The monotonic linear model: Testing for removable interactions

Area of Science:

• Psychology
• Cognitive Science
• Psychometrics

Background:

• The problem of coordination highlights the challenge of linking theoretical concepts (e.g., memory) to their observable measures (e.g., hit rate).
• Additive conjoint measurement (ACM) offers a framework for understanding these links, distinguishing between removable and nonremovable interactions.
• A lack of statistical procedures has hindered the practical application of ACM and the interpretation of research findings.

Purpose of the Study:

• To present a novel statistical procedure for assessing the removability of interaction effects in scientific measurement.
• To bridge the gap between theoretical concepts and their empirical measures, improving research validity.
• To facilitate the practical application of additive conjoint measurement (ACM) principles in empirical research.

Main Methods:

• Development of a statistical procedure to analyze interaction effects within the framework of additive conjoint measurement (ACM).
• Focus on determining the extent to which observed interactions are removable, indicating additivity on the underlying theoretical construct.
• The procedure aims to provide quantitative insights into the coordination function between concepts and measures.

Main Results:

• The proposed procedure offers a method to statistically evaluate the removability of interactions, a previously missing component in ACM.
• This enables researchers to better discern whether observed interactions reflect true additive effects on theoretical concepts or are artifacts of measurement.
• The findings provide a tool to enhance the interpretability of complex psychological phenomena.

Conclusions:

• The introduced statistical procedure addresses a critical limitation in applying ACM to scientific measurement.
• It enhances the ability to interpret interaction effects, thereby improving the validity of research on theoretical concepts.
• This work is expected to significantly impact research practices in psychology and related fields by enabling more rigorous measurement and interpretation.