PhD Researchers & Doctoral Candidates
A correctly specified spatial model for a thesis—dependence tested and spillovers interpreted properly.
Research Methods
Spatial & Regional Analytics
Location is not just a control variable. When outcomes in one place depend on what happens nearby, ignoring that dependence biases your estimates and your standard errors. We model the geography explicitly—spatial spillovers, local variation, and regional dynamics—so your conclusions hold on a map, not just in a table.
Spatial econometrics & panels
Spillovers · GWR · convergence
R (spdep) · GeoDa · PySAL
Reproducible, journal-ready
Sample output
high cluster
low cluster
Overview
Geography that the model has to respect
Tobler's first law of geography—everything is related to everything else, but near things more than distant things—is a problem for ordinary regression, not a footnote. When regions influence their neighbors, or when unobserved shocks are spatially correlated, OLS produces biased coefficients and understated standard errors, and a referee who works with spatial data will see it immediately.
We start by testing for spatial dependence—Moran's I and local LISA statistics—then, when it's present, model it explicitly. The choice among spatial lag, spatial error, and Spatial Durbin models follows from where the dependence originates, guided by specification tests rather than convenience. Crucially, we report the direct and indirect (spillover) impacts correctly, since interpreting raw spatial coefficients as effects is one of the most common errors in the literature.
Whether the work is a spatial-panel study of regional growth, a geographically weighted regression of local variation, or a convergence and inequality analysis, the deliverable is the same: a justified weights matrix, tested dependence, correct impact measures, and reproducible code you keep.
Who We Work With
For research where location matters
If your data is organized by region, city, or geographic unit, this is the right desk to write to.
Regional & Urban Economists
Spatial-panel and convergence analysis for growth, agglomeration, and regional-disparity research.
Development & Environmental Researchers
Spatial spillover and inequality analysis where geography drives the questions and the data.
Policy Organizations & Agencies
Regional evidence and small-area analysis where where matters as much as what.
Real Estate & Housing Researchers
Geographically weighted and spatial-hedonic models for prices that vary across space.
Research Institutes & GIS Teams
Groups with geographic datasets who need rigorous spatial econometric modeling applied.
Capabilities
The full spatial & regional toolkit
Organized by spatial models, exploratory diagnostics, and regional questions. If your study needs a method not listed here, ask—this is the core, not the boundary.
Dependence modeled explicitly
The core spatial-regression family, for cross-sections and spatial panels, chosen by where the dependence lies.
- Spatial econometrics
- Spatial panel models
- SAR
- SEM
- SAC
- Spatial Durbin model
- Spatial GMM
Autocorrelation & spillovers
Diagnostics for spatial structure and methods for effects that vary across the map.
- Moran's I
- LISA
- Spatial spillover analysis
- Geographically weighted regression
Convergence & inequality
The regional-economics questions—whether places are converging, clustering, or diverging.
- Regional convergence
- Club convergence
- Regional inequality
- Urban analytics
How the Analysis Works
Six steps from map to spatial model
A transparent sequence where the spatial structure is tested first and the impact measures are computed correctly—the two places spatial papers most often fail. Nothing is a black box.
Steps are adapted to your data: cross-section vs. spatial panel, the geographic unit, and the weights scheme. We confirm the specification with you before estimation begins.
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1
Build geography
Assemble the geographic data and define the spatial weights matrix—the choice that underpins everything after it.
Inputs: units · geometry · weights (contiguity/kNN/distance)
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2
Test dependence
Diagnose spatial autocorrelation globally and locally before choosing a model.
Tests: Moran's I · LISA · LM tests
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3
Specify
Select the spatial model—lag, error, Durbin, or a spatial panel—that the dependence structure justifies.
Models: SAR · SEM · SAC · SDM · spatial panel
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4
Estimate
Fit the model with appropriate estimation (ML or spatial GMM) and correct inference.
Inference: ML · spatial GMM · robust SE
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5
Decompose impacts
Compute direct, indirect (spillover), and total effects—not raw coefficients—and test robustness to the weights choice.
Output: direct · indirect · total impacts · weights robustness
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6
Report
Deliver choropleth and cluster maps, impact tables, methodology, and reproducible code you keep.
Output: maps · impact tables · methods · R/PySAL code
Rigor by default
The checks a spatial referee will run
Spatial papers fail on untested dependence and misread coefficients. Getting the weights, the tests, and the impacts right is standard on every engagement.
Included on every project
- Spatial autocorrelation testing (Moran's I, LISA)
- Justified spatial weights matrix
- Model-selection tests (LM, SDM nesting)
- Correct direct/indirect impact decomposition
- Reproducible, versioned code you keep
What You Receive
Every engagement, delivered in full
Not a black-box result and a number, but a complete, documented package you can submit, defend, and reproduce.
- Clean, geocoded spatial dataset
- Documented spatial weights matrix
- Spatial-dependence test results
- Model estimates with direct/indirect impacts
- Choropleth and cluster maps
- Interpretation of spillovers and local effects
- Reproducible R (spdep) or PySAL code
- Journal-ready methodology and results sections
- Technical responses to methodological reviewer comments, where required
Where this fits
Part of a larger arc
Spatial analysis is strongest when the panel foundations ahead of it are sound and the reporting after it is precise—each handled with the same care.
Research Design & Planning
Identification strategy, power, and specification decided before estimation begins.
Explore methodsStatistical & Methodological Audit
An independent check of assumptions, specification, and reproducibility before submission.
Explore auditPublication & Research Support
Methods and results reporting, journal selection, and reviewer-response support.
Explore support
FAQ
Common questions
Answers to what most researchers and project leads ask before we begin a spatial or regional-analytics engagement.
Because nearby places tend to resemble each other—spatial autocorrelation—which violates the independence assumption of OLS and biases both coefficients and standard errors. We first test for it (Moran's I, LISA) and, when it's present, use a spatial model that accounts for the dependence rather than ignoring it.
By where the spatial dependence comes from. A spatial lag (SAR) model fits when the outcome in one region depends on outcomes nearby; a spatial error (SEM) model when unobserved shocks are spatially correlated; the Spatial Durbin model when neighbors' characteristics matter too. We use specification tests (LM tests, and the SDM-nesting logic) to let the data guide the choice rather than assuming one.
Through the spatial weights matrix, and the choice matters. Contiguity, k-nearest-neighbors, and distance-based schemes can each be appropriate; we justify the specification, and test whether the conclusions are robust to reasonable alternatives rather than reporting a single convenient one.
Yes. In spatial models the total effect of a variable decomposes into a direct effect (within a region) and an indirect, or spillover, effect (onto neighbors). We compute and report these impact measures correctly, which is where many spatial papers go wrong by interpreting raw coefficients as if they were the effects.
Yes. We estimate beta- and sigma-convergence, test for club convergence where regions cluster into distinct steady states, and measure regional inequality with appropriate spatial and distributional methods—common questions in development, urban, and growth economics.
Often it does, and geographically weighted regression (GWR) is built to capture it—estimating local coefficients that vary across the map rather than forcing a single global relationship. It's the right tool when you expect a driver to matter more in some places than others.
R (spdep, spatialreg, sf, and related packages), with Stata, GeoDa, or Python (PySAL) where preferred. You receive the cleaned spatial dataset, weights specification, versioned code, and a methods section written to journal standards.
Yes, and it is the best time. The geographic unit, the weights scheme, and whether you have a cross-section or a spatial panel all shape which models are valid—settling them up front prevents building an analysis the spatial structure cannot support.
Related Expertise
Often paired with econometrics
Working with geographic data?
Tell us your regions and your question—we'll tell you the right spatial model, the weights scheme, and how to read the spillovers correctly.