A Bayesian Approach to Longitudinal Social Relations Model (C1, I2)
AbstractThe Social Relations Model (SRM) serves as a comprehensive conceptual and methodological framework for analyzing voluntary or involuntary interpersonal relationships and interactions among individuals within groups. Widely employed in social sciences research, SRM has gained particular relevance in the economics of education, given the increasing focus on team learning and collaborative project-based learning.
Longitudinal team learning data is abundant in practice. For instance, the Comprehensive Assessment of Team Member Effectiveness (CATME) system has been utilized by over 1.4 million students and 17,000 instructors. Instructors frequently gather multiple rounds of round-robin peer evaluation and assessment data within student teams throughout a semester or even across several semesters. Although previous research has applied the standard SRM to longitudinal social relations data, the model was originally developed based on cross-sectional data. Consequently, its application to longitudinal data, where the same individuals are observed across multiple periods, has demonstrated critical limitations.
To address the scarcity of methods for analyzing the Longitudinal Social Relations Model (LSRM), we present a Bayesian approach, aimed at developing a general and flexible framework to bridge this gap. Utilizing a simulation-based framework, we first demonstrate that the Bayesian method significantly outperforms two alternative approaches—a two-step method and the Social Relations Structural Equation Model—in terms of estimation accuracy. Furthermore, the Bayesian method is applied on an empirical application to illustrate its additional benefits: it easily incorporates covariates, such as demographic variables, into the Bayesian LSRM, and effectively handles missing data, a common issue in round-robin peer-evaluation datasets.
By introducing the Bayesian LSRM, we pave the way for analyzing a range of impactful and policy-relevant questions in social sciences research. This advanced method enhances the understanding and interpretation of longitudinal interpersonal relationships and interactions within groups, contributing to more effective policy-making and interventions in educational and other social contexts.