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Data simulation and Monte Carlo simulation studies are important skills for researchers and practitioners of educational and psychological measurement, but there are few resources on the topic specific to item response theory. Even fewer resources exist on the statistical software techniques to implement simulation studies. This article presents an introduction to the questions that simulation studies can, and cannot answer, along with the primary steps of the simulation study. We primarily focus on the parts of the simulation for which statistical software is used, presenting syntax for simulating 2PL data, and discuss how to extend the basic syntax to more complex models. We focus on SAS software in the article to build upon an existing syntax base, as most universities have SAS licenses. Two small simulations serve as didactic illustrations and to demonstrate parameter recovery of the SAS IRT procedure and an evaluation of the procedure's item-fit options. [ABSTRACT FROM AUTHOR]

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing environments, including R, Python, MATLAB, Stata, and Mathematica. Programs written in Stan are portable across these interfaces, encouraging collaboration and transparency. These benefits, and others, offer several advantages for measurement practitioners; this review uses a simple example of Stan for a two-parameter logistic IRT model to illustrate the utility of Stan and its relevant features. [ABSTRACT FROM AUTHOR]

This article investigates an effect size (MLM ES) and its variance for cluster randomized trials based on parameter estimates from multilevel modeling analysis. Accuracy and precision of MLM ES were evaluated using Monte Carlo simulation methods and compared with the performance of an effect size, computed from summary statistics, proposed by Hedges (2007; Hedges'dB). Simulation results indicated that MLM ES had acceptable accuracy in all conditions, also demonstrating efficiency and consistency. With small sample sizes, MLM ES did not suffer from the same negative bias as Hedges'dBdue to overestimation of between-cluster variance. With large sample sizes, MLM ES and Hedges'dBwere comparable for accuracy and efficiency. Both MLM ES and Hedges'dBshowed considerable bias in some conditions when cluster sizes were unequal. An illustrative example using real data was provided. [ABSTRACT FROM PUBLISHER]

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of Monte Carlo simulation studies (MCSS) in item response theory (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because they allow researchers to specify and manipulate an array of parameter values and experimental conditions (e.g., sample size, test length, and test characteristics). Dr. Leventhal and Dr. Ames review the conceptual foundation of MCSS in IRT and walk through the processes of simulating total scores as well as item responses using the two‐parameter logistic, graded response, and bifactor models. They provide guidance for how to implement MCSS using other item response models and best practices for efficient syntax and executing an MCSS. The digital module contains sample SAS code, diagnostic quiz questions, activities, curated resources, and a glossary. [ABSTRACT FROM AUTHOR]