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…

Meta-analysis is commonly used to compare two treatments. Network meta-analysis (NMA) is a powerful extension for comparing and contrasting multiple treatments simultaneously in a systematic review of multiple clinical trials. Although the practical utility of meta-analysis is apparent, it is not always straightforward to implement, especially for…

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…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

While computing has become an important part of the statistics field, course offerings are still influenced by a legacy of mathematically centric thinking. Due to this legacy, Bayesian ideas are not required for undergraduate degrees and have largely been taught at the graduate level; however, with recent advances in software and emphasis on…

This study aims to compare the results of the factor analysis performed with Frequentist and Bayesian approaches. The number of sub-dimensions of the measurement tool obtained from different methods, the variation of the items in the sub-dimensions, and the fit statistics' differentiation were examined. 778 students constitute the study sample.…

We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and…

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…

Survival analysis is an important analytic method in the social and medical sciences. Also known under the name time-to-event analysis, this method provides parameter estimation and model fitting commonly conducted via maximum-likelihood. Bayesian survival analysis offers multiple advantages over the frequentist approach for measurement…

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)…

The causal view of categories assumes that categories are represented by features and their causal relations. To study the effect of causal knowledge on categorization, researchers have used Bayesian causal models. Within that framework, categorization may be viewed as dependent on a likelihood computation (i.e., the likelihood of an exemplar with…

Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter.…

Integrating engineering design into K-12 curricula is increasingly important as engineering has been incorporated into many STEM education standards. However, the ill-structured and open-ended nature of engineering design makes it difficult for an instructor to keep track of the design processes of all students simultaneously and provide…

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…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…