An Omega-Hierarchical Extension Index for Second-Order Constructs With Hierarchical Measuring Instruments

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• The omega-hierarchical coefficient is widely used to assess reliability and explained variance in hierarchical scales.
• Existing measures may not fully capture the nuanced influence of higher-order factors on scale component interrelationships.

Purpose of the Study:

• To introduce and describe a novel index that extends the omega-hierarchical coefficient.
• To evaluate the influence of a second-order factor on the interrelationships among components within a hierarchical measuring instrument.
• To provide a complementary measure to the traditional omega-hierarchical coefficient for explained variance.

Main Methods:

• Development of a new index based on model reparameterization.
• Utilizing the latent variable modeling framework for estimation.
• Outlining a point and interval estimation procedure for the new index.

Main Results:

• The proposed index effectively evaluates the impact of a second-order factor on component interrelationships.
• The index serves as an informative addition to the traditional omega-hierarchical coefficient.
• The estimation procedure is practical and applicable with common statistical software.

Conclusions:

• The new index provides a valuable tool for understanding complex hierarchical measurement structures.
• The latent variable modeling approach offers a robust framework for estimating this index.
• This method enhances the comprehensive evaluation of psychometric instruments.