In this research, we re-defined and integrate several concepts and research designs used in psychological and/or educational sciences, such as quasi-experimental designs, hierarchical data (e.g., schools-classes-individuals), meta-analysis, panel studies in developmental sciences, or various designs in test equating, in terms of Rubin's causal model. Under the proposed unified framework, we specified the assumptions for the above models to be identifiable, and developed the estimation methods which are efficient and robust. We also applied the proposed methods to various real data analysis and found interesting implications, which confirmed the validity of the proposed methods.