A Markov Parameter Estimation Strategy for Longitudinal Learning Diagnosis Model：Making Timely Diagnostic Feedback

Abstract: One of the central topics in educational research and assessment is to measure the growth/change in student learning on different occasions. During the last decades, the longitudinal learning diagnosis of objectively quantifying the learning status and providing diagnostic feedback has been increasingly valued, aiming at promoting students’ learning, based on the idea of assessment for learning and cognitive diagnostic assessments. Longitudinal learning diagnosis evaluates students' knowledge skills over time and identifying students’ strengths and weaknesses throughout an extended lesson, curricular unit, school year, or other periods. The data collected from longitudinal learning diagnosis throughout the learning process gives researchers chances to develop models for learning, which not only can be used to track individual growth over time, but also can be used to evaluate the effectiveness of remedial teachings. Timely diagnostic feedback is helpful for students and teachers to timely adjust their follow-up learning and teaching plans according to the current diagnosis. Aiming at the problem that the simultaneity estimation strategy adopted by the current longitudinal learning diagnostic model cannot provide timely diagnostic feedback, this study proposed a new Markov estimation strategy, which follows the Markov property. In the proposed strategy, only the data on two adjacent occasions are analyzed at a time, and the second occasion in the current estimation will be treated as the reference point in the next estimation. At the meanwhile, the estimated parameters (of the second occasion) in the current estimation will be fixed in the next estimation. Compared with the simultaneity estimation strategy, the new strategy ignores the estimation error of the current diagnosis, which may affect the accuracy of the subsequent parameter estimation. However, at the meanwhile, as the new strategy only needs to estimate fewer parameters each time, the robustness of its parameter estimation may be higher, than the simultaneity estimation strategy. A series of simulation study was conducted to explore and compare the performance of four estimation strategies, i.e., the simultaneity, the Markov, the simple separation and the anchor-item separation estimation strategies. The results showed that the performance of them was highly consistent and presented the following relative order: simultaneity > Markov > anchor separation ≥ simple separation. Overall, the proposed strategy can provide timely diagnostic feedback for practitioners, which is more in line with the idea of "assessment for learning" and the needs of formative evaluation.