Pan Qianqian, Qin Lu, Kingston Neal
Department of Educational Psychology, The University of Kansas, Lawrence, KS, United States.
Institutional Research and Assessment, Howard University, Washington, DC, United States.
Front Psychol. 2020 Aug 7;11:1714. doi: 10.3389/fpsyg.2020.01714. eCollection 2020.
A multivariate longitudinal DCM is developed that is the composite of two components, the log-linear cognitive diagnostic model (LCDM) as the measurement model component that evaluates the mastery status of attributes at each measurement occasion, and a generalized multivariate growth curve model that describes the growth of each attribute over time. The proposed model represents an improvement in the current longitudinal DCMs given its ability to incorporate both balanced and unbalanced data and to measure the growth of a single attribute directly without assuming that attributes grow in the same pattern. One simulation study was conducted to evaluate the proposed model in terms of the convergence rates, the accuracy of classification, and parameter recoveries under different combinations of four design factors: the sample size, the growth patterns, the G matrix design, and the number of measurement occasions. The results revealed the following: (1) In general, the proposed model provided good convergence rates under different conditions. (2) Regarding the classification accuracy, the proposed model achieved good recoveries on the probabilities of attribute mastery. However, the correct classification rates depended on the cut point that was used to classify individuals. For individuals who truly mastered the attributes, the correct classification rates increased as the measurement occasions increased; however, for individuals who truly did not master the attributes, the correct classification rates decreased slightly as the numbers of measurement occasions increased. Cohen's kappa increased as the number of measurement occasions increased. (3) Both the intercept and main effect parameters in the LCDM were recovered well. The interaction effect parameters had a relatively large bias under the condition with a small sample size and fewer measurement occasions; however, the recoveries were improved as the sample size and the number of measurement occasions increased. (4) Overall, the proposed model achieved acceptable recoveries on both the fixed and random effects in the generalized growth curve model.
开发了一种多变量纵向诊断性认知模型（DCM），它由两个部分组成，即作为测量模型部分的对数线性认知诊断模型（LCDM），用于评估每次测量时属性的掌握状态，以及一个广义多变量增长曲线模型，用于描述每个属性随时间的增长。所提出的模型是对当前纵向DCM的改进，因为它能够纳入平衡和不平衡数据，并直接测量单个属性的增长，而无需假设属性以相同模式增长。进行了一项模拟研究，以评估所提出模型在四个设计因素的不同组合下的收敛速度、分类准确性和参数恢复情况：样本大小、增长模式、G矩阵设计和测量次数。结果表明：（1）总体而言，所提出的模型在不同条件下具有良好的收敛速度。（2）关于分类准确性，所提出的模型在属性掌握概率方面实现了良好的恢复。然而，正确分类率取决于用于对个体进行分类的切点。对于真正掌握属性的个体，正确分类率随着测量次数的增加而提高；然而，对于真正未掌握属性的个体，正确分类率随着测量次数的增加而略有下降。科恩kappa系数随着测量次数的增加而增加。（3）LCDM中的截距和主效应参数恢复良好。在样本量小且测量次数少的条件下，交互效应参数存在相对较大的偏差；然而，随着样本量和测量次数的增加，恢复情况有所改善。（4）总体而言，所提出的模型在广义增长曲线模型中的固定效应和随机效应方面都实现了可接受的恢复。
