Monte Carlo Simulation Studies in Item Response Theory with the R Programming Language

Monte Carlo simulation studies play an important role in operational and academic research in educational measurement and psychometrics. Item response theory (IRT) is a psychometric area in which researchers and practitioners often use Monte Carlo simulations to address various research questions. Over the past decade, R has been one of the most widely used programming languages in Monte Carlo studies. R is a free, open-source programming language for statistical computing and data visualization. Many user-created packages in R allow researchers to conduct various IRT analyses (e.g., item parameter estimation, ability estimation, and differential item functioning) and expand these analyses to comprehensive simulation scenarios where the researchers can investigate their specific research questions. This study aims to introduce R and demonstrate the design and implementation of Monte Carlo simulation studies using the R programming language. Three IRT-related Monte Carlo simulation studies are presented. Each simulation study involved a Monte Carlo simulation function based on the R programming language. The design and execution of the R commands is explained in the context of each simulation study.