# Unidimensional Item Response Theory Modeling

Fit unidimensional item response theory (IRT) models to mixture
of dichotomous and polytomous data, 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 IRT models.
For the item parameter estimation, marginal maximum likelihood estimation
with expectation-maximization (MMLE-EM) algorithm
(Bock & Aitkin (1981) ) is used.
For the online calibration, Stocking's Method A
(Ban, Hanson, Wang, Yi, & Harris (2011) )
and the fixed item parameter calibration (FIPC) method
(Kim (2006) ) are provided.
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 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, running 'flexMIRT' (Cai, 2017)
through R, 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.