Dimension Reduction of Multivariate Outputs of Socio-Environmental Agent-Based Models

Often, socio-environmental agent-based models (ABMs) are driven by a host of parameters, and their outputs are similarly multidimensional or vastly high-dimensional. While this complex data and its inter-relationships may be rendered tractable, the task is far from trivial. In this paper, we study the multidimensional outcome space of the socio-environmental, land-use RHEA ABM (Risks and Hedonics in an Empirical Agent-based Land Market), specifically the inter-distances among the outcome measures, and their reducibility using several well-known dimension reduction techniques, variants of multidimensional scalings. In testing the efficacy of several reduction algorithms, we temporally characterize the model’s reducibility while exposing changes in behavior across a wide parameter space that can signal sudden or gradual shifts and possible critical transitions. Our findings reveal that the ABM’s signature reducibility trends exhibit idiosyncrasies and unexpected non-linearity as well as discontinuities. These non-linearities and discontinuities are indicative of both gradual and sudden shifts, signaling potential propensity to internal perturbations induced by parameter settings. Additionally, we related the outcome space via their inter-distances to the multidimensional input parameter space, effectively assessing outcome “reducibility to model controls”. This analysis reveals that the model’s sensitivity to parameters is not only temporally dependent, but also can be partitioned by them, some of which suppress variability in this reduction to model controls, raising questions regarding the extent and structure of endogeneity that yields the distinct temporal trends in the relationship between inputs and outputs and their connections to outcome reducibility.

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