臺灣博碩士論文加值系統

本研究旨在探討遺失資料對個人適配統計數（person-fit statistics）適配度之影響，以及使用不同插補法插補遺失資料對回復個人適配統計數（person-fit statistics）適配度的成效，因此以模擬研究使用三種處理遺失值的方法（零插補、熱卡插補、多重插補）、兩種person-fit統計數，在不同遺失比率（10%、20%、30%）及測驗長度（30題、60題）下，來比較ROC曲線下面積大小，樣本大小固定為1000人，藉以了解遺失值對個人適配統計數（person-fit statistics）適配度所造成的影響，以及是否有使用插補法的必要性與插補的成效。
研究結果顯示，遺失值的產生會導致person-fit統計數適配度的偏差，測驗長度的增加能提高person-fit統計數的適配度，60題的測驗長度下，ROC曲線下面積值在不同person-fit統計數以及遺失比率下均較30題的測驗長度接近原始資料之ROC曲線下面積值.5；遺失值比率越高，person-fit統計數的適配度則越低，10%的遺失比率下ROC曲線下面積值較20%的遺失比率接近原始資料之ROC曲線下面積值，20%的遺失比率又較30%的遺失比率接近原始資料之ROC曲線下面積值；若以二種person-fit統計數比較而言，零插補法在H統計數上表現要優於D統計數，其餘兩種插補方法則無太大的差異；插補遺失值能有效回復偏差的person-fit統計數適配度，而研究中的三種插補法以多重插補與熱卡插補表現較佳，零插補則較無法有效回復遺失值。

The purpose of this study was to investigate the impact of missing data on the accuracy of person-fit statistics as well as the effects of different imputation methods. The study manipulated four missing data treatments (zero imputation, hot-deck imputation, multiple imputation), two methods of person-fit statistics under three missing rates (10%, 20%, 30%) and two test lengths (30, 60) to examine the area under the ROC curve. The sample size was fixed to 1000.
Results showed that missing data would have some impact on person-fit statistics.The performance of long test is better than short test.The area under the ROC curve of sixty items is close to .5 than thirty items under two methods of person-fit statistics and three missing rates The lower missing rate have better results than higher missing rate.The reduced area under the ROC curve can be recovered by imputing the missing data. Multiple imputation and hot-deck imputation have better results in three imputations.

目 次
中文摘要...........i
英文摘要...........ii
誌 謝.............iii
目 次.............iv
表 次.............v
圖 次.............vi
第一章 緒論........1
第一節 研究動機....1
第二節 研究目的與研究問題...4
第三節 名詞釋義... 5
第二章 文獻探討... 7
第一節 遺失值之成因與類型...7
第二節 遺失值的處理方法...9
第三節 Person-Fit統計數...16
第三章 研究設計與方法...26
第一節 研究架構... 26
第二節 資料矩陣... 28
第三節 資料分析... 32
第四章 結果與討論...33
第一節 插補後資料信度之結果...33
第二節 ROC曲線下面積值之結果...35
第五章 結論與建議...40
第一節 研究結論... 40
第二節 研究限制... 41
第三節 研究建議... 42
參考文獻...43
附錄一 模擬資料之SPSS語法檔...48
附錄二 熱卡插補法SAS語法檔...52

呂喻恩（2008）。不同遺失機轉遺失資料插補法之比較研究。國立台南大學測驗統計研究所碩士論文。
林曉芳（2002）。以Hot Deck插補法推估成就測驗之不完整作答反應。國立政治大學教育學系教育心理與輔導組博士論文。
吳裕益（2006）。多重插補法在數學成就評量的不完整取樣設計之應用。未出版。
許禎元（1997）。問卷調查資料的處理與統計分析—以SPSS for Windows 7.0的處理為例。復興岡學報，61，76-91。
翁彰佑、程爾觀（1991）。隨機遺失資料插補法估計效用之比較。中國統計學報，29(2)，111-130。
曹志弘（1999）。遺漏值插補方法的比較。國立中央大學統計研究所碩士論文。
陳信木、林佳瑩（1997）。調查資料之遺漏值的處置—以熱卡插補法為例。調查研究，3，75-106。
劉長萱（2001）。第三十八屆中國心理學會年會主題演講：心理學研究的計量基礎。中國心理學刊，43(1)，1-9。
劉長萱、蔡政豐（1997）。問卷調查的不完整取樣設計。調查研究，3，107-127。
Allison, P. D. (2002). Missing data. Thousand Oaks, CA: Sage.
Bernaards, C. A. (2000). Nonresponse and factor analysis, with applications to rating scale data. PhD dissertation. Utrecht: Universiteit Utrecht, Faculteit Sociale Wetenschappen.
Bernaards, C. A., & Sijtsma, K. (2000). Influence of imputation and EM methods on factor analysis when item nonresponse in questionnaire data is nonignorable. Multivariate Behavioral Research, 35, 321-364.
Croninger, R. G., & Douglas, K. M. (2005). Missing data and institutional research. In
P. D. Umbach (Ed.), Survey Research: Emerging Issues. New Directions for
Institutional Research (Vol. 127) (pp.33-49). Jossey-Bass, CA: San Francisco.
De Ayala, R. J., Plake, B. S., & Impra, J. C. (2001). The impact of omitted responses on the accuracy of ability estimation in item response theory. Journal of Educational Measurement, 38(3), 213-234.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39(1), 1-38.
Dodeen, H. (2003). The use of person-fit statistics to analyze placement tests. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
Huisman, M. & Molenaar, I. W. (2001). Imputation of missing scale data with item response models. In A. Boomsma, M. A. J. van Duijn, & T. A. B. Snijder (Eds.), Essays on item response theory (pp.222-244). New York: Springer-Verlag.
Karabatsos, G. (2003). Comparing the aberrant response detection performance of thirty-six person-fit statistics. Applied Measurement in Education, 16(4), 277-298.
Kim, J., & Curry, J. (1977). The treatment of missing data in multivariate analysis. Sociological Methods & Research, 6(2), 215–240.
Kogut, J. (1986). Review of IRT-based indices for detecting and diagnosing aberrant response patterns. (Research Report No.86-4). Enschede, The Netherlands: University of Twente.
Levine, M. V. & Rubin, D. B. (1979). Measuring the appropriateness of multiple-choice test scores. Journal of Educational Statistics, 4, 269-290.
Levine, M. V., Zickar, M. J., & Drasgow, F. (1982). Optimal Identification of Mismeasured Individuals. Applied Measurement in Education, 9(1), 47-64.
Little, R. J. A., & Rubin, D. B. (1987). Statistical analysis with missing data. New York: John Wiley & Sons.
Little, R. J. A. (1988). Missing data adjustments in large surveys. Journal of Business and Economic Statistics, 6(3), 287-296.
Lord, F. M. (1974). Estimation of latent ability and item parameters when there are omitted response. Psychometrika, 39(2), 247-264.
Ludlow, L. H. & O’leary, M. (1999). Scoring omitted and not-reached items: practical data analysis implications. Educational and Psychological Measurement, 59(4),615-630.
Meijer, R. R., & Sijtsma, K. (1994). Detection of aberrant item score patterns: A review of recent developments. Applied Measurement in Education, 8(3), 261-272.
Meijer, R. R. (1996). Person fit research: An introduction. Applied Psychological Measurement, 9(1), 3-8.
Meijer, R. R. (1997). Person fit and criterion-related validity: An extension of the Schmitt,Cortina, and Whitney study. Applied Psychological Measurement, 21(2), 99-113.
Meijer, R. R. & Nering, M. L. (1997). Trait level estimation for nonfitting response vectors. Applied Psychological Measurement, 21(2), 321-336.
Meijer, R. R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25(2), 107-135.
Meijer, R. R. (2001). Diagnosing item score patterns using IRT-based person-fit statistics. Enschede, The Netherlands: University of Twente. (ERIC Document Reproduction Service No. ED467368).
Mislevy, R. J. & Wu, P. (1988). Inferring examinee ability when some item response are missing.( ETS Research Report 88-48-ONR). Princeton NJ: Educational Testing Service.
Mislevy, R. J., & Wu, P. (1996). Missing response and IRT ability estimation: omits, choice, time limits, and adaptive testing.(ETS Research Report 96-30-ONR). Princeton, NJ: Educational Testing Service.
Mokken, R. J. & Lewis, C. (1982). A nonparametric approach to the analysis of ditchotomous item responses. Applied Psychological Measurement, 6(3), 417-430.
Orlando, M., & Thissen, D. (2003). Further investigation of the performance of S-X2: An item fit index for use with dichotomous item response theory models. Applied Psychological Measurement,27, 289-298.
Peugh, J. L., & Enders, C. K. (2004). Missing data in educational research: a review of reporting practices and suggestions for improvement. Review of Educational Research, 74(4), 525–556.
Pyle, D. (1999). Data preparation for data mining. Morgan Kaufmann Publishers.
Reise, S. P. (1990). A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14(2), 127-137.
Reise, S. P. & Due, A. M. (1991). The influence of test characteristics on the detection of aberrant response patterns. Applied Psychological Measurement, 15(3), 217-226.
Reise, S. P. & Flannery, W. P. (1996). Assessing person-fit measurement of typical performance applications. Applied Measurement in Education, 9(3), 9-26.
Rubin, D. B. (1976). Inference and Missing Data. Biometrika, 70, 41-55.
Rubin, D. B. (1987). Multiple imputation for nonresponse in survey. New York: John Wiley & Sons.
Rudner, H. M. (1983). Individual assessment accuracy. Journal of Educational Measurement, 20, 207-219.
Rudner, H. M., Bracey, G., & Skaggs, G. (1996). The use of a person fit statistic with one high quality achievement test. Applied Measurement in Education, 9(3), 91-109.
Schafer, J. L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.
Schafer, J. L. (1999). NORM: Multiple imputation of incomplete multivariate data under a normal model, version 2. Software for Windows 95/98/NT. Retrieved December 30, 2008, from, http://www.stat.psu.edu/~jls/misoftwa.html.
Sijtsma, K., & Meijer, R. R. (1992). A Method for investigating the intersection of item
response functions in Mokken’s non-parametric IRT model. Applied Psychological Measurement, 16(2), 149-157.
Smith, R. M. (1985). A comparison of Rasch person analysis and robust estimation. Educational and Psychological Measurement, 45(4), 433-444.
Smith, R. M. (1986). Person fit in the Rasch model. Educational and Psychological Measurement, 46(4), 359-372.
Swearingen, D. L. (1997). Person fit and its relationship with other measures of response set. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA.
Trabin, T. E., & Weiss, D. J. (1983). The person response curve: Fit of individuals to item response theory models. In D. J. Weiss(Ed.), New horizons in testing. New York: Academic Press.
Wu, M. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31(2-3), 114-128.
Zhang, B., & Walker, C. M. (2008). Impact of missing data on person-model fit and person trait estimation. Applied Psychological Measurement, 32(6), 466-479.