Examining the Interactive Nature of the Integration Hypothesis: A Comparison of Bivariate and Multivariate Meta-Analytical Approaches

While the acculturation strategy of integration (i.e., migrants embracing both their heritage culture and the mainstream culture) is best operationalised as an interaction between heritage and mainstream culture orientations, methods for testing individual-level interactions meta-analytically have only emerged recently. Previously published meta-analyses of the relationship between integration and cross-cultural adaptation used alternative bivariate operationalisations, producing results of unknown accuracy. Here, using two existing datasets (total k = 57, total N = 7,512) and one highly-powered simulation study (total k = 30,000, total N = 8,981,481), we estimate the average effect of integration on adaptation based on the state-of-the-art multivariate approach to meta-analysing interactions and compare it with four bivariate approaches used in previous meta-analyses: the summative approach, the multiplicative approach, Euclidean distance, and the mid-point split approach. The multivariate results indicate that the interaction effect of heritage-culture and mainstream-culture orientations on adaptation is negligible and largely driven by mainstream-culture orientation. Among bivariate approaches, the midpoint split, which best preserves the interactive nature of integration, produces consistently the smallest effects. We discuss the implications of using these approaches and provide recommendations for operationalising integration in meta-analytical research.