Integrating covariates into circumplex structures: an extension procedure for Browne's circular stochastic process...

Area of Science:

• Psychology
• Quantitative Psychology
• Structural Equation Modeling

Background:

• Circumplex structures are fundamental in various psychological domains.
• Existing research primarily assesses indicator ordering and covariate relationships within circumplex models.
• Limitations exist in simultaneously modeling indicator interrelationships and covariate associations with the latent structure.

Purpose of the Study:

• To present an extension of Browne's circumplex model.
• To simultaneously model relationships among circumplex indicators and covariates with a latent circumplex.
• To provide a flexible framework for hypothesis testing and parameter estimation.

Main Methods:

• Utilizes Browne's Fourier series parameterization for correlation functions.
• Extends correlation function shape to covariate correlation profiles.
• Specifies the model within structural equation modeling (SEM) for hypothesis testing.
• Develops procedures for interval estimates of covariate-circumplex parameters.

Main Results:

• The proposed model effectively models circumplex indicator relationships and covariate associations.
• Exemplary applications and simulation studies favored the new model over existing methods.
• Demonstrates successful application to the interpersonal circumplex and narcissism.

Conclusions:

• The extended circumplex model offers a robust approach for analyzing complex psychological data.
• It provides a unified framework for understanding latent structures and their covariate relationships.
• The model advances quantitative methods in psychological research, particularly in personality and social psychology.