Abstract
The R package irtplay provides practical tools for unidimensional item response theory (IRT) models that conveniently enable users to conduct many analyses related to IRT. For example, the irtplay includes functions for calibrating online items, scoring test-takers’ proficiencies, evaluating IRT model-data fit, and importing item and/or proficiency parameter estimates from the output of popular IRT software. In addition, the irtplay package supports mixed-item formats consisting of dichotomous and polytomous items.
Description
The R package irtplay provides practical tools for unidimensional item response theory (IRT) models that conveniently enable users to conduct many analyses related to IRT such as calibrating online items, scoring test-takers’ proficiencies, and evaluating IRT model-data fit. The irtplay software package is quite user-friendly and its functions are easy to implement. In addition, the irtplay package supports mixed-item formats consisting of dichotomous and polytomous items. For the polytomous items, the graded response model and the (generalized) partial credit models are available.
Online Item Calibration Using Stocking’s Method A
In computerized adaptive testing (CAT), online items, which include pretest items and operational items, should be calibrated precisely to ensure a healthy item bank (Stocking, 1988). The irtplay package calibrates the online items using Stocking’s (1988) Method A, which is the maximum likelihood estimation (MLE) of the item parameters given the proficiency estimates. Method A is known to result in accurate, unbiased item parameter calibration when items are randomly administered to examinees (Chen & Wang, 2016; He et al., 2017). Although Method A is the simplest and most straightforward online calibration method in current use, there is little software available to support it. The updated version of irtplay will include fixed item parameter calibration (FIPC; Kim, 2006).
Estimation of Proficiency Parameters
For estimation of proficiency parameters, six popular scoring methods can be implemented using the irtplay package. Available methods include MLE, MLE with fences (MLEF; Han, 2016), maximum a posteriori (MAP) estimation (Hambleton et al., 1991), expected a posteriori (EAP) estimation (Bock & Mislevy, 1982), EAP summed scoring (Thissen & Orlando, 2001), and inverse test characteristic curve scoring (Kolen & Tong, 2010). Although much IRT software has been developed, there are few software packages available to estimate proficiency parameter with the mixed-item format.
Evaluation of IRT Model-Data Fit on Item Level
In terms of assessing the IRT model-data fit, the irtplay package supports computation of popular item-fit statistics. Available fit statistics include χ2 fit statistic (Bock, 1960; Yen, 1981), likelihood ratio χ2 fit statistic (G2; McKinley & Mills, 1985), infit and outfit statistics (Ames & Penfield, 2015), and S-X2 (Orlando & Thissen, 2000). In addition, irtplay provides users with graphical displays to examine residuals between the observed data and model-based prediction for items (Hambleton et al., 1991).
Useful Functions Related to IRT
The irtplay package also includes many other convenient functions such as importing item and/or proficiency parameter estimates from the output of popular IRT software—Bilog-MG, PARSCALE, flexMIRT, and mirt (R package), for example. The software also enables users to implement flexMIRT software through R console, generate simulated item response data, compute asymptotic variance–covariance matrices of item parameter estimates (Li & Lissitz, 2004), compute conditional distribution of observed scores using the Lord and Wingersky (1984) recursion formula, compute item and test information functions, compute item and test characteristic curves, and plot item and test characteristic curves and item and test information functions.
Availability and Distribution
The R package irtplay and its reference manual are available for free from the website http://www.r-project.org and works on Windows, Linux, and MacOS platforms. Version 3.6.0 (or later) of the R software should be installed for optimal functioning of the irtplay package.
Supplemental Material
bring_output – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, bring_output for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
chisq_stat – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, chisq_stat for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
collapse_ftable – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, collapse_ftable for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
countFreq – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, countFreq for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
covirt – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, covirt for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
eap_sum – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, eap_sum for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
equation – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, equation for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
estimation – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, estimation for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
est_item – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, est_item for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
est_score – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, est_score for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
expFreq – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, expFreq for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
gen_weight – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, gen_weight for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
gradient – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, gradient for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
hessian – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, hessian for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
inv_tcc – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, inv_tcc for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
irtfit – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, irtfit for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
irtmodel – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, irtmodel for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
irtplay-package – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, irtplay-package for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
irtplay_manual – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, irtplay_manual for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
itemfit – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, itemfit for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
loglike_item – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, loglike_item for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
loglike_score – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, loglike_score for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
lwrc – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, lwrc for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
metalist – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, metalist for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
plot_info – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, plot_info for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
plot_irtfit – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, plot_irtfit for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
plot_traceline – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, plot_traceline for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
README_installation_example_code – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, README_installation_example_code for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
run_flexmirt – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, run_flexmirt for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
scale_prior – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, scale_prior for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
se_tcc – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, se_tcc for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
shape_df – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, shape_df for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
SimCAT_DC – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, SimCAT_DC for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
SimCAT_MX – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, SimCAT_MX for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
simdat – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, simdat for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
sx2_fit – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, sx2_fit for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
test_info – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, test_info for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
trace – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, trace for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
util – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, util for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Supplemental Material
write_flexmirt – Supplemental material for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT
Supplemental material, write_flexmirt for irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT by Hwanggyu Lim and Craig S. Wells in Applied Psychological Measurement
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
References
Supplementary Material
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