Rejoinder to the discussion on "INTACT: A method for integration of longitudinal physical activity data from multiple...

We thank the discussants for their insightful comments and suggestions. In this rejoinder, we clarify the scope of the INTACT framework and discuss several important extensions motivated by the discussion. We address issues related to model assumptions and robustness to source heterogeneity, including strategies for controlling negative transfer and accommodating partially shared covariate and covariance structures. We further discuss connections to transfer learning and the potential for incorporating task-driven objectives into harmonization. We compare INTACT with existing harmonization approaches, highlighting differences in how biological variability and source effects are balanced. Finally, we consider practical aspects of implementation, including interpretation of harmonized data, computational stability, and handling of missingness. These discussions outline promising directions for extending and applying INTACT in complex multi-source settings.