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The Dirichlet Dual Response Model: An Item Response Model for Continuous Bounded Interval Responses.

Matthias Kloft1, Raphael Hartmann2, Andreas Voss3

  • 1Department of Psychological Methods, University of Marburg, Gutenbergstr. 18, 35032, Marburg, Germany. kloft@uni-marburg.de.

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Summary
This summary is machine-generated.

This study introduces the Dirichlet dual response model (DDRM) to measure response variability using dual-range sliders. The new model captures individual differences in behavior variance, addressing limitations of standard scales.

Keywords:
continuous bounded responsesdual range sliderinterval responsesitem response theoryresponse formatsuncertaintyvariability in behavior

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Area of Science:

  • Psychometrics
  • Psychological Measurement
  • Item Response Theory

Background:

  • Traditional response scales (e.g., rating scales, visual analogue scales) condense response distributions into single values, neglecting variance.
  • Measuring variability in latent states or behaviors is crucial but often overlooked by standard psychometric tools.
  • Interval-response formats, like the dual-range slider (RS2), offer a potential solution for capturing response variability.

Purpose of the Study:

  • To develop an appropriate item response model for the dual-range slider (RS2) response format.
  • To introduce the Dirichlet dual response model (DDRM) as an extension of the beta response model (BRM).
  • To evaluate the performance and validity of the DDRM through simulation and empirical studies.

Main Methods:

  • Development of the Dirichlet dual response model (DDRM), extending the beta response model (BRM).
  • Parameter recovery assessment via a simulation study.
  • Empirical validation by jointly fitting the BRM and DDRM to single-range slider (RS1) and RS2 responses for Extraversion scales.

Main Results:

  • The DDRM demonstrated good overall parameter recovery in simulations, though interval width parameters (reflecting variability) showed weaker recovery than central tendency parameters.
  • Empirical analysis showed acceptable fit for the DDRM, indicating significant respondent differences in behavioral variability.
  • High correlations between BRM and DDRM person parameters suggest convergent validity for interval location measurement across RS1 and RS2.

Conclusions:

  • The DDRM effectively models the dual-range slider (RS2) response format, capturing individual differences in response variability.
  • The model addresses the scale-inherent interdependence of interval location and width in RS2 formats.
  • The DDRM provides a valuable tool for researchers interested in measuring the variance of latent states and behaviors.