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題名:一個CTT和IRT之整合模式
書刊名:初等教育學刊
作者:鄭富森
出版日期:1994
卷期:3
頁次:頁101-137
原始連結:連回原系統網址new window
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本文先簡述當代主要測驗理論,並且簡短分析這些測驗理論的優缺點。基於改進目前各家測驗理論雜然分立,功能不一,數理統計性質隱晦難明,理論基礎假設不清,等等問題,本文提出一個統整性的測驗理論,期望藉此澄清測驗理論的混亂局面。對於研究目標的評價方式,本文亦提出五點評價標準,以便讀者對這個統整性測驗理論的學術與實用價值做一個客觀的評價。 這個統整性測驗理論的基礎與結構分別由受試的特性、試題的特性、評分方式的特性所構成。所有理論的基本假設也在本文中逐一被明確標示出來,而且詳細說明其原由。根據這個統整性測驗理論的基礎與結構,本文綜合整理出八點理論基礎。 在說明過這個統整性測驗理論的基礎後,緊接著就是探討估計未知參數的方法。由於無法直接使用最大可能性估計法 (MLE) 或動差法,本文提出以最小方差法 (LSE) 來估計所有未知參數。為方便說明,先假設試題特徵曲線與受試能力參數之間只有線性關係,然後推演估計公式。經過冗長的推演過程,終於得到直接的理論解 (Close-form solution) 。接著再探討試題特徵曲線與受試能力參數之間可能有非線性關係的LSE,經過討論得知前述過程亦適用於此處。在得到受試能力參數的LSE後,接著就是求試題特徵曲的LSE。經過一段冗長的討論,終於也得到其直接的理論解。 所有估計值的統計性質亦在本文做簡短的討論。首先探討如果假設測量誤差為常態分配,則可證得LSE亦為MLE。接著本文指出受試能力參數的不偏估計值和最小標準誤的統計性質,也指出試題特徵曲線估計值具有均等分配的特性。 在本文結論中,一個新測驗理論的誕生,仍需經過一段時日的實地試驗,才能則確其實用價值。不過就理論推演來看,這個統整性的測驗理論確實具有過去所有測驗理論的功能,也沒有他們的缺點。由此可以推測出:「測驗學術界目前各家理論林立的現象將出現整合統一的局面。」
The dominant measurement theories were briefly reviewed at the begin-niug of this paper. Although many of these measurement theories have a great amount of similarity, each and every theory still has it's own unique part. Aud none of them was completely built on the bases of reasonable model assump-tions and solid theoretical derivation according to mathematical statistics, This phenomenon motivate the research for a new statistical model which can integrate those dominant measurement theories, This paper present a new measurement model which is inteuded to fulfill the object. In order to eval-uate how well does the new measurement model achieve the object, a set of criteria were also presented. The structure of the new measurement model is composed of the charae-ters of subject, item, and scoring rule. All model assumptions were obviously pointed out, and the reason of their existence were also Shown, The new measurement model was summarized in a list of eight model assumptions. Because the method of maximum likelihood estimation and the method of moments were inappropriate for this case, the method of least squares esti-mation was emploied to get the estimators of unknown parameters, Throught a tedious dervation, the dose-form solution of LSE were found and presented in the paper. The result of investigating the statistical properties of estimators was also presented in the paper. With the normality assumption on measurement error, It was shown that MLE is identical to LSE. Then, the unbiased estimator of ability parameter Was shown, The standard error of ability parameter estimator was also Shown to be the minimum one. The distrihution of ICC estimator was Shown to be an uniform distribution. In order to prompt the readers of the paper to evaluate how well does the new measurement model achieve it's object, the criteria for evaluation was presented again in the conclusion the paper. Based on the theoretical aspect, the new measnrement model indeed contains all functions covered by those existing and dominant models all doesn't inherit the defect of those models. Although the new measurement model is so powerful that it can be treated as the genernal model of those existing and dominant models, it should be applied with eantion until a series of tryouts have been successfully carried out. Then, it is the time that the new measurement model can bring an unification to those controversial models.
期刊論文
1.鄭富森(19920100)。Reconstructing Factor Analysis Models: A New Approach。測驗年刊,39,297-307。new window  new window
2.Reinsch, C. H.(1967)。Smoothing by Spline functions。Numerische Mathematik,10,177-183。  new window
3.Shavelson, Richard J.、Webb, Noreen M.、Rowley, Glenn L.(1989)。Generalizability theory。American Psychologist,44(6),922-932。  new window
圖書
1.Lord, Frederic M.、Novick, Melvin R.、Birnbaum, Allan(1968)。Statistical Theories of Mental Test Scores。Addison-Wesley Publishing Company。  new window
2.Johnson, Richard A.、Wichern, Dean W.(1988)。Applied Multivariate Statistical Analysis。Prentice-Hall。  new window
3.Allen, M. J.、Yen, W. M.(1979)。Introduction to measurement theory。Monterey, CA:Brooks/Core Publishing Company。  new window
4.Bevington, P. R.(1969)。Data reduction and error analysis。New York:McGraw-Hill。  new window
5.Gulliksen, H.(1987)。Theory of mental tests。New York:McGraw-Hill。  new window
6.Leon, S. J.(1986)。Linear algebra with applications。New York:Macmillan。  new window
7.Rockafellar, R. Tyrrell(1970)。Convex analysis。Princeton University Press。  new window
8.Hogg, R. V.、Craig, A. T.(1978)。Introduction to Mathematical Statistics。New York:Macmillan Publishing Co.。  new window
9.Lord, F. M.(1980)。Applications of item response theory to practical testing problems。Lawrence Erlbaum Associates。  new window
10.Anderson, T. W.(1984)。An introduction to multivariate statistical analysis。John Wiley & Sons, Inc.。  new window
 
 
 
 
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