# 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.