一种非参数化的Q矩阵估计方法：ICC-IR方法开发

摘要：相对于参数化的方法,本研究根据题目测量模式关系开发出ICC指标,并提出基于理想得分的ICC指标法进行Q矩阵估计。Monte Carlo模拟研究与实证研究发现（1）基于理想得分ICC指标法估计Q矩阵具有很好的效果,当属性个数越少、基础题个数越多,估计效果越好。（2）相对于以往方法——D2统计量的方法,ICC-IR法效果更好,并且是一种非参数化的方法,计算简单快捷。（3）实证数据分析表明,ICC-IR法估计的Q矩阵在模型拟合度上也优于D2统计量方法。     

探索语言水平测验的认知诊断改造和深度分析： 以广州市英语学业考试为例

本研究探索在通用认知诊断模型和相关检验方法的基础上对现有语言水平测验进行诊断改造和分析,分三步进行探索：1）探索对语言水平测试不同的属性和Q矩阵构建途径;2）探索对语言水平测试基于通用模型的建模和效度验证;3）探索对语言水平测试建模后续的深入分析。研究发现：属性分布和总分分布划分的学生水平一致性较高;学生对属性掌握存在性别差异且属性间的难易层级不同;属性模式分布进一步验证了语言属性间关联程度较高以及通用认知诊断模型和相关检验方法对语言测验的适用性。三步式的建模分析可作为对语言水平测验进行认知诊断改造的参考。     

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.     

多级属性Q矩阵的验证与估计

多级属性是将诊断测验中传统的二值(即两种水平, 通常定义为0和1)属性定义为多值(多个水平可以为0, 1, …), 它不但可以描述学生对于知识属性是否掌握, 而且可以描述学生在属性上的掌握程度, 这样使得诊断测验能提供给被试更丰富的知识掌握详情。本文将适用于二级属性Q矩阵的统计量(S统计量)拓展到多级属性下的Q矩阵验证和估计, 在两种常见的条件下, 设计了两种估计算法：联合估计算法和在线估计算法。模拟实验结果表明：联合估计算法适用于对专家界定的初始Q矩阵进行验证, 当初始Q矩阵中包含较少的错误时, 通过联合估计算法有很大可能恢复正确的Q矩阵; 在线估计算法适用于对“新项目”进行属性向量和项目参数的在线标定, 基于一定数量的“基础项目”, 在线估计算法对于新项目的估计也能达到较满意的成功率。实证数据分析则进一步展示了该方法的使用。     

A Limited Information Estimator for Dynamic Factor Models

Structural equation modeling (SEM) is an increasingly popular method for examining multivariate time series data. As in cross-sectional data analysis, structural misspecification of time series models is inevitable, and further complicated by the fact that errors occur in both the time series and measurement components of the model. In this article, we introduce a new limited information estimator and local fit diagnostic for dynamic factor models within the SEM framework. We demonstrate the implementation of this estimator and examine its performance under both correct and incorrect model specifications via a small simulation study. The estimates from this estimator are compared to those from the most common system-wide estimators and are found to be more robust to the structural misspecifications considered.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

Misspecification in Latent Change Score Models: Consequences for Parameter Estimation,Model Evaluation,and Predicting Change

Latent change score models (LCS) are conceptually powerful tools for analyzing longitudinal data (McArdle & Hamagami, 2001). However, applications of these models typically include constraints on key parameters over time. Although practically useful, strict invariance over time in these parameters is unlikely in real data. This study investigates the robustness of LCS when invariance over time is incorrectly imposed on key change-related parameters. Monte Carlo simulation methods were used to explore the impact of misspecification on parameter estimation, predicted trajectories of change, and model fit in the dual change score model, the foundational LCS. When constraints were incorrectly applied, several parameters, most notably the slope (i.e., constant change) factor mean and autoproportion coefficient, were severely and consistently biased, as were regression paths to the slope factor when external predictors of change were included. Standard fit indices indicated that the misspecified models fit well, partly because mean level trajectories over time were accurately captured. Loosening constraint improved the accuracy of parameter estimates, but estimates were more unstable, and models frequently failed to converge. Results suggest that potentially common sources of misspecification in LCS can produce distorted impressions of developmental processes, and that identifying and rectifying the situation is a challenge.     

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。     

基于作答数据的模型参数和Q矩阵联合估计

Q矩阵在认知诊断的模型参数估计和诊断分类中起着重要作用。本文通过研究Liu等人的方法, 设计了同时估计项目参数和Q矩阵的联合估计算法。在DINA模型下, 对项目参数未知时开展模拟研究。研究假设项目为20个, 考察的属性个数分别是3、4和5, 初始Q矩阵中分别存在3、4和5个属性界定错误的项目。结果表明, 联合估计算法能在错误的初始Q矩阵基础上以很高的概率得到正确的Q矩阵。另外, 当专家认定测验的属性个数存在错误时, 该方法推导的Q矩阵和模型参数能提供很好的鉴别Q矩阵错误的信息。