认知诊断模型中项目水平模型比较统计量的健壮性

使用模拟研究方法比较了以往研究中提出的基于观察信息矩阵、三明治矩阵的Wald（分别表示为W_Obs、W_Sw）、似然比（Likelihood Ratio）统计量以及新提出的基于经验交叉相乘信息矩阵的Wald统计量（W_XPD）在模型——数据失拟条件下进行项目水平上模型比较时的表现。结果显示：（1）W_Sw的一类错误控制率有很强的健壮性。（2）W_XPD在Q矩阵错误设定的大多数条件下的表现优于W_Sw。结论：模型—数据拟合良好时可以使用W_Sw进行项目水平上的模型比较,当模型与数据失拟时W_XPD可能是更好的选择。     

认知诊断模型中项目水平模型比较统计量的健壮性

使用模拟研究方法比较了以往研究中提出的基于观察信息矩阵、三明治矩阵的Wald（分别表示为W_Obs、W_Sw）、似然比（Likelihood Ratio）统计量以及新提出的基于经验交叉相乘信息矩阵的Wald统计量（W_XPD）在模型——数据失拟条件下进行项目水平上模型比较时的表现。结果显示：（1）W_Sw的一类错误控制率有很强的健壮性。（2）W_XPD在Q矩阵错误设定的大多数条件下的表现优于W_Sw。结论：模型—数据拟合良好时可以使用W_Sw进行项目水平上的模型比较,当模型与数据失拟时W_XPD可能是更好的选择。     

测验相对拟合检验方法CVLL法在认知诊断中的拓展及应用

本文将IRT中表现较好的CVLL法引入到认知诊断领域,同时比较并分析CVLL及认知诊断领域已有的测验相对拟合检验统计量的表现,为实际工作者在认知诊断模型选用上提供方法学支持和借鉴。结果表明:CVLL的表现比其它传统测验相对拟合统计量要好;且当对Q矩阵进行误设时,该统计量也能选择较优的Q矩阵,说明CVLL在Q矩阵侦查上有较好的应用前景。     

The Generalized DINA Model Framework

The G-DINA (generalized deterministic inputs, noisy “and” gate) model is a generalization of the DINA model with more relaxed assumptions. In its saturated form, the G-DINA model is equivalent to other general models for cognitive diagnosis based on alternative link functions. When appropriate constraints are applied, several commonly used cognitive diagnosis models (CDMs) can be shown to be special cases of the general models. In addition to model formulation, the G-DINA model as a general CDM framework includes a component for item-by-item model estimation based on design and weight matrices, and a component for item-by-item model comparison based on the Wald test. The paper illustrates the estimation and application of the G-DINA model as a framework using real and simulated data. It concludes by discussing several potential implications of and relevant issues concerning the proposed framework.     

基于混合模型（Mixed-CDMs）视角的CD-CAT及其应用研究

传统CD-CAT通常选择一个认知诊断模型（cognitive diagnosis model, CDM）标定题库参数,但在实际应用中一个CDM很难完全拟合题库中所有的题目。G-DINA模型是一般化的饱和模型,可以通过Wald统计量检验在题目水平上,比较简约模型（DINA、DINO、ACDM、LLM和RRUM）是否能够代替饱和模型（G-DINA）,并为每个题目选择一个相对最优的CDM,从而充分发挥各个CDM的优势,从而在一个题库中有的题目采用简约CDM,而有的题目采用饱和CDM,本文把这种思路称为混合模型（Mixed-CDMs）思路。基于此,本文探讨了基于混合模型的CD-CAT,并通过两个模拟研究及其应用研究验证了该方法的效果。研究结果表明基于混合模型建立的CD-CAT具有理想的效果,从而为CD-CAT在实际使用中提供了新思路和新方法。     

认知诊断模型的比较及其应用研究：饱和模型、简化模型还是混合方法？

GDINA是一个饱和认知诊断模型（Cognitive Diagnosis Models, CDM）,Wald检验被用于在题目水平上检验GDINA是否可以被简化模型（如DINA, DINO, ACDM和RRUM）替代,并为测验的每一个题目选择一个最恰当的CDM（简称混合CDM）。选择合适的CDM是进行诊断评估的一个关键步骤,通过Monte Carlo 模拟实验,比较了不同的测验情境下,GDINA、简化CDM和混合CDM在测验整体拟合指标、模式判准率和项目参数估计的返真性等效果,研究发现混合模型的整体表现是最好的,其次是GDINA,最后是简化CDM。     

认知诊断模型Q矩阵修正：完整信息矩阵的作用

Q矩阵是CDM的核心元素之一,反映了测验的内部结构和内容设计,通常由领域专家根据经验进行主观界定,因此需要对可能存在的错误进行修正。本研究提出了一种新的Q矩阵修正方法——基于完整经验交叉相乘信息矩阵的Wald-XPD方法。采用Monte Carlo模拟检验了新方法的表现,并与同类方法进行了比较。研究表明：新开发的Wald-XPD方法在Q矩阵恢复率、保留正确标定属性的比例以及修正错误标定属性的比例这3个主要指标上均有较好的表现,且整体上优于其他方法,尤其是在修正错误标定的属性方面。通过实证数据展示了Wald-XPD方法在Q矩阵修正中的良好表现。总之,本研究为Q矩阵修正提供了有效的方法。     

Two-Stage maximum likelihood estimation in the misspecified restricted latent class model

The maximum likelihood classification rule is a standard method to classify examinee attribute profiles in cognitive diagnosis models (CDMs). Its asymptotic behaviour is well understood when the model is assumed to be correct, but has not been explored in the case of misspecified latent class models. This paper investigates the asymptotic behaviour of a two-stage maximum likelihood classifier under a misspecified CDM. The analysis is conducted in a general restricted latent class model framework addressing all types of CDMs. Sufficient conditions are proposed under which a consistent classification can be obtained by using a misspecified model. Discussions are also provided on the inconsistency of classification under certain model misspecification scenarios. Simulation studies and a real data application are conducted to illustrate these results. Our findings can provide some guidelines as to when a misspecified simple model or a general model can be used to provide a good classification result.     

非参数认知诊断方法下诊断结果的概率化表征

非参数认知诊断分类方法非常适合课堂评估,其诊断结果采用0-1形式而缺乏概率化表征,不能精细地区分被试属性掌握程度的差异或变化,还缺乏可用于评价真实测验分类结果的信度和效度指标。要刻画被试属性掌握程度的差异,首要的问题是要为非参数认知诊断方法提供一种可以量化属性掌握概率的方法。针对此问题,基于二项分布和玻尔兹曼分布提出非参数认知诊断方法下诊断结果的概率化表征方法,并用于构建分类准确性和分类一致性指标。模拟研究与实测数据分析结果显示：概率化表征方法与非参数认知诊断方法的分类结果高度一致;概率化表征方法与认知诊断模型所得的属性掌握概率十分接近;概率化表征方法所得的属性（模式）掌握概率可用于计算属性（模式）分类准确性和分类一致性指标,在实际测验情景下可作为信度和效度指标,评价诊断结果的重测一致率和判准率。     

Detecting Misspecified Multilevel Structural Equation Models with Common Fit Indices: A Monte Carlo Study

This study investigated the sensitivity of common fit indices (i.e., RMSEA, CFI, TLI, SRMR-W, and SRMR-B) for detecting misspecified multilevel SEMs. The design factors for the Monte Carlo study were numbers of groups in between-group models (100, 150, and 300), group size (10, 20, 30, and 60), intra-class correlation (low, medium, and high), and the types of model misspecification (Simple and Complex). The simulation results showed that CFI, TLI, and RMSEA could only identify the misspecification in the within-group model. Additionally, CFI, TLI, and RMSEA were more sensitive to misspecification in pattern coefficients while SRMR-W was more sensitive to misspecification in factor covariance. Moreover, TLI outperformed both CFI and RMSEA in terms of the hit rates of detecting the within-group misspecification in factor covariance. On the other hand, SRMR-B was the only fit index sensitive to misspecification in the between-group model and more sensitive to misspecification in factor covariance than misspecification in pattern coefficients. Finally, we found that the influence of ICC on the performance of targeted fit indices was trivial.     

A General Method of Empirical Q-matrix Validation

In contrast to unidimensional item response models that postulate a single underlying proficiency, cognitive diagnosis models (CDMs) posit multiple, discrete skills or attributes, thus allowing CDMs to provide a finer-grained assessment of examinees’ test performance. A common component of CDMs for specifying the attributes required for each item is the Q-matrix. Although construction of Q-matrix is typically performed by domain experts, it nonetheless, to a large extent, remains a subjective process, and misspecifications in the Q-matrix, if left unchecked, can have important practical implications. To address this concern, this paper proposes a discrimination index that can be used with a wide class of CDM subsumed by the generalized deterministic input, noisy “and” gate model to empirically validate the Q-matrix specifications by identifying and replacing misspecified entries in the Q-matrix. The rationale for using the index as the basis for a proposed validation method is provided in the form of mathematical proofs to several relevant lemmas and a theorem. The feasibility of the proposed method was examined using simulated data generated under various conditions. The proposed method is illustrated using fraction subtraction data.     

G-DINA认知诊断模型在语言测验中的验证

G-DINA模型是DINA 模型的一般化模型,具有补偿性和饱和性两个主要特征。G-DINA模型的补偿性特征契合了语言测验的综合性和多元性,G-DINA模型的饱和性特征则可以比较理想地应对语言技能的抽象性和难区分性。此项研究以代表性的语言测验类型阅读测验为案例,应用G-DINA模型对1029名被试的PISA英语阅读测验结果进行实证分析,证明了两个假设：补偿饱和型认知诊断模型对多元抽象的语言测验的适应程度较高;G-DINA这一新生认知诊断模型可以被用来诊断较为复杂抽象的语言测验,且经得起统计学和语言学理论的双重考验。     

基于分部评分模型思路的多级评分认知诊断模型开发

基于分部评分模型的思路, 本文提出了一般化的分部评分认知诊断模型(General Partial Credit Diagnostic Model, GPCDM), 与国际上已有的基于分部评分模型思路的多级评分模型GDM (von Davier, 2008)和PC-DINA (de la Torre, 2012)相比, GPCDM的Q矩阵定义更加灵活, 项目参数的约束条件更少。Monte Carlo实验研究表明, GPCDM模型的参数估计精度指标RMSE介于[0.015, 0.043], 表明估计精度尚可; TIMSS (2007)实证数据应用研究表明, 与GDM和PC-DINA模型相比, GPCDM与该数据的拟合度更好, 并且使用GPCDM分析该数据的诊断效果也更优。总之, 本研究提供了一种约束条件更少、功能更为强大的多级评分认知诊断模型。     

基于假设检验的项目相合性指标研究

在认知诊断评估中,评价认知模型与作答数据的拟合非常重要。已有的层级相合性指标(HCI)仅能用于评价连接规则下模型与数据的拟合情况,有必要研究分离规则下相合性指标。HCI假设某项目上正确作答,便推断其子项目上的错误作答为失拟。由于作答反应的随机性,提出基于假设检验的项目相合性指标。该指标可用于区分连接规则和分离规则的作答数据、评价Q矩阵质量和衡量作答数据中的噪音、还可为评价认知模型和选择认知诊断模型提供参考。     

基于类别水平的多级计分认知诊断Q矩阵修正：相对拟合统计量视角

多级计分认知诊断模型的开发对认知诊断的发展具有重要作用, 但对于多级计分模型下的Q矩阵修正还有待研究。本研究尝试对多级计分认知诊断Q矩阵修正进行研究, 并聚焦更具诊断价值的基于项目类别水平的Q矩阵修正。将相对拟合统计量应用于多级计分认知诊断Q矩阵修正, 并与已有方法Stepwise方法( Ma & de la Torre, 2019)进行比较。研究表明：BIC方法对多级计分认知诊断模型的Q矩阵修正具有较高的模式判准率和属性判准率, 其对Q矩阵的恢复率也高于Stepwise方法, BIC方法修正后的Q矩阵与数据更加拟合; 在复杂模型中, 相对拟合指标BIC比AIC和-2LL表现更好, 在实践中, 使用者可以选择BIC法进行测验Q矩阵修正; Q矩阵修正效果受到被试人数的影响, 增加被试人数可以提高Q矩阵修正的正确率。总之, 本研究为多级计分认知诊断Q矩阵修正提供了重要的方法支持。     

Information matrix estimation procedures for cognitive diagnostic models

Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models (CDMs), the inverse of the observed information matrix and the sandwich-type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross-product information matrix, the sandwich-type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat., 34, 115) are discussed. Simulation results show that, for a correctly specified CDM and Q-matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich-type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich-type covariance matrix exhibits robust performance.     

The Problem with Having Two Watches: Assessment of Fit When RMSEA and CFI Disagree

The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.     

Q矩阵包含错误的诊断测验分类准确性比较

Q矩阵是认知诊断测验的重要组成部分之一,围绕Q矩阵构建的诊断模型对Q矩阵中包含的错误较敏感。贝叶斯网分类模型是基于网络结点之间的关系构建的模型,将朴素贝叶斯网作为诊断模型,与DINA模型进行比较。模拟实验结果表明：Q矩阵中是否包含可达矩阵和错误界定的项目数量对DINA模型影响较大,对贝叶斯网模型影响较小;项目数量对DINA和贝叶斯网模型影响都较大;样本大小对贝叶斯网模型影响较大,对DINA模型影响较小。模拟研究结果显示,当Q矩阵中不包含可达阵、包含5个以上错误项目或样本数较大时,贝叶斯网分类模型优于DINA模型;而当Q矩阵中包含可达阵和5个(以下)错误项目时,DINA模型优于贝叶斯分类模型。     

Balancing fit and parsimony to improve Q-matrix validation

The Q-matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q-matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q-matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut-off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo-R²). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut-off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q-matrix specification problem in applied settings. This proposal is illustrated using real data.     

基于可达阵的一种Q矩阵标定方法

Q矩阵标定是实施认知诊断评估的前提,已有Q矩阵修正方法并不太适合测验中已知属性向量的题目数较少的情形。根据拓展Q矩阵理论中可达阵R列与简化Q阵列存在布尔“或”关系,在一定认知假设下,率先提出可达阵R与简化Q阵的潜在反应列存在布尔“与”关系,并由此提出基于可达阵的Q矩阵标定方法。研究显示：在已知一个可达阵下,当可达阵项目的猜测或失误参数在.20以下且待标定项目的项目参数约在.30以下时,新方法所得Q矩阵元素返真率基本在.90以上,并且真实Q矩阵与估计Q矩阵下被试分类准确率差异很小;对于含5个属性的独立结构,新方法要求的随机样本的样本量较小;实证研究也印证了模拟研究的结论。新方法只需专家标定少量题目的Q矩阵,即已经标定的Q矩阵对应属性层级结构的可达阵。