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Explanatory item response models for continuous data: A tutorial in R.

Joshua B Gilbert1

  • 1Harvard Graduate School of Education, 13 Appian Way, Cambridge, MA, 02138, USA. joshua_gilbert@g.harvard.edu.

Behavior Research Methods
|April 16, 2026
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Summary
This summary is machine-generated.

This tutorial introduces fitting the extended two-parameter logistic (E2PL) model for continuous data using R. Researchers can now analyze continuous item response data with the explanatory item response model (EIRM).

Keywords:
Bayesian multilevel modelsExplanatory item response modelPsychometricsRResponse theory

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Area of Science:

  • Psychometrics and Quantitative Psychology
  • Statistical Modeling
  • Educational Measurement

Background:

  • The explanatory item response model (EIRM) is widely used to analyze person and item characteristics.
  • Current tutorials primarily focus on dichotomous or polytomous item responses.
  • A gap exists in practical guidance for modeling continuous item response data within the EIRM framework.

Purpose of the Study:

  • To provide a tutorial on fitting the extended two-parameter logistic (E2PL) item response model for continuous data.
  • To demonstrate the application of the EIRM for continuous responses using the brms package in R.
  • To equip researchers with methods for data exploration, model building, and interpretation for continuous EIRM.

Main Methods:

  • Utilized the brms package in R for fitting the E2PL item response model.
  • Employed two worked examples using visual analog scale (VAS) data.
  • Illustrated data exploration, model specification, and result interpretation techniques.

Main Results:

  • Successfully demonstrated the fitting of the E2PL model for continuous item responses.
  • Provided practical code and interpretation guidance for researchers.
  • Showcased the utility of the EIRM for analyzing continuous data, such as VAS.

Conclusions:

  • The EIRM can be effectively extended to model continuous item response data.
  • The brms package in R offers a flexible tool for implementing these models.
  • This tutorial empowers researchers to analyze continuous response data using the EIRM framework.