Evaluation of Model-Data Fit in Item Response Theory (IRT) and Useful Functions Related to IRT

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). 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, infit and oufit statistics (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)). More evaluation methods will be included in the future updated version. In addition to the evaluation of IRT model-data fit, there are several useful functions such as estimating proficiency parameters, calibrating item parameters given the fixed effects (aka. ability values) (Baker & Kim (2004, ISBN:9780824758257)), 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 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.