InDisc: An R Package for Assessing Person and Item Discrimination in Typical-Response Measures

Abstract

InDisc is an R Package that implements procedures for estimating and fitting unidimensional Item Response Theory (IRT) Dual Models (DMs). DMs are intended for personality and attitude measures and are, essentially, extended standard IRT models with an extra person parameter that models the discriminating power of the individual. The package consists of a main function, which calls subfunctions for fitting binary, graded, and continuous responses. The program, a detailed user’s guide, and an empirical example are available at no cost to the interested practitioner.

Program Description

A unified approach for obtaining and estimating unidimensional Item Response Theory (IRT) Dual Models (DMs) has been proposed by Ferrando (2019). DMs are intended for personality and attitude measures, are based on a Thurstonian response process, and are, essentially, extended standard IRT models with an extra person parameter that models the discriminating power of the individual. Consequently, both items and individuals are considered as sources of measurement error in DMs.

InDisc (for Item and Individual Discrimination) is an R package consisting of a main function (InDisc), which calls all the subfunctions that implement the procedures described in Ferrando (2019) for fitting binary, graded, and continuous response DMs. Estimation is based on a two-stage (calibration and scoring) random-regressors approach (McDonald, 1982). Item calibration at the first stage is the same as in the corresponding standard IRT models, is based on a factor-analytic underlying-variables approach, and uses an unweighted least squares (ULS) minimum-residual criterion as implemented in the “psych” R package (Revelle, 2018). Individual trait scores and individual discriminations are obtained at the second stage using Expected a Posteriori (EAP) Bayes estimation. Overall, the combined ULS-EAP estimation procedure is simple, robust, and can handle large datasets, both in terms of sample size and test length.

For input, the main function requires (a) the N (individuals) ×n (items) data matrix containing the item scores, (b) the number of quadrature points for EAP estimation (default is 30), and (c) the model to be used (“graded” or “linear”). The output is printed in the console in text form (output can also be saved) and includes (a) item parameter estimates with standard errors and measures of model-data fit at the calibration stage and (b) point estimates of the trait level and person discrimination, with the corresponding posterior standard deviations, marginal reliabilities, and measures of appropriateness of the DM at the scoring stage.

InDisc has been developed in R version 3.6.1 and runs with R versions more recent than 3.5.0. In principle, it is operational in any operating system that supports R (Windows, Linux, Mac OS). The number of variables and respondents the program can handle is not limited. Available documentation includes internal R documentation including one empirical example as well as a detailed 31-page user’s guide.

Availability, Documentation, and Distribution

The package, the documentation, and a sample illustrative dataset are available at no cost at CRAN repository (https://CRAN.R-project.org/package=InDisc). The user’s guide can be obtained at no cost at https://psico.fcep.urv.cat/utilitats/InDisc.