Spatial Science and Urban Systems, UC Irvine Spatial Science and Urban Systems, UC Irvine

Department of Urban Planning and Public Policy · UC Irvine

We build open-source methods, models, and software for understanding sociospatial structure.

SSUS is the research lab of Elijah Knaap at the University of California, Irvine, and the institutional home of oturns, open tools for urban, regional, and neighborhood science. We study who lives where and why: how households sort across neighborhoods, how housing and land markets price location, and how the resulting patterns of segregation and opportunity change over time.

The questions come from policy. Our models have informed a federal fair-housing evaluation, a regional plan, and public health work on fatal overdoses, and the methods behind them ship as software so others can check the analysis and use it on their own decisions.

Research areas

Sorting and markets

  • Segregation
  • Residential sorting
  • Location choice
  • Housing and land markets
  • Neighborhood dynamics

Spatial methods

  • Spatial data science
  • Urban analytics
  • Computational social science
  • Spatial econometrics

Inequality and policy

  • Social inequality
  • Neighborhood change
  • Access to opportunity
  • Spatial dimensions of public health
Nine small line charts, one per metropolitan area, each showing a segregation index falling as the distance defining the neighborhood grows, with one line per census year from 1980 to 2010.

From the work

Segregation depends on the scale you measure it at

A multiscalar profile recomputes segregation as the neighborhood around each location widens. Here, nine U.S. metropolitan areas from 1980 to 2010: the curves fall with distance, and the shape of the fall differs from one metro to the next.

The segregation package computes these profiles

Projects

All projects
The PySAL logo: a central node branching into colored clusters of packages.

Current · 2024–2027

An Open-Source Ecosystem for Spatial and Urban Data Science

Long-term viability for an open-source ecosystem for spatial data science, with PySAL at its core.

NSF POSE Phase II, award 2345820

Map of Riverside County showing age-adjusted opioid overdose death rates by area in 2020, from the project dashboard.

2021–2025

Opioid Overdose Disparities in Inland Southern California: Ethnography Meets Advanced Spatial Analytics

Ethnography and spatial data science on where and why fatal overdoses occur in Riverside County.

NIH / NIDA, award R21DA054611

Three maps of San Diego County shaded by median rent by census tract in 1990, 2000, and 2010.

2020–2025

Neighborhood Influences over the Life Course: Families, Twins, and Spatial Contexts

High-resolution neighborhood data joined to a thirty-year study of twins, siblings, and families.

NIH / NIA, award 2R01AG046938

Map of schools in the Los Angeles area colored by local Moran cluster type: high-high, low-low, outliers, and not significant.

2020–2024

geosnap4ed: Neighborhood Analysis in Education Research

Neighborhood analysis methods for education research, delivered through geosnap.

Bill & Melinda Gates Foundation, INV-024366

2023–2024

Proof-of-Concept Land Value Models: A Spatial Econometric Approach

Proof-of-concept models of land value built with spatial econometric methods.

Robert Schalkenbach Foundation

Line chart of mean neighborhood opportunity scores from 2003 to 2013 for three types of housing assistance; the Baltimore Housing Mobility Program line rises well above housing choice vouchers and public housing.

Completed

Modeling the Geography of Opportunity for Fair Housing Policy

Opportunity models behind HUD's evaluation of the Baltimore Housing Mobility Program and the Baltimore regional plan.

Selected publications

All publications
  1. 2026
    segregation: Segregation Analysis, Inference, and Decomposition in Python

    Renan X. Cortes, Elijah Knaap, Sergio J. Rey · Journal of Open Source Software

  2. 2025
    Exploring Space-Time Interactions in Fatal Opioid Overdoses

    Sergio J. Rey, Elijah Knaap, Alejandra Cabral, Jennifer Syvertsen · Geographical Analysis

  3. 2024
    Segregated by design? Street network topological structure and the measurement of urban segregation

    Elijah Knaap and Sergio Rey · Environment and Planning B: Urban Analytics and City Science

  4. 2024
  5. 2024
    The Legacy of Redlining: A Spatial Dynamics Perspective

    Sergio J. Rey and Elijah Knaap · International Regional Science Review

  6. 2017

Software

All software

SSUS Numerical and statistical tools developed in the lab.

sparsax Lead

Sparse direct solvers for JAX, backed by SuiteSparse: factorizations, solves, and log-determinants that run natively inside compiled code.

pip install sparsax Source
pgjax Lead

Pólya-Gamma sampling on device for JAX, inside compiled, scanned, and parallel programs.

pip install pgjax Source
bayesplain Lead

The Bayesian version of the tests an introductory statistics course teaches, printed beside the conventional test.

pip install bayesplain Source
neighbayes Pre-release

Bayesian estimation of spatial econometric models in Python.

pip install neighbayes Source
locpick Pre-release

Discrete choice models of location decisions: households, individuals, or firms choosing among places.

pip install locpick Source

oturns Open tools for urban, regional, and neighborhood science.

geosnap Lead

The Geospatial Neighborhood Analysis Package: exploring, modeling, and visualizing the social context and spatial extent of neighborhoods and regions over time.

pip install geosnap Source
pandarm Lead

The pandas routing machine: travel network analysis on contraction hierarchies, with a pandas interface.

pip install pandarm Source
netweave Experimental

Transit and pedestrian networks woven into one routable multimodal graph for accessibility analysis.

Source

PySAL The Python Spatial Analysis Library. The lab leads the packages below; Eli is a core developer and serves on the steering committee.

segregation Lead

Segregation measurement: single-group, multigroup, and local indices, spatial and aspatial, with inference and decomposition.

pip install segregation Source
tobler Lead

Areal interpolation, dasymetric mapping, change of support, and small area estimation.

pip install tobler Source

People

Elijah Knaap Director Assistant Professor of Urban Planning and Public Policy, UC Irvine.