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Improving precision of ability estimation: Getting more from response times.

Maria Bolsinova¹, Jesper Tijmstra²

¹Department of Psychology, University of Amsterdam, The Netherlands.

The British Journal of Mathematical and Statistical Psychology

|June 22, 2017

Summary

This study introduces a new statistical model to improve ability estimation by using both response accuracy and response time (RT). The enhanced model captures additional information in RTs, leading to more precise ability estimates than traditional methods.

Keywords:

collateral information hierarchical model item response theory measurement precision response times

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Area of Science:

Psychometrics
Educational Measurement
Statistical Modeling

Background:

Joint models for response accuracy (RA) and response time (RT) can enhance ability estimation precision compared to RA-only models.
The standard hierarchical model assumes conditional independence between RT and ability given speed, potentially ignoring valuable information in residual RTs.
This assumption may be violated in practice, limiting the full potential of joint modeling.

Purpose of the Study:

To propose a posterior predictive check for evaluating the conditional independence assumption between RT and ability given speed.
To introduce an extended hierarchical model incorporating cross-loadings between ability and RT to utilize collateral information.
To assess the performance and precision gains of the proposed model compared to existing methods.

Main Methods:

Development of a posterior predictive check for the conditional independence assumption.
Extension of the hierarchical model to include cross-loadings between ability and RT.
Bayesian estimation procedure for the proposed extended model.
Simulation studies to evaluate parameter recovery and precision gains.

Main Results:

The proposed posterior predictive check can evaluate the conditional independence assumption.
The extended hierarchical model effectively incorporates additional collateral information from RTs.
Simulation studies demonstrate the model's performance and potential for increased precision in ability estimation.

Conclusions:

The proposed methods offer improvements over standard hierarchical and RA-only models for ability estimation.
The extended model provides a more comprehensive approach by leveraging richer information from response times.
The model was successfully applied to data from a high-stakes educational test, showing practical utility.