# 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.