ISSN 0439-755X
CN 11-1911/B
主办:中国心理学会
   中国科学院心理研究所
出版:科学出版社

心理学报 ›› 2013, Vol. 45 ›› Issue (10): 1179-1186.doi: 10.3724/SP.J.1041.2013.01179

• 论文 • 上一篇    

二参数逻辑斯蒂模型项目参数的估计精度

杜文久;周娟;李洪波   

  1. (1西南大学数学与统计学院, 重庆 400715) (2重庆市教育考试院, 重庆 401147)
  • 收稿日期:2012-12-07 出版日期:2013-10-25 发布日期:2013-10-25
  • 通讯作者: 杜文久
  • 基金资助:

    重庆市教育科学规划项目(2011KS035)资助。

The Item Parameters’ Estimation Accuracy of Two-Parameter Logistic Model

DU Wenjiu;ZHOU Juan;LI Hongbo   

  1. (1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China) (2 Chongqing Educational Examination Authority, Chongqing 401147, China)
  • Received:2012-12-07 Online:2013-10-25 Published:2013-10-25
  • Contact: DU Wenjiu

摘要: 项目参数的估计精度对于测验的编制尤其是题库的建立十分重要。目前, 国内外对项目参数估计精度的研究, 大部分是基于在已知项目参数真值的情况下, 运用各种参数估计方法产生新的估计值, 再和真值进行偏度(BIAS)和均方根差(RMSE)的比较, 从而说明该种估计方法的有效性。但是这种方法不能提供不同的参数真值之间的估计误差的变化规律。为了弥补这一缺陷, 本文尝试从项目参数估计信息函数的角度出发研究项目参数的估计精度问题。本研究以二参数Logistic模型作为研究对象, 首先定义了项目参数的估计信息函数, 然后基于完全随机实验设计, 通过模拟研究的方法探索影响项目参数的估计精度的因素, 实验共设计了(2×3×2)种情形。研究结果表明:(1)项目参数(a,b)的估计精度均随着被试样本量的增大而提高; (2)被试的能力分布对难度参数的估计精度影响较大, 对区分度参数的估计精度影响相对较小; (3)难度参数和区分度参数的估计精度都分别受到参数a和参数b的共同作用。

关键词: 项目反应理论, 二参数逻辑斯蒂模型, 项目参数估计精度, 信息函数

Abstract: The item parameters’ estimation accuracy is very important to test development, especially to the construction of item bank. Nowadays, in domestic and foreign, the study of item parameters’ estimation accuracy is mostly based on that the true values of the item parameters are known, under this circumstances, applying kinds of estimation methods to estimate new estimators, then evaluating methods’ effectiveness by comparison with the true values about the root-mean-square-error (RMSE) and Bias. But this method can’t present the change rules of estimation error among the different parameters’ true values. In order to solve this problem, this article attempts to explore the item parameters’ estimation accuracy issue on the point of item parameters estimation information function. Based on the two-parameter Logistic model, given the definition of the item parameters’ estimation information function firstly, then generated examinee sample to explore the factors which affected item parameters’ estimation accuracy by computer simulation randomly. The experiments were designed (2 × 3 × 2) cases. The study is conducted and revealed: (1) The accuracy of the estimators enhance as the quantity of the sample increases. (2) The examinee’s ability distribution has more influences on difficulty parameter estimation accuracy, while less influences on discrimination parameter. (3) The estimation accuracy of item discrimination and item difficulty parameter are both influenced by parameter a and parameter b’s true value.

Key words: Item response theory, two parameter logistic model, item parameters estimation precision, information function