Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department


Major Professor

Stephen E. Stark, Ph.D.

Co-Major Professor

Brenton M. Wiernik, Ph.D.

Committee Member

Walter C. Borman, Ph.D.

Committee Member

Michael Coovert, Ph.D.

Committee Member

Marina Bornovalova, Ph.D.

Committee Member

Logan M. Steele, Ph.D.


Circulant, Confirmatory Factor Analysis, Quasi-circumplex, Simulation


The circumplex offers a useful paradigm for simultaneously modeling relationships between latent variables and visually representing an individual’s profile. Previous research has demonstrated the Circular Stochastic Process Model (CSPM) can establish the presence of the circumplex in sample data using Confirmatory Factor Analysis (CFA), allowing researchers to test the circumplex with familiar global fit indices such as the Confirmatory Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Squared Error of Approximation (RMSEA), and Unbiased Standardized Root Mean Squared Residual (SRMRu). However, it is not yet clear if these fit indices are sensitive to detect circumplexes under a variety of conditions. The current Monte Carlo simulation study evaluates how the number of common scores, sample size, and position of the common scores on the circumplex affects the sensitivity of these global fit indices to detect and accept circumplexes and reject non-circumplexes. In general, the results suggest the CFI, TLI, and RMSEA are too likely to erroneously accept non-circumplexes, while the SRMR accurately distinguished between circumplexes and non-circumplexes. Researchers are advised to plot common score theta locations, cosine factor loadings, sine factor loadings, β0 values, and β1 values carefully before accepting the circumplex. Thresholds for global fit indices when evaluating the CSPM are also provided. Supplemental code, figures, and tables are available at

Included in

Psychology Commons