一种高效的CD-CAT在线标定新方法：基于熵的信息增益与EM视角

项目增补(Item Replenishing)对认知诊断计算机自适应测验(CD-CAT)题库的维护有着至关重要的作用, 而在线标定是一种重要的项目增补方式。基于数据挖掘中特征选择(Feature Selection)的思路, 提出一种高效的基于熵的信息增益的在线标定方法(记为IGEOCM), 该方法利用被试在新旧题上的作答联合估计新题的Q矩阵和项目参数。研究采用Monte Carlo模拟实验验证所开发新方法的效果, 并同时与已有的在线标定方法SIE、SIE-R-BIC和RMSEA-N进行比较。结果表明：新开发的IGEOCM在各实验条件下均具有较好的项目标定精度和项目估计效率, 且整体上优于已有的SIE等方法; 同时, IGEOCM标定新题所需的时间低于SIE等方法。总之, 研究为CD-CAT题库中项目的增补提供了一种更为高效、准确的方法。     

Selecting polychoric instrumental variables in confirmatory factor analysis: An alternative specification test and effects of instrumental variables

The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small-sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IVs are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IVs outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IVs for correctly specified factor loadings at small samples.     

一种多策略认知诊断方法:MSCD方法的开发

当前国内外开发的认知诊断模型基本上只能处理单策略的测验情景,并假设所有被试均采用同一种加工策略/解题策略,从而忽视了加工策略的多样性及差异性.本研究根据de la Torre和Douglas (2008)采用多个Q矩阵来表征多个加工策略的思想,并结合使用丁树良等(2009)修正的Q矩阵理论及孙佳楠,张淑梅、辛涛和包珏(2011)的广义距离判别法,开发了一种新的多策略认知诊断方法——MSCD方法.Monte Carlo模拟研究结果表明:在单策略测验情景下,传统的单策略认知诊断方法与采用MSCD方法的诊断正确率均比较理想,且差异不大;但在多策略测验情景时,传统的单策略认知诊断方法诊断正确率较低,而MSCD方法的诊断正确率却仍较理想;当加工策略增至5种时,MSCD方法仍有较高的边际判准率、模式判准率以及加工策略判准率.研究表明MSCD方法基本合理、可行.这为实现对加工策略的诊断提供了方法学支持,有利于拓展认知诊断在实际中的应用.     

Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value

A method is presented for constructing a covariance matrix Σ*₀ that is the sum of a matrix Σ(γ₀) that satisfies a specified model and a perturbation matrix,E, such that Σ*₀=Σ(γ0) +E. The perturbation matrix is chosen in such a manner that a class of discrepancy functionsF(Σ*₀, Σ(γ₀)), which includes normal theory maximum likelihood as a special case, has the prespecified parameter value γ₀ as minimizer and a prespecified minimum δ A matrix constructed in this way seems particularly valuable for Monte Carlo experiments as the covariance matrix for a population in which the model does not hold exactly. This may be a more realistic conceptualization in many instances. An example is presented in which this procedure is employed to generate a covariance matrix among nonnormal, ordered categorical variables which is then used to study the performance of a factor analysis estimator. We are grateful to Alexander Shapiro for suggesting the proof of the solution in section 2.     

基于DINA模型的Q矩阵修正方法

本研究开发了一种基于DINA模型的认知诊断测验Q矩阵修正方法—— g 法, 为侦查并修正Q矩阵中的错误提供方法学支持, 从而为保证Q矩阵的合理性提供基础, 并为进一步提高认知诊断的准确率服务。本文采用Monte Carlo模拟及与国外同类研究相比较的方法进行, 研究发现：(1)不论在何种作答失误概率(5%, 10%, 15%)情况下, 当s,g临界值为0.2, 0.25或0.3时, 本研究提出的g 法均能有效地修正错误Q矩阵; 同时, 当Q矩阵无错误时, g 法对该Q矩阵未做任何修改。表明g 法对Q矩阵是否存在错误具有较强的识别能力及修正能力。(2)与国外同类研究相比, 本研究提出的g 法具有较理想的修正率, 且与de la Torre (2008)提出d法的修正效果相当。但相比较而言, g 法较d 法更为简单。(3) g 法不仅能有效地修正错误的Q矩阵, 而且还可以进一步提高认知诊断的正确率, 尤其是对模式判准率(PMR), 诊断正确率的最高增幅高达40%, 大大改善了认知诊断的准确率。     

一种基于Q矩阵理论朴素的认知诊断方法

现有的认知诊断方法均是在复杂的统计测量学知识基础上构建的, 需要经过大量的运算才可实现对被试的诊断分类。这使得相关研究者及一线教师在理解和运用某一认知诊断方法时困难重重。相比之下, 孙佳楠、张淑梅、辛涛和包钰(2011)提出的广义距离判别法(GDD)较其他认知诊断方法更简单易用且分类准确率高。本研究在改进的Q矩阵理论(丁树良, 祝玉芳, 林海菁, 蔡艳, 2009; 丁树良, 杨淑群, 汪文义, 2010)的基础上, 借鉴GDD的思路, 提出一种无需进行参数估计的朴素的认知诊断方法, 即海明距离判别法(HDD)。根据判别方式的不同将其分为R方法和B方法。采用Monte Carlo模拟的研究方法, 以模式判准率(PMR)和属性平均判准率(AAMR)作为衡量被试知识状态分类准确率的指标, 与GDD进行比较。结果表明, HDD具有更简便的操作步骤和更好的分类准确率。     

An empirical Q-matrix validation method for the sequential generalized DINA model

As a core component of most cognitive diagnosis models, the Q-matrix, or item and attribute association matrix, is typically developed by domain experts, and tends to be subjective. It is critical to validate the Q-matrix empirically because a misspecified Q-matrix could result in erroneous attribute estimation. Most existing Q-matrix validation procedures are developed for dichotomous responses. However, in this paper, we propose a method to empirically detect and correct the misspecifications in the Q-matrix for graded response data based on the sequential generalized deterministic inputs, noisy ‘and’ gate (G-DINA) model. The proposed Q-matrix validation procedure is implemented in a stepwise manner based on the Wald test and an effect size measure. The feasibility of the proposed method is examined using simulation studies. Also, a set of data from the Trends in International Mathematics and Science Study (TIMSS) 2011 mathematics assessment is analysed for illustration.     

Diagnostic Classification Models: Recent Developments,Practical Issues,and Prospects

More than three decades after their introduction, diagnostic classification models (DCM) do not seem to have been implemented in educational systems for the purposes they were devised. Most DCM research is either methodological for model development and refinement or retrofitting to existing nondiagnostic tests and, in the latter case, basically for model demonstration or constructs identification. DCMs have rarely been used to develop diagnostic assessment right from the start with the purpose of identifying individuals’ strengths and weaknesses (referred to as true applications in this study). In this article, we give an introduction to DCMs and their latest developments along with guidelines on how to proceed to employ DCMs to develop a diagnostic test or retrofit to a nondiagnostic assessment. Finally, we enumerate the reasons why we believe DCMs have not become fully operational in educational systems and suggest some advice to make their advent smooth and quick.