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Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

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Published on: September 27, 2019

Linking classical test theory and two-level hierarchical linear models.

Yasuo Miyazaki¹, Gary Skaggs

¹Department of Educational Leadership and Policy Studies, School of Education, 219 E. Eggleston Hall (0302), Virginia Polytechnic Institute and State University, Blacksburg, VA 20461, USA. yasuom@vt.edu

Journal of Applied Measurement

|December 19, 2008

Summary

This study links classical test theory (CTT) with hierarchical linear models (HLM). HLM provides a unified framework for CTT measurement analysis, yielding equivalent reliability estimates and other key psychometric quantities.

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Area of Science:

Psychometrics
Educational Measurement
Statistical Modeling

Background:

Classical Test Theory (CTT) is a foundational framework for psychometric analysis.
Hierarchical Linear Models (HLM) are advanced statistical techniques for nested data structures.
A conceptual gap exists in unifying CTT principles within modern statistical modeling.

Purpose of the Study:

To reformulate the classical ANOVA test model within a two-level Hierarchical Linear Model (HLM) framework.
To demonstrate how item difficulty and subject ability parameters can be represented by fixed and random effects in HLM, respectively.
To establish a systematic approach for measurement analysis by integrating CTT with HLM.

Main Methods:

Conceptualizing items nested within subjects to reformulate the CTT ANOVA model as an HLM.
Representing item difficulty as fixed effects and subject ability as random effects within the HLM.
Deriving explicit formulas for parameter estimates in the HLM framework.

Main Results:

The HLM framework successfully represents CTT parameters, with item difficulty as fixed effects and subject ability as random effects.
Population reliability estimates derived from HLM precisely match CTT reliability, equivalent to Cronbach's alpha under specific assumptions.
Key CTT quantities, including item difficulty, standard error of measurement, true score, and person ability, are obtainable within a single HLM model.

Conclusions:

HLM offers a unified and systematic approach to classical test theory measurement analysis.
The HLM formulation confirms the theoretical link between CTT and advanced statistical modeling.
This integration facilitates a comprehensive understanding of measurement properties and individual differences.