The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article, we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of [tau], the between-study standard deviation, and the shrunken estimates of the study effects as a…

An application of Bayesian factor analysis for evaluation of scale reliability is discussed, which is developed within the framework of latent variable modeling. The method permits direct point and interval estimation of the reliability coefficient of multiple-component measuring instruments using Bayesian inference. The approach allows also point…

A Bayesian statistics-based approach is discussed that can be used for direct evaluation of the popular Cronbach's coefficient alpha as an internal consistency index for multiple-component measuring instruments, as well as for testing its identity to scale reliability. The method represents an application of confirmatory factor analysis within the…

How do teachers learn about what learners already know? How do learners aid teachers by providing them with information about their background knowledge and what they find confusing? We formalize this collaborative reasoning process using a hierarchical Bayesian model of pedagogy. We then evaluate this model in two online behavioral experiments (N…

Item response theory (IRT) models are often compared with respect to predictive performance to determine the dimensionality of rating scale data. However, such model comparisons could be biased toward nested-dimensionality IRT models (e.g., the bifactor model) when comparing those models with non-nested-dimensionality IRT models (e.g., a…

This dissertation used synthetic datasets, semi-synthetic datasets, and a real-world dataset from an educational intervention to compare the performance of 15 machine learning and multiple imputation methods to estimate the individual treatment effect (ITE). In addition, it examined the performance of five evaluation metrics that can be used to…

We discuss an application of Bayesian factor analysis for estimation of the optimal linear combination and associated maximal reliability of a multi-component measuring instrument. The described procedure yields point and credibility interval estimates of this reliability coefficient, which are readily obtained in educational and behavioral…

The Bayesian piecewise growth model (PGM) is a useful class of models for analyzing nonlinear change processes that consist of distinct growth phases. In applications of Bayesian PGMs, it is important to accurately capture growth trajectories and carefully consider knot placements. The presence of missing data is another challenge researchers…

The meta-analytic-predictive (MAP) approach is a Bayesian meta-analytic method to synthesize and incorporate information from historical controls in the analysis of a new trial. Classically, only a single parameter, typically the intercept or rate, is assumed to vary across studies, which may not be realistic in more complex models. Analysis of…

Rater comparison analysis is commonly necessary in the social sciences. Conventional approaches to the problem generally focus on calculation of agreement statistics, which provide useful but incomplete information about rater agreement. Importantly, one-number agreement statistics give no indication regarding the nature of disagreements, nor do…

Publication bias is a ubiquitous threat to the validity of meta-analysis and the accumulation of scientific evidence. In order to estimate and counteract the impact of publication bias, multiple methods have been developed; however, recent simulation studies have shown the methods' performance to depend on the true data generating process, and no…

Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a…

Bayesian methods to infer model dimensionality in factor analysis generally assume a lower triangular structure for the factor loadings matrix. Consequently, the ordering of the outcomes influences the results. Therefore, we propose a method to infer model dimensionality without imposing any prior restriction on the loadings matrix. Our approach…

Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and…

One of the most prominent social influences on human decision making is conformity, which is even more prominent when the perceptual information is ambiguous. The Bayes optimal solution to this problem entails weighting the relative reliability of cognitive information and perceptual signals in constructing the percept from self-sourced/endogenous…