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An analysis of dimensionality using factor analysis (true-score theory) and Rasch measurement: what is the
Russell F Waugh1, Elaine S Chapman
1Graduate School of Education, The University of Western Australia, Stirling Highway, Nedlands, WA, 6009, Australia. Russell.Waugh@uwa.edu.au
Journal of Applied Measurement
|February 11, 2005
Summary
Factor analysis indicates reliable measures for social anxiety and math attitude, while Rasch measurement questions data validity. Rasch analysis suggests developing items on an easy-to-hard scale for valid measurement.
Area of Science:
- Educational Measurement
- Psychometrics
- Item Response Theory
Background:
- Traditional psychometric methods like factor analysis (FA) and principal components analysis (PCA) are widely used for questionnaire data.
- These methods are often based on true-score theory, assuming measurement reliability and validity.
- Rasch measurement, an item response theory (IRT) model, offers an alternative approach to data analysis and scale development.
Purpose of the Study:
- To compare factor analysis (FA) and Rasch measurement in assessing the dimensionality and validity of questionnaire data.
- To investigate the implications of using different analytical approaches for psychological constructs.
- To evaluate the suitability of true-score theory-based methods versus IRT models for educational and psychological measurement.
Main Methods:
- Comparative analysis of two datasets using both FA/PCA and Rasch measurement techniques.
- Dataset 1: Social anxiety in primary school students (N=436, I=10).
- Dataset 2: Attitude to mathematics in primary-aged students (N=774, I=10).
Main Results:
- Factor analysis suggested reliable and valid measures for both social anxiety and attitude to mathematics.
- Rasch measurement analysis raised concerns about the reliability, dimensionality, and conceptualization of items for both datasets.
- Inferences based on true-score theory were questioned by the Rasch analysis, indicating potential invalidity.
Conclusions:
- Rasch measurement challenges the assumptions and findings of traditional factor analysis for the studied datasets.
- The study highlights the importance of item conceptualization and ordering (easy-to-hard) for Rasch measurement.
- Developing items with a clear conceptual progression is crucial for creating valid linear scales using Rasch models and achieving consistent units (logits).