A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their "cols :…

For efficiency, Computerized Adaptive Test (CAT) algorithm selects items with the maximum information, typically with a 50% probability of being answered correctly. However, examinees may not be satisfied if they only correctly answer 50% of the items. Researchers discovered that changing the item selection algorithms to choose easier items (i.e.,…

As the international large-scale assessments (ILSAs) become more popular, policy makers and education practitioners are interested in collecting as much student background information as possible to better understand the learning context of their students. To collect such abundant information, administrators need to develop a lot of questions.…

Lagrange multiplier (LM) or score tests have seen renewed interest for the purpose of diagnosing misspecification in item response theory (IRT) models. LM tests can also be used to test whether parameters differ from a fixed value. We argue that the utility of LM tests depends on both the method used to compute the test and the degree of…

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

The study utilised a fine-grained diagnostic checklist to assess first-year undergraduates in Hong Kong and evaluated its validity and usefulness for diagnosing academic writing in English. Ten English language instructors marked 472 academic essays with the checklist. They also agreed on a Q-matrix, which specified the relationships among the…