In this article, we propose using the Bayes factors (BF) to evaluate person fit in item response theory models under the framework of Bayesian evaluation of an informative diagnostic hypothesis. We first discuss the theoretical foundation for this application and how to analyze person fit using BF. To demonstrate the feasibility of this approach,…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

Although social scientists devote considerable effort to mitigating measurement error during data collection, they often ignore the issue during data analysis. And although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because of implausible assumptions, high levels of model…

This paper is about performance assessment in serious games. We conceive serious gaming as a process of player-lead decision taking. Starting from combinatorics and item-response theory we provide an analytical model that makes explicit to what extent observed player performances (decisions) are blurred by chance processes (guessing behaviors). We…

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,…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

Making causal inferences from a quasi-experiment is difficult. Sensitivity analysis approaches to address hidden selection bias thus have gained popularity. This study serves as an introduction to a simple but practical form of sensitivity analysis using Monte Carlo simulation procedures. We examine estimated treatment effects for a school-based…

A central issue in nonexperimental studies is identifying comparable individuals to remove selection bias. One common way to address this selection bias is through propensity score (PS) matching. PS methods use a model of the treatment assignment to reduce the dimensionality of the covariate space and identify comparable individuals. parallel to…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

A large number of approaches have been proposed for estimating and testing the significance of indirect effects in mediation models. In this study, four sets of Monte Carlo simulations involving full latent variable structural equation models were run in order to contrast the effectiveness of the currently popular bias-corrected bootstrapping…

Arthur Cropley (2006) emphasized the critical place that convergent thinking has in creativity. Although he briefly refers to the blind variation and selective retention (BVSR) theory of creativity, his discussion could not reflect the most recent theoretical and empirical developments in BVSR, especially the resulting combinatorial models.…

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study…

Missing data mechanisms, methods of handling missing data, and the potential impact of missing data on study results are usually not taught until graduate school. However, the appropriate handling of missing data is fundamental to biomedical research and should be introduced earlier on in a student's education. The Summer Institute for Training in…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…