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Identifying and Addressing Disparities in Public Libraries with Bayesian Latent Variable Modeling
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Bayesian latent variable model of book checkouts across NYPL branches (browser vs. hold checkouts) that disentangles book desirability, branch demand, and hold usage to measure and mitigate socioeconomic disparities in library access.
Problem
Public library systems may provide unequal access to books across neighborhoods, but system-level checkout counts cannot reveal whether causes are collection quality, resident demand/access, or operational policies such as the online hold system.
Approach
A zero-inflated Bayesian binomial model with per-branch demand and hold-usage parameters and per-title desirability, fit to book-branch availability and checkout-day data, which separates browser and hold checkouts while controlling for availability; used to quantify book flows from holds and simulate a paging-list intervention.
Key results
- The Bayesian model substantially outperforms pooled regression and separate browser/hold regression baselines in predicting book-branch checkouts (MSE, r2, Pearson) on held-out data.
- Hold checkouts concentrate on more desirable books; for the most desirable bin (0.95-1.00), about 78.25% of checkouts are via holds.
- A proposed paging-list policy that pulls holds from branches with highest net inflow brings net book desirability flows close to zero with no significant correlation to hold usage (p = .705).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add zero-inflation to the hold checkout model (ablation) | Bayesian latent variable model · NYPL checkout prediction | balance of hold and browser checkout prediction performance | Helped |
| Add a paging-list policy that pulls available books from branches with the highest net inflow | NYPL holds system · NYPL branches, counterfactual hold flows | net book desirability inflow | Helped |
| Add a paging-list policy that pulls available books from branches with the highest net inflow | NYPL holds system · NYPL branches, counterfactual hold flows | relationship between net inflows and patron median income: p-value = .705 | Helped |
Surprising findings
- Branch collection quality (ACDR) is only weakly associated with median income (p = .055), so disparities arise mainly from hold-driven book flows rather than collection quality.
Limitations
- Single-dimensional demand and desirability parameters; does not model substitution between books or individual discrete choice.
- Does not model time-varying effects such as COVID-19 Omicron impacts; uses only 2022 data.
- Patron data is not individual-level; socioeconomic analysis relies on branch service-area census aggregates, and data cannot be shared publicly.
Experimental setup
Datasets: NYPL 2022 transaction logs NYPL monthly collection snapshots US Census socioeconomic data for branch service areas
Benchmarks: held-out book-branch checkout prediction on NYPL 2022 data
Metrics: mean squared error r2 Pearson correlation
Baselines: pooled regression separate browser/hold regressions
Builds on: zero-inflated models (Hall 2000)
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