  Surrogate modeling and active subspaces have emerged as powerful paradigms in
computational science and engineering. Porting such techniques to computational
models in the social sciences brings into sharp relief their limitations in
dealing with discontinuous simulators, such as Agent-Based Models, which have
discrete outputs. Nevertheless, prior applied work has shown that surrogate
estimates of active subspaces for such estimators can yield interesting
results. But given that active subspaces are defined by way of gradients, it is
not clear what quantity is being estimated when this methodology is applied to
a discontinuous simulator. We begin this article by showing some pathologies
that can arise when conducting such an analysis. This motivates an extension of
active subspaces to discontinuous functions, clarifying what is actually being
estimated in such analyses. We also conduct numerical experiments on synthetic
test functions to compare Gaussian process estimates of active subspaces on
continuous and discontinuous functions. Finally, we deploy our methodology on
Flee, an agent-based model of refugee movement, yielding novel insights into
which parameters of the simulation are most important across 8 displacement
crises in Africa and the Middle East.
