cs.LGFeb 20, 2026

Student Flow Modeling for School Decongestion via Stochastic Gravity Estimation and Constrained Spatial Allocation

Authors: Sebastian Felipe R. Bundoc, Paula Joy B. Martinez, Sebastian C. Ibañez, Erika Fille T. Legara

Organizations: Center for AI Research, Department of Education, Philippines, PH

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Abstract

School congestion, where student enrollment exceeds school capacity, is a major challenge in low- and middle-income countries. It highly impacts learning outcomes and deepens inequities in education. While subsidy programs that transfer students from public to private schools offer a mechanism to alleviate congestion without capital-intensive construction, they often underperform due to fragmented data systems that hinder effective implementation. The Philippine Educational Service Contracting program, one of the world's largest educational subsidy programs, exemplifies these challenges, falling short of its goal to decongest public schools. This prevents the science-based and data-driven analyses needed to understand what shapes student enrollment flows, particularly how families respond to economic incentives and spatial constraints. We introduce a computational framework for modeling student flow patterns and simulating policy scenarios. By synthesizing heterogeneous government data across nearly 3,000 institutions, we employ a stochastic gravity model estimated via negative binomial regression to derive behavioral elasticities for distance, net tuition cost, and socioeconomic determinants. These elasticities inform a doubly constrained spatial allocation mechanism that simulates student redistribution under varying subsidy amounts while respecting both origin candidate pools and destination slot capacities. We find that geographic proximity constrains school choice four times more strongly than tuition cost and that slot capacity, not subsidy amounts, is the binding constraint. Our work demonstrates that subsidy programs alone cannot resolve systemic overcrowding, and computational modeling can empower education policymakers to make equitable, data-driven decisions by revealing the structural constraints that shape effective resource allocation, even when resources are limited.

Figures & tables

Figure 1. Overview of the computational policy framework for student redistribution. Institutional data from multiple national government agencies and open-source geospatial datasets are unified to represent the national school network. A stochastic gravity model estimated via negative binomial regression derives behavioral elasticities for distance, net tuition cost, and other determinants. Predicted flows are then allocated through a doubly constrained mechanism that iteratively assigns students until candidate pools or slot capacities are exhausted, enabling counterfactual evaluation of subsidy and slot allocation policies.
VariableCoef.Std. Errorzz -valuepp -value
Intercept3.39440.13026.1210.000
ln⁡(distance)\ln(\text{distance})-0.45090.010-46.4880.000
ln⁡(net cost)\ln(\text{net cost})-0.10040.013-7.5820.000
ESC School Rating-0.02040.008-2.5030.012
ln⁡(origin LGU income)\ln(\text{origin LGU income})-0.02070.004-5.0530.000
ln⁡(dest. LGU income)\ln(\text{dest. LGU income})-0.04890.004-11.4060.000
Table 1. Negative Binomial Regression Results
ScenarioNet CostPredictedΔ\Delta fromΔ\Delta from
 ReductionFlow Yˉ(s)\bar{Y}^{(s)}Observed−- 1K
Observed ( bjb_{j} )—74,232——
−- 1K₱1,00099,992++ 34.7%—
−- 5K₱5,000100,442++ 35.3%++ 0.4%
−- 10K₱10,000100,944++ 36.0%++ 1.0%
−- 15K₱15,000101,428++ 36.6%++ 1.4%
Table 2. Constrained Simulation Results Across Subsidy Scenarios
Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

MetricPoisson RegressionNegative Binomial
Log-Likelihood−64,568.73-64{,}568.73−53,653.45\mathbf{-53{,}653.45}
AIC129,155.47129{,}155.47107,326.91\mathbf{107{,}326.91}
Dispersion ( α\alpha )Fixed at 00.3948∗∗∗0.3948^{***}
Appendix
Table 3. Comparison of Count-Based Models
ModelLog-Lik.AICBICLRT Statp-valueα\alpha
0. Baseline (Dist. + Cost)−53,838.5-53{,}838.5107,684.9107{,}684.9107,718.0107{,}718.0——0.4022
1. + School Rating−53,837.2-53{,}837.2107,684.4107{,}684.4107,725.8107{,}725.82.490.1150.4021
2. + Origin Region−53,800.1-53{,}800.1107,614.3107{,}614.3107,672.3107{,}672.374.13<< 0.0010.4014
3. + Dest. Region−53,790.0-53{,}790.0107,598.0107{,}598.0107,672.6107{,}672.620.28<< 0.0010.4007
4. + Origin Income Only−53,653.5-53{,}653.5107,326.9107{,}326.9107,409.7107{,}409.7273.11<< 0.0010.3948
5. + Dest. Income Only−53,653.5-53{,}653.5107,326.9107{,}326.9107,409.7107{,}409.70.001.0000.3948
Appendix
Table 4. Hierarchical Model Comparison and Specification Tests
MetricBootstrap Median95% CI
MAE1.5980[1.5602, 1.6359]
RMSE3.8782[3.6566, 4.0998]
Appendix
Table 6
VariableLower 2.5%MedianUpper 97.5%
Intercept3.14063.39463.6407
ln⁡(distance)\ln(\text{distance})−0.4693-0.4693−0.4506-0.4506−0.4292-0.4292
ln⁡(net cost)\ln(\text{net cost})−0.1260-0.1260−0.1007-0.1007−0.0762-0.0762
ESC School Rating−0.0372-0.0372−0.0207-0.0207−0.0050-0.0050
ln⁡(origin LGU income)\ln(\text{origin LGU income})−0.0283-0.0283−0.0205-0.0205−0.0128-0.0128
ln⁡(dest. LGU income)\ln(\text{dest.\ LGU income})−0.0575-0.0575−0.0488-0.0488−0.0403-0.0403
Appendix
Table 7

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