以LVQ-ESW推估受訪者未知抽樣權重之研究

Estimating Missing Sampling Weights by Using LVQ-ESW Method in a CFA Model

10.6129/CJP.2009.5103.01

楊志堅(Chih-Chien Yang)；蔡良庭(Liang-Ting Tsai)；楊志強(Chih-Chiang Yang)

估算分層權重 ； 學習向量量化網絡 ； 驗證性因素分析 ； MAR ； CFA ； Estimated Stratum Weights ； LVQ ； Missing at Random

中華心理學刊

51卷3期（2009 / 09 / 01）

277 - 293

繁體中文

本研究主要提出未知分層權重(stratum weights)的估算法以協助推估母體之確認性因素分析(CFA)之參數｡在大型調查研究中，需因應樣本的抽樣機率的不均等，而必須搭配使用正確的取樣權重資料，才能正確地推論母體的統計模型參數。但是當樣本的分層權重資料未知時，若將這些資料全數剔除(listwise deletions)或忽略權重效應，尤其是當未知或遺失資料並非完全隨機遺失（如：MAR）時，將很可能導致推估母體樣貌時的嚴重偏誤。 本研究提出LVQ-ESW權重估算方法，即應用學習向量量化網絡(learning vector quantization network, LVQ)的計算方法以估算樣本在不同分層間的可能權重，再以此插補為其分層權重估算值(Estimated Stratum Weights, ESW)。LVQ的方法並不需事先假設資料之統計分配，依此所得的分層權重可以客觀地區辨各個分層。本研究以數值模擬實驗方法評估LVQ-ESW的正確性及穩定度，實驗設計中包含了多種不同組合的遺失比例、取樣數、取樣不均勻及層間變異。研究結果顯現LVQ-ESW在各個向度中都明顯優於剔除法及不使用權重，也證實了它有相當的正確率及穩定度。本文最後並對此方法的實際應用提出討論及建議。

The paper proposes estimated missing stratum weights (ESW) to infer populationwise parameters of confirmatory factor analysis (CFA) models in a stratified sampling survey. In large survey research, using stratum weights has been proved to be able to ensure proper statistical inferences for populationwise parameters in CFA models (e.g., 蔡良庭、 楊志堅，2008; Asparouhov, 2005; Yang & Tsai, 2006) and others (e.g., Little, 1991). Similarly, importance of properly dealing with missing at random (MAR) data (e.g., Little & Rubin, 1987; Little & Schenker, 1994) in survey research cannot be overemphasized. Yet, methods to analyze observations with missing stratum weights received less attention than they should. The estimated stratum weights (ESW) is thus proposed to impute missing weights of observations; specifically, ESW is implemented by optimumizing learning vector quantization networks (LVQ) (蔡良庭、楊志堅，2004; White, 1989). Experimental factors, including missing proportions, sampling sizes, unbalanced stratifications and stratified variations, are designed to examine performances of LVQ-ESW in numerical simulation studies. Results show that accuracies and stabilities of LVQ-ESW are much better than the other two methods in all categories of comparisons. Conclusions and discussions are provided for some practical guidelines.

1. 楊志堅、蔡良庭(2008)。評估取樣權重於檢定Likert問卷之測量恆等性研究。中華心理學刊，50，257-269。
   連結：
2. 蔡良庭、楊志堅(2004)。學習向量量化網路分類之模擬研究。測驗統計年刊，12，269-291。
   連結：
3. Asparouhov, T.(2005).Sampling weights in latent variable modeling.Structural Equation Modeling,12,411-434.
4. Bollen, K. A.(1989).Structural equations with latent variables.New York:Wiley.
5. Ender, C. K.,Bandalos, D. L.(2001).The relative performance of full information maximum likelihood estimation for missing data in structural equation models.Structural Equation Modeling,8,430-457.
6. Ender, C. K.,Peugh, J. L.(2004).Using an EM covariance matrix to estimate structural equation models with missing data: Choosing an adjusted sample size to improve the accuracy of inferences.Structural Equation Modeling,11,1-19.
7. Gonzalez, E. J.,Kennedy, A. M.(2003).PIRLS 2001 user guide for the international database.Chestnut Hill, MA:Boston College.
8. Grilli, L.,Pratesi, M.(2004).Weighted estimation in multilevel ordinal and binary models in the presence of informative sampling designs.Survey methodology,30,4-14.
9. Kaplan, D.,Ferguson, A. J.(1999).On the utilization of sample weights in latent variable models.Structural Equation Modeling,6,305-321.
10. Little, R. J. A.(1991).Inference with survey weights.Journal of Official Statistics,7,405-424.
11. Little, R. J. A.,Rubin, D. B.(1987).Statistical analysis with missing data.New York:John Wiley.
12. Little, R. J. A.,Schenker, N.,G. Arminger (Eds.),C. C. Clogg (Eds.),M. E. Sobel (Eds.)(1994).Handbook of statistical modeling for the social and behavioral sciences.New York:Plenum.
13. Martin, M. O.(2004).TIMSS 2003 user guide for the international database.Chestnut Hill, MA:Boston College.
14. Muthén, L. K.,Muthén, B. O.(1998).Mplus user's guide.Los Angeles, CA:Muthen & Muthen.
15. OECD(2005).PISA 2003 technical report.
16. Scheaffer, R. L.,Mendenhall III, W.,Ott, R. L.(2006).Elementary survey sampling.NewYork:Duxbury Press.
17. White, H.(1989).Some asymptotic results for learning in single hidden layer feedforward Network Models.Journal of the American Statistical Associate,84,1003-1013.
18. Yang, C. C.,Tsai, L. T.(2006).A simulation study on computation and inference accuracy of factor loadings for large data mines.Wseas Trans on Information Science and Application,12,2577-2579.
19. Yang, M. S.,Yang, J. H.(2002).A fuzzy-soft learning vector quantization for control chart pattern recognition.International Journal of Production Research,40,2721-2731.
20. 張苙雲、關秉寅、黃敏雄、王麗雲(2002)。行政院國家科學委員會專題研究計畫報告行政院國家科學委員會專題研究計畫報告,未出版
21. 章英華、傅仰止(2004)。台灣地區社會變遷基本調查計畫：第四期第四次調查計畫執行報告。
22. 蔡良庭、楊志堅(2008)。取樣權重值於應用SEM模式分析之參數估算正確性研究。教育與心理研究，31，155-170。

1. 蔡良庭、楊志堅(2013)。多階層取樣單位異質性對科學調查之母體推論研究。調查研究：方法與應用，29，7-36。
2. 蔡良庭、楊志堅(2014)。LVQ與多變數反覆加權法於測驗效度檢驗影響。測驗學刊，61(3)，361-384。
3. 王郁琮(2014)。台灣青少年異質性憂鬱發展軌跡之性別差異及與違常行為之關係。中華心理衛生學刊，27(1)，97-130。