Accurate item parameters and standard errors (SEs) are crucial for many multidimensional item response theory (MIRT) applications. A recent study proposed the Gaussian Variational Expectation Maximization (GVEM) algorithm to improve computational efficiency and estimation accuracy (Cho et al., 2021). However, the SE estimation procedure has yet to…

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain…

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

Differential item functioning (DIF) analysis refers to procedures that evaluate whether an item's characteristic differs for different groups of persons after controlling for overall differences in performance. DIF is routinely evaluated as a screening step to ensure items behavior the same across groups. Currently, the majority DIF studies focus…

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational…

Biased sampling occurs frequently in economics, epidemiology, and medical studies either by design or due to data collecting mechanism. Failing to take into account the sampling bias usually leads to incorrect inference. We propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for…