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. 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.

Outcomes in one place depend on its neighbors, so these questions need spatial models: we develop spatial econometric and Bayesian models of sorting and spillovers, and the sparse numerical tools that make them feasible for whole metropolitan regions.

The questions come from policy. Our models have informed a federal fair-housing evaluation and a regional plan, and show where harm-reduction services would reach the most overdose risk. The methods behind them ship as open-source software, so others can check the analysis and apply it to their own decisions.

Research areas

Urban spatial structure

Fields

  • Urban economics
  • Residential sorting
  • Housing and land markets
  • Neighborhood dynamics

Methods

  • Discrete choice models
  • Land value models
  • Agglomeration measurement
  • Geodemographic clustering

Spatial science

Fields

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

Methods

  • Spatial autoregressive models
  • Bayesian estimation at scale
  • Areal interpolation
  • Regionalization
  • Network accessibility

Inequality and policy

Fields

  • Segregation
  • Neighborhood effects
  • Access to opportunity
  • Housing policy
  • Public health

Methods

  • Multiscalar segregation profiles
  • Opportunity mapping
  • Facility location models
  • Space-time analysis
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

The book

Urban Analysis & Spatial Science

Theory, Methods, & Code for Studying Neighborhoods, Cities, & Regions

Knaap's textbook introduces the theory and intermediate quantitative methods of urban and regional analysis as a series of executable computational notebooks in Python. Each chapter takes a topic from the social science and policy literature and carries out a real analysis step by step.

CRC Press, forthcoming 2027 · draft online, CC BY-NC-ND

Read the draft
Bid-rent curves around a market centerThree bid-rent lines fall with distance from the market center. Commercial bids are highest and steepest and win out to distance a; residential bids win from a to b; agricultural bids, lowest and flattest, win from b to c. Land rent follows the upper envelope of the three lines.Land rentabcabcMarket centerCommercialResidentialAgriculture
Bid rent, from the book's part on urban spatial structure: each land use outbids the others over one band of distance from the market center, so land rent follows the upper envelope of the three bids.
  1. Spatial Data
  2. Interpolation and Change of Support
  3. Spatial Analysis
  4. Accessibility and Interaction
  5. Urban Spatial Structure
  6. Segregation
  7. Urban Factor Models
  8. Neighborhood Delineation
  9. Neighborhood Change
  10. Spatial Econometrics
  11. Location Models
  1. Upcoming

    PySAL workshop and new segregation research at NARSC, Philadelphia

    Knaap and Sergio Rey teach Spatial Data Analysis and Econometrics with PySAL on the first day of the North American Regional Science Council’s annual meeting, November 11–14, and Knaap presents Separated, Polarized, and Factioned?

  2. Release

    sparsax 0.11.0

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

  3. News

    Knaap joins the editorial board of Regional Science Policy & Practice

Projects

All projects

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 J. Rey · Environment and Planning B: Urban Analytics and City Science

  4. 2024
    Measuring two decades of urban spatial structure: The evolution of agglomeration economies in American metros

    Elijah Knaap and Sergio J. Rey · Computers, Environment and Urban Systems

Software

All software