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Polytomous Effectiveness Indicators in Complex Problem-Solving Tasks and Their Applications in Developing Measurement Model

Published online by Cambridge University Press:  01 January 2025

Pujue Wang Open the ORCID record for Pujue Wang [Opens in a new window]  and
Hongyun Liu Open the ORCID record for Hongyun Liu [Opens in a new window]
Pujue Wang
Affiliation:
Beijing Normal University Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University)
Hongyun Liu*
Affiliation:
Beijing Normal University Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University)
*
Correspondence should be made to Hongyun Liu, Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Faculty of Psychology, Beijing Normal University, No. 19, Xin Jie Kou Wai St., Hai Dian District, Beijing100875, People’s Republic of China. Email: hyliu@bnu.edu.cn
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Abstract

Recent years have witnessed the emergence of measurement models for analyzing action sequences in computer-based problem-solving interactive tasks. The cutting-edge psychometrics process models require pre-specification of the effectiveness of state transitions often simplifying them into dichotomous indicators. However, the dichotomous effectiveness becomes impractical when dealing with complex tasks that involve multiple optimal paths and numerous state transitions. Building on the concept of problem-solving, we introduce polytomous indicators to assess the effectiveness of problem states ds\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d_{s}$$\end{document} and state-to-state transitions Δds→s′\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathrm {\Delta }d}_{\mathrm {s\rightarrow s'}}$$\end{document}. The three-step evaluation method for these two types of indicators is proposed and illustrated across two real problem-solving tasks. We further present a novel psychometrics process model, the sequential response model with polytomous effectiveness indicators (SRM-PEI), which is tailored to encompass a broader range of problem-solving tasks. Monte Carlo simulations indicated that SRM-PEI performed well in the estimation of latent ability and transition tendency parameters across different conditions. Empirical studies conducted on two real tasks supported the better fit of SRM-PEI over previous models such as SRM and SRMM, providing rational and interpretable estimates of latent abilities and transition tendencies through effectiveness indicators. The paper concludes by outlining potential avenues for the further application and enhancement of polytomous effectiveness indicators and SRM-PEI.

Keywords

polytomous effectiveness indicatorsSRM-PEIprocess dataproblem-solving
Type
Theory & Methods
Information
Psychometrika , Volume 89 , Issue 3 , September 2024 , pp. 877 - 902
Copyright
Copyright © 2024 The Author(s), under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-024-09963-8.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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