reduced RUM model for Phonological Short-Term Memory (PSTM) tasks
In this study, we administered a group test to sixth-grade students that included a digit-span or a nonword-span task. Each task comprised 13 items with a span ranging from 3 to 7. Using a reduced RUM model with a reduced skill space, we were able to estimate the memory span of the children. Different from an individual setting, children complete all tasks without any stop criteria in a group setting. Therefore, the average number of correct answers may not accurately represent the reached span (digits or nonwords). To obtain information about children’s memory span, recall patterns were created based on their item performance (1 = right, 0 = wrong) and a reduced RUM model (RRUM, Hartz, 2002) with a reduced skill space. The RRUM is a type of cognitive diagnostic model (CDM) that predicts correct or incorrect item responses from the children’s estimated mastery of the skills required for an item. The skills were specified as the memory capacity necessary to reach a span (3, 4, 5, 6, or 7 elements). Skill space reduction was used to ensure that skill combinations that were theoretically implausible (e.g., being able to recall 7- but not 3 elements) were not considered. The reduction of the skill space led to models that fit worse than the unrestricted models (digit-span task: RRUM hierarchical = -13068.28 vs. RRUM unrestricted = -13059.87; nonsense span task: RRUM hierarchical = -11373.95 vs. RRUM unrestricted = -11357.41). However, we chose to retain the restricted models for the following reasons: (1) They still showed excellent absolute fit (digit-span task: maxX2 = 5.741892, SRMSR = 0.0164; nonword-span task: maxX2 = 7.792292, SRMSR = 0.0179), (2) they discriminated very well between masters and non-masters (children who were vs. who were not estimated to possess the necessary skills for an item), and finally (3) they are more theoretically sound. The models were estimated using the package CDM (George et al., 2016; Robitzsch et al., 2022b) for R (R Core Team, 2023). Due to the sensitive nature of the questions asked in this study, children and parents were assured raw data would be kept confidential and not shared. In order to allow nonetheless a replication of the main findings of our study, we provided the complete script and output of the reduced RUM model.