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

Department of Urban Planning and Public Policy · UC Irvine

We study the spatial organization of neighborhoods, cities, and regions.

Spatial methods for urban processes, open science for public decisions.

SSUS is the research lab of Elijah Knaap at the University of California, Irvine. We draw on urban economics, sociology, and geography to explain why activity concentrates where it does, how neighborhoods and regions change, and who gains or loses from the change.

People and places depend on one another through the networks that connect them in space, such as commutes, moves, markets, and the influence of neighbors. We build the formal geographic models those dependencies call for: spatial econometric and Bayesian models of spillovers, sorting, and flows, with the sparse solvers that make them feasible for whole metropolitan regions.

Research areas

Structure and Form

How land, housing, and jobs are arranged across a region.

  • Land and housing markets
  • Economic geography
  • Agglomeration
  • Urban form

Sorting and Change

Who lives where, and how neighborhoods change.

  • Residential sorting
  • Segregation
  • Income polarization
  • Neighborhood change
  • Neighborhood effects

Access and Policy

Who can reach what, and how public decisions change it.

  • Access to opportunity
  • Schools
  • Public health
  • Transportation
  • Fair housing
  • Zoning

How We Work

  • Spatial econometrics
  • Spatial statistics
  • Spatial causal inference
  • Bayesian estimation at scale
  • Discrete choice models
  • Location models
  • Measurement models
  • Areal interpolation
  • Regionalization
  • Network accessibility
  • Open-source software
A map of San Clemente, California, centered on a marked point: a large translucent red circle covers everything within one mile as the crow flies, while a much smaller blue polygon covers only the streets reachable within a one-mile walk; the polygon is a fraction of the circle across the hilly, cul-de-sac neighborhood.

From the work

The built environment defines the neighborhood

Segregation indices usually draw each neighborhood as a circle. Measured along the street network instead, the neighborhood shrinks to the streets a person can actually reach — and with it the city's measured segregation: across all 380 U.S. metropolitan areas, the network-based measure runs about 20 percent higher, and the gap is widest where streets are winding and sparsely connected.

Read the paper in Environment and Planning B

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

News

All news

  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

    augax 0.3.0

    Data-augmentation draws for JAX that make a model conditionally Gaussian, inside compiled, scanned, and parallel programs.

  3. News

    Knaap joins the editorial board of Regional Science Policy & Practice

Projects

All projects
Two maps of the census tracts of Los Angeles and Orange counties, blue for tracts on the low-income side of an income cut and orange for tracts on the affluent side. At the $40,000 cut, the low-income side, in the north and in scattered clusters across central Los Angeles, carries 59 percent of the concordance; at the $150,000 cut, the blue core in central Los Angeles is larger and joined, and the largest orange component carries 72 percent.

Current

A Spatial Concordance Index of Income Segregation

A new spatial segregation index that locates where in a region's income distribution its geography is most organized.

Line chart of the estimated treatment effect against the spatial structure of unit heterogeneity, from 0 to 0.8. The within-unit estimate stays at 10, the true effect, throughout; the between-group estimate falls steadily from 10.2 to 3.2. Line chart of the estimated treatment effect against the spatial structure of unit heterogeneity, from 0 to 0.8. The within-unit estimate stays at 10, the true effect, throughout; the between-group estimate falls steadily from 10.2 to 3.2.

Current

Space Is Not a Control Group: Quasi-Experimental Design in the Presence of Spatial Dependence

Why difference-in-differences cannot recover the effect of a treatment defined by location, and the spatial fixed-effects design that can.

Journal of Regional Science, under review

Two maps of census tracts shaded by the share of residents who are non-Hispanic Black, Dallas–Fort Worth at left and Houston at right, each principal city outlined in orange. The city of Dallas covers a small part of its metro and holds 18 percent of its residents; the city of Houston, a large, irregular area at the center of its metro, holds 33 percent. Two maps of census tracts shaded by the share of residents who are non-Hispanic Black, Dallas–Fort Worth at left and Houston at right, each principal city outlined in orange. The city of Dallas covers a small part of its metro and holds 18 percent of its residents; the city of Houston, a large, irregular area at the center of its metro, holds 33 percent.

Current

Zoning and Segregation in Principal Cities and Suburbs: Another Look at the Examples of Houston and Dallas, Texas

Houston's lack of zoning is the standing natural experiment in land-use scholarship; re-run the comparison inside each metropolis, principal city against suburbs, and the answer changes.

Annals of Regional Science, under review

Selected publications

All publications
  1. 2025
    Exploring Space-Time Interactions in Fatal Opioid Overdoses

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

  2. 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

  3. 2024
    The Legacy of Redlining: A Spatial Dynamics Perspective

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

  4. 2017

Software

All software

SSUS neighbayeslocpicksparsaxaugaxbayesplain

oturns geosnappandarmnetweave

PySAL segregationtobler