Design a mixed-methods research study to investigate the impact of remote work patterns on urban economies across five diverse metropolitan areas over a 10-year period. Your methodology should address: (1) longitudinal research design challenges, (2) integration of quantitative and qualitative methods, (3) selection of appropriate statistical techniques for panel data, (4) strategies for addressing selection bias and confounding variables, (5) ethical considerations in data collection, and (6) approaches for validating findings across different urban contexts. Explain how you would ensure the study's reproducibility and generalizability.