When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in…

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

In education, sample characteristics can be complex due to the nested structure of students, teachers, classrooms, schools, and districts. In the past, not many considerations were given to such complex sampling schemes in statistical power analysis. More recently in the past two decades, however, education scholars have developed tools to conduct…

Social networks in education commonly involve some form of grouping, such as friendship cliques or teacher departments, and blockmodels are a type of statistical social network model that accommodate these grouping or blocks by assuming different within-group tie probabilities than between-group tie probabilities. We describe a class of models,…

Multivariate analysis of variance (MANOVA) is widely used in educational research to compare means on multiple dependent variables across groups. Researchers faced with the problem of missing data often use multiple imputation of values in place of the missing observations. This study compares the performance of 2 methods for combining p values in…

Planned missing designs are becoming increasingly popular, but because there is no consensus on how to implement them in longitudinal research, we simulated longitudinal data to distinguish between strategies of assigning items to forms and of assigning forms to participants across measurement occasions. Using relative efficiency as the criterion,…

Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…

A common question asked by researchers using regression models is, What sample size is needed for my study? While there are formulae to estimate sample sizes, their assumptions are often not met in the collected data. A more realistic approach to sample size determination requires more information such as the model of interest, strength of the…

In a traditional regression-discontinuity design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous assignment variable. The treatment effect is measured at a single cutoff location along the assignment variable. This article introduces the multivariate regression-discontinuity design (MRDD), where multiple…

Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with…

Large-scale assessment programs such as the National Assessment of Educational Progress (NAEP), Trends in International Mathematics and Science Study (TIMSS), and Programme for International Student Assessment (PISA) use a sophisticated assessment administration design called matrix sampling that minimizes the testing burden on individual…

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

Since heterogeneity between reliability coefficients is usually found in reliability generalization studies, moderator analyses constitute a crucial step for that meta-analytic approach. In this study, different procedures for conducting mixed-effects meta-regression analyses were compared. Specifically, four transformation methods for the…