Online Item Calibration, Scoring, and Evaluation of Model-Data Fit in Item Response Theory (IRT) and Useful Functions Related to IRT Models

Calibrate online item parameters (i.e., pretest and operational items), estimate examinees abilities, and examine the IRT model-data fit on item-level in different ways as well as provide useful functions related to unidimensional item response theory (IRT) models. For the online calibration, Stocking's Method A (Ban, Hanson, Wang, Yi, & Harris (2011) ) is provided. More methods of online calibration (e.g., fixed item parameter calibration) will be included in the future updated version. For the ability estimation, several popular scoring methods (e.g., MLE, EAP, and MAP) are implemented. In terms of assessing the IRT model-data fit, one of distinguished features of this package is that it gives not only well-known item fit statistics (e.g., chi-square (X2), likelihood ratio chi-square (G2), infit and oufit statistics, and S-X2 statistic (Ames & Penfield (2015) )) but also graphical displays to look at residuals between between the observed data and model-based predictions (Hambleton, Swaminathan, & Rogers (1991, ISBN:9780803936478)). In addition, there are many useful functions such as computing asymptotic variance-covariance matrices of item parameter estimates (Li & Lissitz (2004) ), importing item and/or ability parameters from popular IRT software, generating simulated data, computing the conditional distribution of observed scores using the Lord-Wingersky recursion formula (Lord & Wingersky (1984) ), computing the loglikelihood of individual items, computing the loglikelihood of abilities, computing item and test information functions, computing item and test characteristic curve functions, and plotting item and test characteristic curves and item and test information functions.