Abstract This study proposes a new Bayesian differential item functioning (DIF) detection method using posterior predictive model checking (PPMC). Item fit measures including infit, outfit, observed score distribution (OSD), and Q1 were considered as discrepancy statistics for the PPMC DIF methods. The performance of the PPMC DIF method was…

When meta-analyzing heterogeneous bodies of literature, meta-regression can be used to account for potentially relevant between-studies differences. A key challenge is that the number of candidate moderators is often high relative to the number of studies. This introduces risks of overfitting, spurious results, and model non-convergence. To…

Diagnostic classification models (DCMs) are psychometric models that can be used to estimate the presence or absence of psychological traits, or proficiency on fine-grained skills. Critical to the use of any psychometric model in practice, including DCMs, is an evaluation of model fit. Traditionally, DCMs have been estimated with maximum…

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard goodness-of-fit statistics. Limited-information fit…

These are the appendixes for the report, "Stabilizing School Performance Indicators in New Jersey to Reduce the Effect of Random Error." This study applied a stabilization model called Bayesian hierarchical modeling to group-­level data (with groups assigned according to demographic designations) within schools in New Jersey with the aim…

Nowadays, Massive Open Online Courses (MOOC) has been gradually accepted by the public as a new type of education and teaching method. However, due to the lack of timely intervention and guidance from educators, learners' performance is not as effective as it could be. To address this problem, predicting MOOC learners' performance and providing…

Background/Context: Methodological background: Meta-analysis typically depends on the assumption that true effects follow the normal distribution. While assuming normality of effect "estimates" is often supported by a central limit theorem, normality for the distribution of interventions' "true" effects is a computational…

Problem solving is considered an essential ability for becoming an expert in physics, and individualized feedback on the structure of problem-solving processes is a key component to support students in developing this ability. Problem-solving processes consist of multiple elements whose order forms the sequential structure of these processes.…

An online learning system has the capacity to offer customized content that caters to individual learner's need and has seen growing interest from industry and academia alike in recent years. Different from traditional computerized adaptive testing setting which has a well-calibrated item bank with new items periodically added, online learning…

The purpose of this paper is to extend and evaluate methods of "Bayesian historical borrowing" applied to longitudinal data with a focus on parameter recovery and predictive performance. Bayesian historical borrowing allows researchers to utilize information from previous data sources and to adjust the extent of borrowing based on the…

The purpose of this paper is to extend and evaluate methods of "Bayesian historical borrowing" applied to longitudinal data with a focus on parameter recovery and predictive performance. Bayesian historical borrowing allows researchers to utilize information from previous data sources and to adjust the extent of borrowing based on the…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student's "t" distributions are used to account for nonnormal…