Bayesian and Maximum-Likelihood Modeling and Higher-Level Scores of Interpersonal Problems With Circumplex Structure

Abstract

Difficulties in interpersonal behavior are often measured by the circumplex-based Inventory of Interpersonal Problems. Its eight scales can be represented by a three-factor structure with two circumplex factors, Dominance and Love, and a general problem factor, Distress. Bayesian confirmatory factor analysis is well-suited to evaluate the higher-level structure of interpersonal problems because circumplex loading priors allow for data-driven adjustments and a more flexible investigation of the ideal circumplex pattern than conventional maximum likelihood confirmatory factor analysis. Using a non-clinical sample from an online questionnaire study (N = 822), we replicated the three-factor structure of the IIP by maximum likelihood and Bayesian confirmatory factor analysis and found great proximity of the Bayesian loadings to perfect circumplexity. We found additional support for the validity of the three-factor model of the IIP by including external criteria-Agreeableness, Extraversion, and Neuroticism from the Big Five and subclinical grandiose narcissism-in the analysis. We also investigated higher-level scores for Dominance, Love, and Distress using traditional regression factor scores and weighted sum scores. We found excellent reliability (with Rtt ≥ 0.90) for Dominance, Love, and Distress for the two scoring methods. We found high congruence of the higher-level scores with the underlying factors and good circumplex properties of the scoring models. The correlational pattern with the external measures was in line with theoretical expectations and similar to the results from the factor analysis. We encourage the use of Bayesian modeling when dealing with circumplex structure and recommend the use of higher-level scores for interpersonal problems as parsimonious, reliable, and valid measures.

ClusterCirc: Finding item clusters for circumplex instruments

“…And someone who is "conflict averse" (HI7) is likely to be "indulgent" (JK4) as well. This finding is in line with previous research on the interpersonal circumplex, where the two subscales HI and JK have been found to be closer than the expected 45° as well (Alden et al, 1990;Jacobs & Scholl, 2005;Weide et al, 2021). To better differentiate between the two subscales, it could be beneficial to generate new items that better capture the domain "JK/Unassuming-ingenuous" and disentangle it from its neighboring domain.…”

“…We used data from an online-questionnaire study, from which a different part of the data has been published within another project (Weide et al, 2021). The study conformed with the Declaration of Helsinki and was approved by the ethics board of the University of Bonn.…”

Coefficients of Factor Score Determinacy for Mean Plausible Values of Bayesian Factor Analysis

“…However, there are cautionary notes on the use of default settings for convergence (Zitzmann & Hecht, 2019) or on the use of default prior distributions (Smid & Winter, 2020). Nevertheless, Bayesian factor analysis (BFA) is meanwhile regularly used (e.g., Bonafede et al, 2021; Wang et al, 2021; Weide et al, 2021). It follows from the regular use of BFA that plausible values as factor score estimates computed from BFA (Asparouhov & Muthén, 2010a, 2010b) may also be used regularly.…”

Correlation-Preserving Mean Plausible Values as a Basis for Prediction in the Context of Bayesian Structural Equation Modeling

“…Advantages of BSEM are that it can be performed with relatively small samples (Bonafede, Chiorri, Azzolina, 2021) and that priors for the variability of loadings can be specified. BSEM thereby allows to overcome problems of specifying fixed zero loadings in the independent clusters model (Beauducel & Hilger, 2020) and it also allows for the specification of complex loading patterns as, for example, circumplex models (Weide, Scheuble, & Beauducel, 2021).…”