Subjects: Other Disciplines >> Synthetic discipline submitted time 2023-10-09 Cooperative journals: 《心理学报》
Abstract： Cognitive diagnostic models (CDMs) are psychometric models that have received increasing attention within fields such as psychology, education, sociology, and biology. It has been argued that an inappropriate convergence criterion for a maximum likelihood estimation using the expectation maximization (MLE-EM) algorithm could result in unpredictable and inaccurate model parameter estimates. Thus, inappropriate convergence criteria may yield unstable and misleading conclusions from the fitted CDMs. Although several convergence criteria have been developed, it remains an unexplored question, how to specify the appropriate convergence criterion for fitted CDMs. A comprehensive method for assessing convergence is proposed in this study. To minimize the influence of the model parameter estimation framework, a new framework adopting the multiple starting values strategy (mCDM) is introduced. To examine the performance of the convergence criterion for MLE-EM in CDMs, a simulation study under various conditions was conducted. Five convergence assessment methods were examined: the maximum absolute change in model parameters, the maximum absolute change in item endorsement probabilities and structural parameters, the absolute change in log-likelihood, the relative log-likelihood, and the comprehensive method. The data generating models were the saturated CDM and the hierarchical CDM. The number of items was set to J = 16 and 32. Three levels of sample sizes were considered: 500, 1000, and 4000. The three convergence tolerance value conditions were 10-4, 10-6, and 10-8. The simulated response data were fitted by the saturated CDM using the mCDM and the R package GDINA. The maximum number of iterations was set to 50000.The simulation results suggest the following. (1) The saturated CDM converged under all conditions. However, the actual number of iterations exceeded 30000 under some conditions, implying that when the predefined maximum iteration number is less than 30000, the MLE-EM algorithm might inadvertently stop.(2) The model parameter estimation framework affected the performance of the convergence criteria. The performance of the convergence criteria under the mCDM framework was comparable or superior to that of the GDINA framework. (3) Regarding the convergence tolerance values considered in this study, 10-8 consistently had the best performance in providing the maximum value of the log-likelihood and 10-4 had the worst performance. Compared to all other convergence assessment methods, the comprehensive method in general had the best performance, especially under the mCDM framework. The performance of the maximum absolute change in model parameters was similar to the comprehensive method, but this good performance was not consistent. On the contrary, the relative log-likelihood had the worst performance under the mCDM and GDINA frameworks.The simulation results showed that the most appropriate convergence criterion for MLE-EM in CDMs was the comprehensive method with tolerance 10-8 under the mCDM framework. The results from the real data analysis also demonstrated that the proposed comprehensive method and mCDM framework had good performance.
Subjects: Statistics >> Social Statistics submitted time 2023-06-15 Cooperative journals: 《中国科学院院刊》
Abstract：党的二十大报告指出，高质量发展是全面建设社会主义现代化国家的首要任务。以科技创新赋能产业高质量发展，是促进“经济高质量发展取得新突破，科技自立自强能力显著提升，构建新发展格局和建设现代化经济体系取得重大进展”的重要抓手。文章从历史与现实、理论与实践、目标与规划等方面梳理了一线科学家与经济学家的思考，提出了技术创新对于经济发展和国力提升的关键性作用，要减少资源消耗走集约化发展道路；从过去的技术追赶转向构建局部领先优势，从终端产品创新转向中间品创新，从鼓励集成创新转向鼓励原始创新；从产业界和技术领域发力，在微观层面建立起真正的市场竞争机制，形成以产业技术为主的科技文化导向等观点。
Subjects: Psychology >> Psychological Measurement Subjects: Psychology >> Statistics in Psychology submitted time 2023-05-11
Abstract： Cognitive diagnostic models (CDMs) are psychometric models which have received increasing attention within the field of psychological, educational, social, biological, and many other disciplines. It has been argued that an inappropriate convergence criterion for MLE-EM (maximum likelihood estimation using the expectation maximization) algorithm could result in unpredictably distorted model parameter estimates, and thus may yield unstable and misleading conclusions drawn from the fitted CDMs. Although several convergence criteria have been developed, it remains an unexplored question, how to specify the appropriate convergence criterion for the fitted CDMs.
A comprehensive method for assessing convergence is proposed in this study. To minimize the impact by the model parameter estimation framework, a new framework adopting the multiple starting values strategy mCDM is introduced. To examine the performance of the convergence criterion for MLE-EM in CDMs, a simulation study under various conditions was conducted. Five convergence assessment methods were examined: the maximum absolute change in model parameters, the maximum absolute change in item endorsement probabilities and structural parameters, the absolute change in log-likelihood, the relative log-likelihood, and the comprehensive method. The data generating models were the saturated CDM and the hierarchical CDM. The number of items was set to J = 16 and 32. Three levels of sample sizes were considered: 500, 1000, and 4000. Three convergence tolerance value conditions were: 10-4 , 10-6 , and 10-8 . The simulated response data were fitted by the saturated CDM using the mCDM and the R package GDINA. And the maximum number of iterations was set to 50000.
Simulation results suggest that:
(1) The saturated CDM converged under all conditions. However, the actual number of iterations exceeded 30000 under some conditions, which implies that when predefined maximum iteration number is less than 30000, the MLE-EM algorithm might mistakenly stop.
(2) The model parameter estimation framework affected the performance of the convergence criteria. The performance of the convergence criteria under the mCDM framework was comparable or superior to that of the GDINA framework.
(3) Regarding the convergence tolerance values considered in this study, 10-8 consistently had the best performance in providing the maximum value of the log-likelihood and 10-4 had the worst as suggested by the higher log-likelihood value. Compared to all other convergence assessment methods, the comprehensive method in general had the best performance, especially under the mCDM framework. The performance of the maximum absolute change in model parameters was similar to the comprehensive method, however, its good performance was not guaranteed. On the contrary, the relative log-likelihood had the worst performance under the mCDM or GDINA framework.
The simulation results showed that, the most appropriate convergence criterion for MLE-EM in CDMs was the comprehensive method with tolerance 10-8 under the mCDM framework. Results from the real data analysis also demonstrated the good performance of the proposed comprehensive method and mCDM framework.
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