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 
    with expectation-maximization (MMLE-EM) algorithm 
    (Bock & Aitkin (1981) <doi:10.1007/BF02294168>) is used. 
    For the online calibration, Stocking's Method A 
    (Ban, Hanson, Wang, Yi, & Harris (2011) <doi:10.1111/j.1745-3984.2001.tb01123.x>) 
    and the fixed item parameter calibration (FIPC) method 
    (Kim (2006) <doi:10.1111/j.1745-3984.2006.00021.x>) 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) <doi:10.1111/emip.12067>)) 
    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) 
    <doi:10.1111/j.1745-3984.2004.tb01109.x>), 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) <doi:10.1177/014662168400800409>), 
    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.