A dyadic multivariate mixture model for ordinal responses: application to coach–athlete interactions

Abstract

Dyadic data analysis is increasingly used to model intra- and inter-personal mechanisms across disciplines such as psychology, education, healthcare, and the social sciences. Examples of dyads include husband–wife, doctor–patient, parent–child, and coach–athlete relationships. Such data typically violate the standard independence assumption due to the inherent interdependence between dyad members, requiring more sophisticated modeling approaches. In this paper, we introduce a novel statistical framework—the Dyadic Multivariate Mixture Model (DMMM)—designed to address these complexities in the context of ordinal multivariate responses. The DMMM integrates techniques from dyadic analysis, finite mixtures, copula-based dependence modeling, and ordinal regression, offering a flexible and parsimonious way to capture latent interpersonal traits and heterogeneous patterns of interaction. While the motivating application concerns coach–athlete relationships in competitive swimming—where both members of the dyad responded to a series of Likert-scale items—the model itself is general and applicable across a wide range of domains where dyadic ordinal data are observed. These include clinical psychology (e.g., therapist–client), organizational settings (e.g., supervisor–employee), and educational contexts (e.g., teacher–student). The proposed methodology allows for the identification of latent dyadic profiles, the modeling of interdependence between responses, and the inclusion of covariates at multiple levels. A case study involving elite swimmers demonstrates the model’s ability to address three key research questions: measuring the strength of relational ties, identifying group differences in communication dynamics, and evaluating personality-related covariates that shape latent relational patterns.