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Fused SDT/IRT Models for Mixed-Format Exams.

Lawrence T DeCarlo¹

¹Teachers College, Columbia University, New York, NY, USA.

Educational and Psychological Measurement

|November 1, 2024

Summary

This summary is machine-generated.

This study proposes a unified psychological framework for mixed-format exams. By fusing signal detection theory (SDT) for multiple-choice (MC) and item response theory (IRT) for open-ended (OE) items, it offers new insights into examinee knowledge states.

Keywords:

FIMS TIMSS item response theory multiple-choice items open-ended items partial-credit sequential logit signal detection theory

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Area of Science:

Psychometrics
Educational Measurement
Cognitive Psychology

Background:

Mixed-format exams combine multiple-choice (MC) and open-ended (OE) items.
Existing models like signal detection theory (SDT) for MC and item response theory (IRT) for OE items operate independently.
A unified framework is needed to understand the psychological processes underlying performance across different item formats.

Purpose of the Study:

To propose a unified psychological framework for analyzing mixed-format exams.
To integrate SDT and IRT models through the concept of examinee knowledge.
To provide a method for simultaneously analyzing MC and OE items.

Main Methods:

A choice model based on signal detection theory (SDT) for MC items.
An item response theory (IRT) model for OE items.
A general model fusing SDT and a generalized sequential logit model for OE items, linked by the probability of knowing.

Main Results:

SDT and IRT models share a common conceptualization of latent 'know/don't know' states.
The proposed fused model allows simultaneous fitting of SDT and IRT.
The approach was illustrated using data from large-scale international exams.

Conclusions:

The fused model offers a comprehensive approach to mixed-format test analysis.
Simultaneous fitting allows examination of psychological process differences and covariate effects.
This framework provides potential estimation benefits and deeper insights into examinee cognition.