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

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 profilesThe 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.
Read the draft- Spatial Data
- Interpolation and Change of Support
- Spatial Analysis
- Accessibility and Interaction
- Urban Spatial Structure
- Segregation
- Urban Factor Models
- Neighborhood Delineation
- Neighborhood Change
- Spatial Econometrics
- Location Models
News
All newsUpcoming
PySAL workshop and new segregation research at NARSC, PhiladelphiaKnaap 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?
Release
sparsax 0.11.0Sparse direct solvers for JAX, backed by SuiteSparse: factorizations, solves, and log-determinants that run natively inside compiled code.
News
Knaap joins the editorial board of Regional Science Policy & Practice
Projects
All projectsCurrent
Spatial Concordance Indices of Income Segregation
A new spatial segregation index that locates where in a region's income distribution its geography is most organized.

Current
Fast and Unbiased Log-Determinants for Large Spatial Autoregressive Models
Log-determinant methods that make Bayesian spatial autoregressive models fast and unbiased at the scale of every U.S. census tract.

Current
A Bayesian Lagrange-Multiplier Framework for Spatial Cross-Section, Panel, and Flow Models
Bayesian counterparts of the Lagrange-multiplier tests that spatial econometrics uses to choose a specification.
Spatial Economic Analysis, forthcoming
Selected publications
All publications- 2026
- 2025
- 2024
- 2024