# Unidimensional Item Response Theory Modeling

Fit unidimensional item response theory (IRT) models to a 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
via expectation-maximization (MMLE-EM) algorithm
(Bock & Aitkin (1981) ) is used.
For the online calibration, the fixed item parameter calibration method
(Kim (2006) ) and
the fixed ability parameter calibration method
(Ban, Hanson, Wang, Yi, & Harris (2011) )
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 analyzing differential item
functioning, 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.