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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.
Psychometrika
|July 20, 2023
Summary
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.
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.
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