Item Response Theory (IRT) -------------------------------------------- This is a good place to start for a brief overview of IRT as well as common methodological and application related topics. **Introduction** *"Item response theory (IRT) was first proposed in the field of psychometrics for the purpose of ability assessment. It is widely used in education to calibrate and evaluate items in tests, questionnaires, and other instruments and to score subjects on their abilities, attitudes, or other latent traits. During the last several decades, educational assessment has used more and more IRT-based techniques to develop tests. Today, all major educational tests, such as the Scholastic Aptitude Test (SAT) and Graduate Record Examination (GRE), are developed by using item response theory, because the methodology can significantly improve measurement accuracy and reliability while providing potentially significant reductions in assessment time and effort, especially via computerized adaptive testing. In recent years, IRT-based models have also become increasingly popular in health outcomes, quality-of-life research, and clinical research (Hays, Morales, and Reise 2000; Edelen and Reeve 2007; Holman, Glas, and de Haan 2003; Reise and Waller 2009)." [(An & Yung, 2014)][1]* ---------- **IRT Models** - The **one-parameter logistic (1PL) model** -aka **the Rasch model**- items differ only in difficulty; the slopes of the curves are equal (held constant). - The **two-parameter logistic (2PL) model** estimates two parameters: difficulty and discrimination parameters estimated. - The **three-parameter logistic (3PL) model** estimates the difficulty and discrimination parameters and includes guessing as a pseudo-parameter. ---------- **Methodology & Applications** - 1 parameter IRT (most common) - [Columbia University Mailman School of Public Health][2] (linked 2018) - Addressing the assumption of dimensionality for IRT - [*Checking Dimensionality in Item Response Models With Principal Component Analysis on Standardized Residuals* (Chou & Wang, 2010)][3] - Multidimensional Rasch Model - [*Introducing Multidimensional Rasch Model in Measuring Traffic Police Officers' Behavior* (Shih, Chang, & Cheng, 2013)][4] - Mixed Rasch Model (MRM) Approach - [*Rasch Models in Latent Classes: An Integration of Two Approaches to Item Analysis* (Rost, 1990)][5] [1]: https://support.sas.com/resources/papers/proceedings14/SAS364-2014.pdf [2]: https://www.mailman.columbia.edu/research/population-health-methods/rasch-modeling [3]: http://journals.sagepub.com/doi/abs/10.1177/0013164410379322 [4]: https://www.jstage.jst.go.jp/article/easts/10/0/10_2049/_article [5]: http://journals.sagepub.com/doi/10.1177/014662169001400305