Migration is a complex and interdisciplinary problem involving multiple factors such as social interactions, resource scarcity, and geographical features. These factors must be incorporated in migration models, but how? We feel that the issue how different factors should be incorporated is not carefully addressed in existing models. Configuring factors in ways that are theoretically unsound can lead to false migration patterns and undermine the usefulness of models; indeed, factor configurations may be more critical than the factors themselves or other inputs. Therefore, we ask: i) How important is factor configuration to output results comparing with other inputs?; ii) How do different factor configurations produce different migration patterns?; and iii) How can multimodality of certain output distributions be controlled in a management perspective? To address the questions, we develop a “toy” migration agent-based model (ABM) and explore three possible configurations between two factors: i) two factors are perfectly substitutable (ADD), ii) both factors are indispensable (AND), and iii) either is enough (OR). ABM results are analyzed by global sensitivity analysis (GSA) and Monte-Carlo Filtering (MCF). The relative importance of factor configurations quantified by GSA emphasizes why we need to consider how the factors are incorporated. Depending on factor configurations, we also observe unimodal or multimodal output distributions. MCF is then applied to the ABM-GSA results to address how policymakers should control certain inputs to sustain systems with desirable outputs. Altogether, we have integrated ABM, GSA, and MCF to disentangle complexity of migration models and better understand underlying mechanisms and patterns of migration.