# 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 (X2), likelihood ratio chi-square (G2), 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 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.