貝氏方法在探索差異試題功能潛在因素中的應用

Application of Bayesian Approach in Exploring the Latent Dimensions of DifferentialItem Functioning

10.6773/JRMS.200912.0001

楊瓊(Qiong Yang)；曹亦薇(Yi-Wei Cao)

差別試題功能 ； 貝式分類 ； MCMC法 ； 錯誤反應 ； 多重對應分析 ； Differential Item Functioning ； Bayesian classification ； MCMC method ； error responses ； Multiple Correspondence Analysis

測驗統計年刊

17期_下（2009 / 12 / 01）

1 - 17

繁體中文

本研究目的旨在探測辭彙理解能力測驗中性别DIF的產生原因。本文以小學一年級的測驗結果為例，通過三個步驟探索性别DIF潛在組別與受試者錯誤反應類別之間的關係：首先基於性别DIF的探測結果在混合二參數模型中實現貝氏分類，求取每個受試者的潛在組別；其次將受試者在干擾項上的錯誤反應數據通過主成份分析進行降維後，利用混合多元高斯模型實現錯誤分類；最後使用多重對應分析方法來整合前面的分類結果，找出性別、DIF潛在組別及錯誤類別間的對應關係。 結果顯示： 一、性別因素只能解釋性别DIF產生的60.4%，還存在某個或某些未知的潛在因素； 二、通過分析受試者在干擾項上的反應，可將受試者按其所犯錯誤的特點分為三類，並各有其特點； 三、不同的錯誤類型與不同的DIF潛在組別之間存在著對應關係； 四、研究採用的貝式分類程式準確合理，可推廣到以後的錯誤診斷研究中。

This study focuses on exploring the cause of gender DIF by taking the example of vocabulary test for Grade One of an elementary school using the Bayesian classification approach. Three steps are included this article. The purpose of step 1 is to obtain the examinees' latent membership using Bayesian mixture 2-parameter model based on the result of gender DIF detecting. In Step 2, after reducing the dimensions of the participants' error responses using PCA, the Bayesian classification was carried out in Mixture Multivariate Gaussian model. Step 3 combines the classification results of the two previous steps using Multiple Correspondence Analysis to explore the correspond relationship through gender, latent membership and error type. The following conclusions are obtained by summing up the three steps above: 1. There are some latent dimensions besides gender that causes the gender DIF; 2. All the participants can be classified into three error types based on their error responses, and each group has its own special characteristic; 3. There are some corresponding relationship between different error type and latent membership; 4. The Bayesian classification procedure using in this study is not only accurate and also can be explored to error diagnose studies in the future.

1. Angoff, W. H.,P.W. Holland (Eds.),H. Wainer (Eds.)(1993).Differential item functioning.Hillsdale, NJ:Lawrence Earlbaum.
2. Bolt, D. M.,Cohen, A. S.,Wollack, J. A.(2001).A mixture item response model for multiple-choice data.Journal of Educational and Behavioral Statistics,26,381-409.
3. Cao, Y. W.,Zhang, H. C.(2004).Correspondence analysis of the person-misfit error responses in a Chinese vocabulary comprehension test.International Journal of Psychology,39,474-474.
4. Cohen, A. S.,Bolt, D. M.(2005).A Mixture Model Analysis of Differntial Item Functioning.Journal of Educational Measurement,42,133-148.
5. Congdon, P.(2003).Applied Bayesian Modelling.New York:Wiley.
6. Emenogu, B. C.,Childs, R. A.(2005).Curriculum, Translation, and Differential Functioning of Measurement and Geometry Items.Canadian Journal Of Education,28,128-146.
7. Gelfand, A. E.,Smith, F. M.(1990).Sampling-based approaches to calculating marginal densities.Journal of the American Statistical Association,85,398-409.
8. Holland, P. W.,Wainer, H.(1993).Differential item functioning.Hillsdale, NJ:Lawrence Erlnaum.
9. Lawrence, I. M.,Curley, W. E.,McHale, F. J.(1989).Differential Item Functioning for males and females on SAT-Verbal Reading subscore items: follow-up study.Educational Testing Service Research Report.
10. Mallick, B. K.,Ghosh, D.,Ghosh, M.(2005).Bayesian classification of tumours by using gene expression data.Journal of the Royal Statistical Society: Series B (Statistical Methodology),67,219-234.
11. Panagiotakos, D. B.,Pitsavos, C.(2004).Interpretation of Epidemiological Data Using Multiple Correspondence Analysis and Log-linear Models.Journal of Data Scienc,2,75-86.
12. Read, J.(1993).The development of a new measure of L2 vocabulary knowledge.Language Testing,10,355-371.
13. Reise, S. P.,Widaman, K. F.,Pugh, R. E.(1993).Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance.Psychological Bulletin,114,552-566.
14. Rost, J.(1990).Rasch models in latent classes: An integration of two approaches to item analysis.Applied Psychological Measurement,14,271-282.
15. Samsó, M.,Palumbo, M.,Radermacher, M.,Liu, J.,Lawrence, C.(2002).A Bayesian method for classification of images from electron micrographs.Journal of Structure biology,138,157-170.
16. SAS Institute Inc.(1988).SAS/STAT user's guide.Cary, NC:SAS Institute Inc..
17. Spiegelhalter, D. J.,Thomas, A.,Best, N. G.,Lunn, D.(2003).WinBUGS User Manual.Cambridge, UK:MRC Biostatistics Unit..
18. Stout, W. F.(1987).A nonparametric approach for assessing latent trait unidimensionality.Psychometrika,52,589-617.
19. Vaithyanathan, S.,Mao, J.,Dom, B.(2000).Hierarchical Bayes for Text Classification.Proceedings of international workshop on text and web mining (PRICAI'00).
20. 茆詩松(2005)。貝葉斯統計。北京:中國統計出版社。
21. 馬佳、靜進(2005)。學習障礙兒童認知特徵及影響因素分析。中國行為醫學科學，14(9)，835-837。
22. 張文彤(2004)。SPSS統計分析高級教程。北京:高等教育出版社。
23. 曹亦薇(1999)。初中辭彙理解能力量表的編制。心理學報，31(4)，215-221。
24. 郭建華(1999)。兒童學習困難與感覺統合失調及注意力缺陷測查。中國心理衛生雜誌，13(6)，360。