  School choice mechanism designers use discrete choice models to understand
and predict families' preferences. The most widely-used choice model, the
multinomial logit (MNL), is linear in school and/or household attributes. While
the model is simple and interpretable, it assumes the ranked preference lists
arise from a choice process that is uniform throughout the ranking, from top to
bottom. In this work, we introduce two strategies for rank-heterogeneous choice
modeling tailored for school choice. First, we adapt a context-dependent random
utility model (CDM), considering down-rank choices as occurring in the context
of earlier up-rank choices. Second, we consider stratifying the choice modeling
by rank, regularizing rank-adjacent models towards one another when
appropriate. Using data on household preferences from the San Francisco Unified
School District (SFUSD) across multiple years, we show that the contextual
models considerably improve our out-of-sample evaluation metrics across all
rank positions over the non-contextual models in the literature. Meanwhile,
stratifying the model by rank can yield more accurate first-choice predictions
while down-rank predictions are relatively unimproved. These models provide
performance upgrades that school choice researchers can adopt to improve
predictions and counterfactual analyses.
