This Title All WIREs
How to cite this WIREs title:
WIREs Comp Stat

Item response theory and its applications in educational measurement Part I: Item response theory and its implementation in R

Can't access this content? Tell your librarian.

Abstract Item response theory (IRT) is a class of latent variable models, which are used to develop educational and psychological tests (e.g., standardized tests, personality tests, tests for licensure, and certification). We review the theory and practices of IRT across two articles. In Part 1, we provide a broad range of topics such as foundations of educational measurement, basics of IRT, and applications of IRT using R. We focus particularly on the topics that the mirt package covers. These include unidimensional and multidimensional IRT models for dichotomous and polytomous items with continuous and discrete factors, confirmatory analysis and multigroup analysis in IRT, and estimation algorithms. In Part 2, on the other hand, we focus on more practical aspects of IRT, namely scoring, scaling, and equating. This article is categorized under: Applications of Computational Statistics > Psychometrics Software for Computational Statistics > Software/Statistical Software
Item information curves (IICs), test information curve (TIC), and the corresponding standard error of estimate. The four items have the following item parameters: Item 1: (a1, b1, c1) = (1.0, 0.0, 0.0), Item 2: (a2, b2, c2) = (1.0, 1.5, 0.0), Item 3: (a3, b3, c3) = (1.5, − 1.5, 0.0), and Item 4: (a4, b4, c4) = (1.0, 0.0, 0.2)
[ Normal View | Magnified View ]
Three item characteristic curves (ICCs) and the corresponding test characteristic curve (TCC). Item parameters: (a1, b1, c1) = (1.0, 0.0, 0.2), (a2, b2, c2) = (2.0, −1.0, 0.1), and (a3, b3, c3) = (0.5, 0.5, 0.3)
[ Normal View | Magnified View ]
Item characteristic curves (ICCs) with different item parameter values. The subplots (a)–(c) have different values for discrimination parameter a, difficulty parameter b, and pseudo‐guessing parameter c, respectively. The other parameters are set at a = 1.0, b = 0.0, c = 0.0
[ Normal View | Magnified View ]
Example of a bifactor model with three specific factors. Errors are omitted
[ Normal View | Magnified View ]
A hypothetical example of an MIRT model with between‐item multidimensionality. Dashed lines represent paths of which coefficient is fixed at zero
[ Normal View | Magnified View ]
Item response surface (IRS) and contours of equal probabilities for compensatory two‐parameter logistic model (Item 1) and noncompensatory two‐parameter logistic model (Item 2). Note that both models have aj = (1, 1) and dj = 0
[ Normal View | Magnified View ]
Category characteristic curves (CCCs) of generalized partial credit model with different sets of parameter values. Subplot (a) is a baseline. Subplot (b) has larger aj value than (a) and has unequally distant categories. Subplot (c) has “reverse” categories (i.e., b1 < b3 < b2)
[ Normal View | Magnified View ]