parametric IPW and AIPW estimator in multinomial logistic regression for citizenship (voice for work) 45
C.8 Comparison of analyses by CC, MI, (non)parametric IPW and AIPW estimator in multinomial logistic regression for citizenship (enhancement of our city and country) 46
D.9 Comparison of the ratios of standard errors to CC by (b-a)/a with b denoting those of other methods for religion and culture 48
D.10 Comparison of the ratios of standard errors to CC by (b-a)/a with b denoting those of other methods for citizenship (strong defense power) 49
D.11 Comparison of the ratios of standard errors to CC by (b-a)/a with b denoting those of other methods for citizenship (voice for work) 50
D.12 Comparison of the ratios of standard errors to CC by (b-a)/a with b denoting those of other methods for citizenship (enhancement of our city and country) 51

Copas, J. B. (1983). Plotting p against x. Applied Statistics, 32, 25-31.
Lei, S.-Y. C., Kao, F. F. and Zou, Y. R. (2009). The analysis of weights for the Taiwan Social Change Survey. 第九屆調查研究方法與應用學術研討會. 台北.
Lei, S.-Y. C. and Wang, S. (2001). Diagnostic tests for bias of estimating equations in weighted regression with missing covariates. The Canadian Journal of Statistics, 29(2), 239-250.
Little, R. J. A. and Rubin, D. B. (1987). Statistical Analysis with Missing Data. New York: Wiley.
Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data, John Wiley and Sons, 2nd Edition. New York.
Nadaraya, E. A. (1964). On estimating regression, Theory of Probability and its Applications, 9, 141-142.
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592.
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.
Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846-866.
Schafer, J. L. (1997). Analysis of incomplete multivariate data. London: Chapman and Hall.
Schafer, J. L. and Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147-177.
Tang, G., Little, R.J. and Raghunathan, T. (2004). Analysis of Multivariate Monotone Missing Data by a Pseudo - Likelihood Method. In Proceedings of the 2nd. Seattle Symposium in Biostatistics: Analysis of Correlated Data. Lin, D.Y.; Heagerty, P.J. (Eds.). Lecture Notes in Statistics, 2004. New York: Springer Verlag.
Vriens, M., E. Melton, B. Graham (2002). Managing Missing Data in Media Research with Multiple Imputation. ARF Week of Workshops - Paper Summaries for October 7, 2002 - Print Research.
Wang, C. and Paik, M. C. (2006). Efficiencies of methods dealing with missing covariates in regression analysis. Statistica Sinica, 16, 1169-1192.
Wang, C. Y., Lee, S. M. and Chao, E. C. (2007). Numerical Equivalence of Imputing Scores and Weighted Estimators in Regression Analysis with Missing Covariates. Biostatistics, 8, 468-473.
Wang, C. Y., Wang, S., Zhao, L. P. and Ou, S. T. (1997). Weighted semiparametric estimation in regression analysis with missing covariate data. Journal of the American Statistical Association, 92, 512-525.
Zhao, L. P. and Lipsitz, S. (1992). Designs and analysis of two-stage studies. Statistics in Medicine, 11, 769-782.