Finding Pure Sub-Models for Improved Differentiation of Bi-Factor and Second-Order Models

Area of Science:

• Psychometrics
• Statistical Modeling
• Multivariate Analysis

Background:

• Bi-factor models are frequently favored over second-order models for psychometric data.
• This preference may stem from un-modeled complexities, such as cross-factor loadings, biasing statistical measures.
• Prior research suggests this bias favors bi-factor models, potentially misrepresenting true model fit.

Purpose of the Study:

• To investigate how un-modeled complexity affects the distinction between bi-factor and second-order models.
• To develop methods for reducing statistical bias that favors bi-factor models.
• To enhance the reliability of distinguishing between these two important measurement models.

Main Methods:

• Extended simulation studies based on Murray and Johnson (2013).
• Utilized theorems on rank constraints of covariance matrices to identify sub-models with reduced complexity.
• Applied these methods to mitigate bias in statistical measures favoring bi-factor models.

Main Results:

• The ability to differentiate between bi-factor and second-order models decreases as un-modeled complexity increases.
• Identifying and analyzing sub-models with less complexity successfully reduced the bias favoring bi-factor models.
• The proposed approach allows for more accurate and reliable model selection.

Conclusions:

• Un-modeled complexity is a significant factor in the apparent superiority of bi-factor models.
• By accounting for and reducing model complexity, researchers can more accurately distinguish between bi-factor and second-order models.
• This methodology improves the validity of psychometric model comparisons and interpretations.