Testing item fit is central in item response theory (IRT) modeling, since a good fit is necessary to draw valid inferences from estimated model parameters. "Infit" and "outfit" fit statistics, widespread indices for detecting deviations from the Rasch model, are affected by data factors, such as sample size. Consequently, the…

In large-scale educational assessments, it is generally required that tests are composed of items that function invariantly across the groups to be compared. Despite efforts to ensure invariance in the item construction phase, for a range of reasons (including the security of items) it is often necessary to account for differential item…

This study compares five cognitive diagnostic models in search of optimal one(s) for English as a Second Language grammar test data. Using a unified modeling framework that can represent specific models with proper constraints, the article first fit the full model (the log-linear cognitive diagnostic model, LCDM) and investigated which model…

Using a sample of schools testing annually in grades 9-11 with a vertically linked series of assessments, a latent growth curve model is used to model test scores with student intercepts and slopes nested within school. Missed assessments can occur because of student mobility, student dropout, absenteeism, and other reasons. Missing data…

Item-level information, such as difficulty and discrimination are invaluable to the test assembly, equating, and scoring practices. Estimating these parameters within the context of large-scale performance assessments is often hindered by the use of unbalanced designs for assigning examinees to tasks and raters because such designs result in very…