Anomalous results in G-factor models: Explanations and alternatives

Area of Science:

• Psychology
• Psychometrics
• Statistical Modeling

Background:

• G-factor models, including bifactor and hierarchical models, are widely used in psychological research.
• Empirical applications frequently report anomalous results, such as vanishing specific factors and irregular loading patterns, contradicting theoretical expectations.

Purpose of the Study:

• To explain anomalous results in G-factor model applications from the perspective of stochastic measurement theory.
• To propose alternative G-factor models suitable for single-level sampling processes common in psychological studies.

Main Methods:

• Analysis of G-factor models within stochastic measurement theory.
• Derivation and definition of two alternative models: bifactor-(S-1) and bifactor-(S·I-1).
• Illustration of model properties using an empirical example.

Main Results:

• Anomalous results in G-factor models are expected when applied to single-level sampling processes instead of the required two-level process.
• The proposed bifactor-(S-1) and bifactor-(S·I-1) models are well-defined for single-level sampling designs.
• The study details the properties and application of these alternative models.

Conclusions:

• The application of standard G-factor models requires a two-level sampling process, which is often absent in empirical psychological studies.
• Alternative models, such as bifactor-(S-1) and bifactor-(S·I-1), provide more appropriate frameworks for analyzing data from single-level sampling.
• The findings offer a theoretical explanation for common anomalies and suggest improved modeling strategies for multidimensional data analysis.