Explanatory Item Response Models for Polytomous Item Responses

Abstract

Item response theory is a widely used framework for the design, scoring, and scaling of measurement instruments. Item response models are typically used for dichotomously scored questions that have only two score points (e.g., multiple-choice items). However, given the increasing use of instruments that include questions with multiple response categories, such as surveys, questionnaires, and psychological scales, polytomous item response models are becoming more utilized in education and psychology. This study aims to demonstrate the application of explanatory item response theory (IRT) models to polytomous item responses in order to explain common variability in item clusters, person groups, and interactions between item clusters and person groups. Explanatory forms of several IRT models -such as Partial Credit Model and Rating Scale Model -are demonstrated and the estimation procedures of these models are explained. Findings of this study suggest that explanatory IRT models can be more parsimonious than traditional IRT models for polytomous data when items and persons share common characteristics. Explanatory forms of the polytomous IRT models can provide more information about response patterns in item responses by estimating fewer item parameters.

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Estimating Explanatory Extensions of Dichotomous and Polytomous Rasch Models: The eirm Package in R

“…In this model, the common variability among items and persons can be explained using a set of item and person properties. There are also different variants of explanatory IRT models, such as explanatory IRT models for polytomous response data [15,16], person-by-item models with an interaction between item and person properties to examine differential item or facet functioning [17][18][19], multidimensional models [20], multilevel models [21,22], and item response tree models [23,24].…”

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“…The latent regression LLTM model can be further extended by adding an interaction term between item and person properties (e.g., wording*gender2). For more information on the interpretation of the estimated effects for item and person properties, as well as their interactions, readers can review De Boeck et al [30], Bulut et al [19], and Stanke and Bulut [16]. Although the eirm() function returns the model output as an eirm object, it still retains the original model output from the lme4 package (i.e., a glmerMod object).…”

“…To tackle this problem, the polyreformat() function in the eirm package allows users to reorganize polytomous responses by creating a set of pseudo-dichotomous responses from the original (ordinal) responses. The polyreformat() function elongates the long-format data by adding new rows depending on the number of response categories in the polytomous items (see [16] for more details on the polyreformat procedure). It must be noted that the polyreformat() function assumes ordered response categories (i.e., ordinal scale), and thus polytomous responses with nominal response categories should not be restructured using this function.…”