When analyzing large-scale assessments (LSAs) that use complex sampling designs, it is important to account for probability sampling using weights. However, the use of these weights in multilevel models has been widely debated, particularly regarding their application at different levels of the model. Yet, no consensus has been reached on the best…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

Differential test functioning, or DTF, occurs when one or more items in a test demonstrate differential item functioning (DIF) and the aggregate of these effects are witnessed at the test level. In many applications, DTF can be more important than DIF when the overall effects of DIF at the test level can be quantified. However, optimal statistical…

Investigation of peer effects on achievement with sample survey data on schools may mean that only a random sample of the population of peers is observed for each individual. This generates measurement error in peer variables similar in form to the textbook case of errors-in-variables, resulting in the estimated peer group effects in an OLS…

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We…

Three methods for the estimation of the reliability of single dichotomous items are discussed. All methods are based on the assumptions of nondecreasing and nonintersecting item response functions and the Mokken model of double monotonicity. Based on analytical and Monte Carlo studies, it is concluded that one method is superior to the other two…