Punishing Places

Spatial Capabilities and Bayesian Methods for Transforming Community Supervision in Utah

Sheena Yoon · Department of Economics · University of Utah

March 6, 2026

Dissertation Architecture

Each chapter builds on the limitations of the prior: critique → baseline → evidence → policy

Chapter 1
Theoretical Framework
Spatial Capabilities

→

Chapter 2
Frequentist Replication
Simes’ Punishing Places Framework

→

Chapter 3
Extension
Spatial Bayesian Model

→

Chapter 4
Policy
Spatial Policy Targeting

➡️ Ch. 2’s residual spatial autocorrelation → motivates Ch. 3’s Spatial Bayesian methodology
➡️ Ch. 3’s coefficient contributions → feed Ch. 4’s targeting framework

My defense today is organized in this way…

Three Research Questions: Where, Why, What to do about it

RQ 1: Where?

How is the correctional supervision population spatially distributed across Utah communities?

RQ 2: Why?

What is the spatial relationship between community conditions and capability deprivations (place-based deficits)?

RQ 3: What now?

How can spatial Bayesian methods inform place-based policy interventions?

Frame the progressive structure: where → why → what to do about it. Click through each fragment. ~2 min cumulative.

Research Motivation: The Empirical Puzzle

Why does punishment concentrate in specific places?

• Vast spatial heterogeneity in Utah: Adjacent census tracts — same laws, same law enforcement, same sentencing guidelines — exhibit radically different supervision rates.

• Well-designed individual programs consistently produce null results (Doleac, 2019).

• This dissertation argues that the answer lies in community conditions — the place-based factors that shape what residents can actually achieve. These conditions are identifiable, measurable, and most importantly, modifiable.

Community supervision rate per 1,000 individuals by census tract. The contrast between deep red and yellow tracts is the puzzle motivating this dissertation.

Heterogeneity in Utah. The contrast between deep red and yellow tracts is the puzzle motivating the entire dissertation. ~1 min.

The Stakes: Why does this matter?

💡 This dissertation provides the evidence base for where, what, and how to invest in community conditions to reduce community supervision rates.

• Research gap: Most studies focus on prison admissions from urban areas, while most people in the system are on community supervision. Occuring increasingly in non-metropolitan areas.

• 49,829 supervision episodes across 708 census tracts (2016–2023)

• 128 high-risk tracts where supervision concentrates at rates up to 35× the state average

• Current Policy Context: increased supervision vs health/social services

$130M for 768 new prison beds in Utah
Utah 2026 proposal (Baird, 2026)

$195M RHTP — invest in community conditions that can prevent criminal justice contact over the next 5 years
Rural Health Transformation Plan

Emphasize the gap: most research studies prison admissions from urban areas, while most people in the system are on community supervision, increasingly in non-metropolitan areas. ~2 min.

CHAPTER 1

Place as Conversion Factor:

A Spatial Capabilities Framework for Understanding the Geography of Community Supervision

The Causal Inversion

Neoclassical Economics

Individual Choices

↓

Aggregate to Crime Rates

↓

Community Supervision Rates = Sum of Individual Decisions

Policy: Change individual incentives

Spatial Capabilities

Behavior Emerges Within Constrained Possibilities Embedded in Space

↑

Shape Capability Sets

↑

Community Conversion Factors

Policy: Transform community conditions

🏡 ⚖️ Someone tethered to the CJ system in a community with robust transportation, accessible healthcare, dignified jobs, and strong collective efficacy faces a fundamentally different capability set than one returning to institutional withdrawal and environmental degradation.

Simes & Jahn (2022): Medicaid expansion → 20–32% reduction in arrest rates across 3,035 U.S. counties.

Spatial Capabilities Theory: Place as Multidimensional Conversion Factor

↗️ click figure to expand

Place = multidimensional conversion factor — it shapes which conversion factors exist. No clinic, no bus route, no community college, no childcare → no conversion.

Resources × Conversion Factors → Capabilities
A credential without transportation to employers is not a capability. The conversion step is where place enters.

Community Outcomes (bottom): Crime reduction, community integration, and supervision success emerge from capability formation — not solely from individual deterrence.

The spatial trap: Outcomes feed back into the spatial environment — incarceration depletes the very conversion factors communities need, deepening the cycle.

A neighborhood is not merely a location where individuals happen to reside but a configuration of conditions that constitute the capability sets available to residents

The person returning from incarceration to a community with robust transportation, accessible healthcare, and strong collective efficacy faces a fundamentally different capability set than one returning to institutional withdrawal and environmental degradation

Credentials are resources requiring conversion factors to become capabilities:

• Transportation to reach employers
• Childcare during interviews
• Social networks providing referrals
• Employer willingness to hire

Without these conversion factors, a credential cannot become employment — the individual program “fails” not because of its logic but because of community conditions

Three Forms of Spatial Capability: In Practice

INDIVIDUAL

Personal mobility & spatial agency — the ability to access opportunities across geographic space

In rural Utah, limited public transportation severely constrains access to employment, treatment, and supervision compliance — a returning citizen without a car cannot reach a parole office 45 miles away

COLLECTIVE

Community-level capacities achieved only through coordinated action — collective efficacy, mutual trust, resource mobilization

Sampson (2012): Neighborhoods with high collective efficacy produce lower crime rates regardless of poverty — this is a community property, not an individual one

CROSS-BOUNDARY

Resources accessed beyond one’s own community — when what you need doesn’t exist where you live

Geographic isolation becomes a form of capability deprivation

💡 These three forms operate across different scales — and φ = mixing parameter in the empirical analysis directly tests the collective dimension

Walk through each form with the Utah-specific examples. The cross-boundary form is unique to this framework and essential for understanding rural dynamics. ~2 min.

Bridging Theory to Method

What the Theory Predicts 🔎

Spatial capabilities theory makes testable empirical claims:

1. Correctional supervision concentrates spatially — not randomly
2. Specific conversion factors drive that concentration — not generic disadvantage
3. Neighboring communities share capability profiles — spatial dependence is real
4. Different communities have different binding constraints

Simes, Beck & Eason (2025): Spatial concepts and methodologies remain underutilized in criminal justice research — this dissertation responds to that research gap.

This is the theory-to-method bridge. Each theoretical prediction maps to a specific methodological capability. Sets up the Chapter 2 transition. ~1.5 min.

CHAPTER 2

Punishing Places in Utah

Replicating & Extending Simes’ Punishing Places

Simes’ Punishing Places (2021)

The Most Thorough Spatial Analysis

• Simes documents the geographic transformation of American punishment — from large cities to smaller cities, towns, and rural communities.

Key findings from Massachusetts:

15% of tracts → 52% of prison admissions

Moran’s I = 0.30 — strong spatial clustering of prison admissions

Concentrated disadvantage explains much, but significant spatial structure persists

Element	MA	UT
Outcome	Prison admits	Supervision
N tracts	1,359	708
Land area (mi²)	10,554	84,899
Moran’s I	0.30	0.40
Concentration	15%→52%	21%→50%
Disadvantage	+31%	+28.5%

Adopts Simes, Beck, & Eason’s (2024) “spatial-contextual approach” — examining both place-based social processes within local areas and spatial relationships between them

The table: Nearly identical concentration despite profoundly different geographies. The relationship between what a place provides and how much correctional control it experiences appears to be structural, not contextual.

Limitations motivating this dissertation

• Only Massachusetts (urban, northeastern)
• Composite disadvantage index — can’t identify which conversion factors
• No spatial random effects decomposition

• For every standard deviation increase in concentrated disadvantage, the model estimates a 28.5% higher supervision rate.
• References: Simes, J. T. (2018a). Place and punishment: The spatial context of mass incarceration. Journal of Quantitative Criminology, 34(3), 513–533. https://doi.org/10.1007/s10940-017-9344-y

  Simes, J. T. (2021). Punishing places: The geography of mass imprisonment. University of California Press.

Why Utah? A Critical Case Study

Utah’s combination of metropolitan–rural contrast, rapid prison growth, and healthcare infrastructure deficits creates a natural laboratory for testing whether community conditions predict the geographic concentration of correctional supervision

6×

Prison population growth vs. national average (2004–2013)
despite declining crime rates (Pew, 2017)

42%

Increase in supervision revocations (2015–2018)
technical violations driving prison growth

80%

Non-metropolitan geography
vast rural landscape with dispersed services

The majority of the community supervision population consists of people on probation who have never been incarcerated — yet place-based research almost exclusively studies prison admissions. First study of Utah.

Justify the case study to the committee. Utah is not a convenient sample — it’s a critical case that uniquely combines the dynamics this framework addresses. ~2 min.

Data Pipeline

Variables & Sources

Variable	Source	Years	Obs.
Community supervision (probation & parole)	Utah DOC	2016–2023	86,734 → 49,829
Concentrated Disadvantage Index (PCA)
Poverty rate (% families)	ACS 5-Yr	2017–2021	709 tracts
Unemployment rate	ACS 5-Yr	2017–2021	709 tracts
Female-headed HHs w/ children	ACS 5-Yr	2017–2021	709 tracts
Adults without HS degree	ACS 5-Yr	2017–2021	709 tracts
Public assistance (dropped, loading = 0.31)	ACS 5-Yr	2017–2021	709 tracts
Demographic Controls
% NH Black, % Hispanic, % NH Asian	ACS 5-Yr	2017–2021	709 tracts
% Foreign born	ACS 5-Yr	2017–2021	709 tracts
% Residential mobility (new residents)	ACS 5-Yr	2017–2021	709 tracts

Key Difference from Simes

Simes measures prison admissions. This dissertation measures community supervision (probation and parole), capturing the broadest reach of correctional control (3.7M nationally vs. 1.8M incarcerated).

If supervision alone concentrates in the same disadvantaged places, place is already shaping criminal justice outcomes before anyone enters prison.

Concentrated Disadvantage Index ⭐

PCA following Sampson et al. (1997): % families in poverty, % unemployment, % female-headed households, % no HS degree.

Utah adaptation: public assistance dropped (loading = 0.31) — reflects LDS Church welfare substitution and rural access barriers. Sensitivity: 5-var/4-var correlation = 0.979

Four schemes tested following Simes’ (2018) approach: Simes 4-Region adapted from her MA framework (Salt Lake County as reference, Other Wasatch Front, Secondary Urban Centers, Rural/Non-Metro); 9-Region developed to capture heterogeneity within rural categories (Uinta Basin, Wasatch Back, Southeastern Utah); Local Health District using Utah’s 13 administratively-defined health regions (strongest differentiation: F = 2.95, p < 0.001); and RUCA 4-Category from USDA Economic Research Service codes (Metropolitan, Micropolitan, Small Town, Rural; non-significant: F = 0.23, p = 0.874).

Ch. 2 Methodology: Model Specification

Negative Binomial Regression

log(E[Y_i]) = log(Pop_i) + β₀ + β₁Disadvantage_i + β₂Region_i + β₃Demographics_i + β₄TreatmentCenter_i + ε_i

Component	What It Captures
log(E[Yi])	Expected supervision count in tract i — log-link ensures positive predictions; coefficients exponentiate to rate ratios (e.g., exp(0.251) = 1.285 → +28.5%)
log(Popi)	Offset — converts counts to rates so tracts are comparable regardless of population
Disadvantagei	Standardized PCA index: poverty, unemployment, female-headed HH, no HS degree
Regioni	Varies by specification (A–D)
Demographicsi	% NH Black, % Hispanic, % NH Asian, % foreign born, % new residents
TreatmentCenteri	Residential facility proximity control
εi	NB error with dispersion θ (variance ≈ 28× mean)

Spatial-Durbin (SLX) Extension (Model E)

log(E[Y_i]) = … + β₁X_i + β₂(WX)_i + ε_i

Term	Meaning
Xi	Own-tract disadvantage
(WX)i	Neighbors’ average disadvantage
W	Queen’s contiguity matrix, row-standardized

Tests whether collective capabilities cross tract boundaries — does the disadvantage of surrounding neighborhoods independently predict a tract’s supervision rate?

Why negative binomial? Our dependent variable is a count — number of supervision episodes per tract. Poisson would be the default for count data, but our data is heavily overdispersed: the variance is roughly 28 times the mean, with a skewness of 3.92. A handful of tracts have rates exceeding 100 per 1,000 while the median is just 11. Negative binomial adds a dispersion parameter theta that accounts for this — it lets the variance exceed the mean, which Poisson cannot.

The population offset is key. By including log of population as an offset, we’re not predicting raw counts — we’re predicting rates. A tract with 10,000 people and 100 episodes is fundamentally different from a tract with 1,000 people and 100 episodes. The offset handles that.

The concentrated disadvantage index is a standardized PCA composite of four variables — poverty, unemployment, female-headed households, and educational deficit. Coefficients are in standard deviation units, so an RR of 1.285 means each one standard deviation increase in disadvantage is associated with 28.5% higher supervision rates.

The regional term varies across models A through D — that’s the whole point. Each specification swaps in a different way of carving up Utah’s geography to test which boundaries best capture the spatial pattern. Model E adds something fundamentally different: not just a different classification, but the average disadvantage of neighboring tracts via Queen’s contiguity.

The treatment center variable is a control, not a finding. It captures the mechanical fact that people under supervision who live in residential treatment facilities get geocoded to the host tract, inflating that tract’s count. Without it, those tracts would look like hotspots for the wrong reason.

The five demographic controls follow Simes’ Table 3 specification exactly — percent non-Hispanic Black, Hispanic, non-Hispanic Asian, foreign born, and new residents. This enables direct comparison with her Massachusetts results.

Queen’s contiguity defines neighbors as tracts sharing a boundary or corner. Row-standardization makes each spatial lag a simple average of neighbors’ values regardless of neighbor count.

Ch. 2 Five Model Specifications: Results

Model	Regional Term	Source	Disadv. RR	Key Regional Finding	ΔAIC	Moran’s I
A: Simes 4-Region	SL, Wasatch, Secondary, Rural	Simes (2018a)	1.285	Rural RR = 1.626 (p < 0.01); 4-region p = 0.056	ref	0.326
B: LHD	13 health districts	Utah DHHS	1.229	SE Utah RR = 3.718, TriCounty RR = 3.295; F = 2.95	−24.3	0.287
C: RUCA	Metro, Micro, SmallTown, Rural	USDA ERS	1.280	Metro RR = 0.679 (−32.1%***); Micro, SmallTown n.s.	worst	0.313
D: Full	4-Region + RUCA	Combined	1.277	Regional effects hold; no RUCA category significant	−18.7	0.320
E: SLX	4-Region + neighbors’ disadv.	Extension	1.196	Neighbors’ RR = 1.440***; Rural persists RR = 1.495	−41.0	0.335

Model fit: LHD outperforms all geographic schemes — institutional infrastructure matters more than administrative boundaries. Concentrated Disadvantage remains the dominant structural predictor. Each standard deviation increase is associated with 22.9% higher correctional supervision rates. [SLX best → LHD → Full → Simes → RUCA]

*RR = exp(coefficient): exp(0.179) = 1.196 means +19.6% per SD

AIC balances how well the model fits the data against how many parameters it uses

Persistent autocorrelation: Spatial spillovers capture variation that regional classifications cannot. Moran’s I = 0.287–0.335 across all models (MA benchmark: 0.30). No categorical classification fully captures continuous spatial processes → motivates INLA-BYM2 in Ch. 3.

Moran’s I measures spatial autocorrelation — whether nearby tracts have more similar residuals than expected by chance. Values near 0 = random; positive = neighbors resemble each other.

• After controlling for regional classification and five demographic variables, each standard deviation increase in concentrated disadvantage is associated with a 28.5% higher tract-level supervision rate.

• Utah’s disadvantage effect, 19.6%–28.5% across specifications, converges with Simes’ MA estimate (~31%) despite profoundly different contexts — dense post-industrial urban geography vs. dispersed non-metropolitan geography. 💡 Something fundamental rather than context-specific is operating.

• Particular kinds of rural — extraction and post-industrial rural — have dramatically elevated rates, while other rural areas don’t.

• Rural elevation persists even after accounting for neighboring conditions, meaning something about rural places beyond just their poverty levels drives higher supervision.

• ** Incidence Rate Ratios (IRR) — the multiplicative change in the expected count of supervision episodes for a one-unit (or one SD) increase in the predictor.

• Race reframed: Racial composition largely proxies for compounding regional disadvantage. In every model (A–D), Hispanic and Black population shares significantly predict higher supervision. But once neighbors’ disadvantage enters Model E, the Hispanic effect disappears entirely (IRR → 1.007, n.s.) and Black effect declines to marginal significance.

Ch. 2 Key Insight: Neighbors Matter

1.196

Own-Tract Disadvantage

vs.

1.440

Neighbors’ Disadvantage

A 1 SD increase in neighbors’ averaged concentrated disadvantage is associated with a 44% higher supervision rate, after controlling for own-tract disadvantage, demographics, and region.

The Decomposition

• Where you are surrounded by matters more than where you are. Model E reveals neighbors’ disadvantage (β = 0.365) is more than double the own-tract effect (β = 0.179).

• Model A’s 28.5% increase blends both — Model E separates them: 19.6% from own-tract conditions, 44.0% independently from neighbors’. Standard models miss this because they treat each tract as if it exists in isolation.

What This Validates

Collective capabilities are real. Shared labor markets, transportation networks, institutional catchment areas — conversion factors operate at geographic scales larger than individual census tracts.

Even after accounting for neighbors’ disadvantage, nearby tracts still look more alike than they should (Moran’s I = 0.335) ➡️ Something else is spatially clustered beyond just disadvantage: 🏞️, 🏥, 🚌, 📚 These are the conversion factors Chapter 3 will identify.

**RR = exp(coefficient): exp(0.179) = 1.196 means +19.6% per SD; exp(0.365) = 1.440 means +44.0% per SD

Ch. 2 → Ch. 3 Bridge 🌉

Four Contributions

1. Disadvantage concentrates punishment universally — comparable in MA (+31%) and UT (+28.5%) despite different geographies

2. LHD boundaries outperform all regional classifications — institutional (health) infrastructure shapes punishment geography

3. Neighborhood spillovers are substantial — SLX validates collective capabilities theory (1.440 vs. 1.196)

4. Extractive post-industrial rural — Rural elevation persists even after accounting for neighboring conditions

“When places lose the conditions people need to stay out of the criminal justice system, incarceration concentrates there”

CHAPTER 3

An Empirical Portrait of Punishing Places:

Spatial Bayesian Analysis of Place-Based Capabilities

Why Integrated Nested Laplace Approximations – Besag-York-Mollié 2 (INLA-BYM2)?

Ch. 2 Established ✅

• Disadvantage predicts supervision
• The models explain that disadvantage matters, but the errors still cluster on the map — nearby tracts over- and under-predict together (Moran’s I ≈ 0.29–0.34)
• Neighbors matter (SLX: RR = 1.440)

Ch. 2 Cannot ❌

• Identify which conversion factors
• Model spatial dependence precisely
• Decompose spatial vs. non-spatial variation
• Provide tract-specific guidance

Ch. 3 Advances

Ch. 2 Limitation	Ch. 3 Solution
Composite disadvantage	22 individual conversion factors
Regional fixed effects	BYM2 spatial random effects
Frequentist estimation	Full Bayesian posteriors
Statewide predictions, no tract-level residual adjustment	Tract-specific residual adjustments
Single model	9 specs across 3 datasets

Why Bayesian?

• Instead of just asking “is this significant?” (p < 0.05), Bayesian credible intervals answer a more useful question: how big is the effect, and how sure are we? Policymakers need to know the plausible range — not just a point estimate and a yes/no threshold.

the spatial random effects already captures the geographic pattern more precisely than any set of regional boundaries can, because risk doesn’t stop and start at county lines.

• BYM2 spatial random effects say: “each tract gets its own adjustment, informed by its specific neighbors.” A tract surrounded by high-risk tracts gets pulled up; a tract surrounded by low-risk tracts gets pulled down — regardless of which county or region it sits in. The adjustment is continuous across the map rather than jumping at arbitrary administrative boundaries.

Ch. 3 Data Pipeline

Data Sources & Coverage

Source	Variables	Coverage
Utah DOC Supervision episodes	Probation & parole counts (2016–2023)	49,829 episodes 35,052 individuals 716 tracts
Utah HPI Healthy Places Index	8 domain scores + disaggregated indicators (education, transport, environment, housing, social)	702 tracts
ACS 5-Year 2017–2021	Educational attainment, MHI, homeownership, cost burden, living alone	709 tracts
GeoDaCenter Health metrics	Diabetes, obesity, physical activity, poor health days, cognitive difficulty	450 tracts
EPA EJ Environmental Justice	Diesel particulate matter concentrations	702 tracts

All continuous variables z-scored to enable cross-domain comparison. Coefficients represent effect of 1 SD change.

Three Model Specifications

Full Coverage (n = 689)

22 predictors from ACS + HPI + EPA. Maximizes geographic representation. Primary specification. DIC = 5,247.3

Partial Coverage (n = 450)

39 predictors adding GeoDaCenter health metrics. Best overall fit (DIC = 3,460.4) but limited geographic scope.

HPI Domain Scores (n = 689)

9 composite domain indices. Parsimonious alternative — tests whether broad domains suffice for policy. DIC = 5,270.8

Variable Selection

Bayesian Model Averaging evaluates all 90+ candidate predictors simultaneously (50K iterations), ranking each by its probability of belonging in the true model — but spatial autocorrelation is removed first so that BMA selects variables on substantive merit rather than geographic proximity, before INLA-BYM2 reintroduces proper spatial structure.

• Lower DIC means better fit-to-complexity balance. DIC estimates how many parameters the model is effectively using given how much information is shared across tracts.

The Integrated Nested Laplace Approximation-BYM2 Model

• Plain Language
• Formal Specification
• Interpretation

What makes a tract’s supervision rate higher or lower than the statewide expectation?

Baseline

Expected count if this tract
matched the state average

+

Conversion Factors

Measured community
conditions

+

Collective Capabilities

Shared neighborhood
spatial processes

+

Local Variation

This tract’s
unique factors

↕

log(RR_i) = β₀ + Σβ_jx_ij + u_i + v_i   →   exp(·) = RR_i

β₀

baseline deviation from the statewide rate

Σβ_jx_ij

Measured conversion factors push RR up or down

u_i

Collective capabilities: spatial residual shared with neighbors

v_i

Tract-specific residual

RR_i

Relative Risk — exp(total)

RR_i is the model’s best estimate of each tract’s true underlying risk — combining everything measured with everything unmeasured, smoothed to filter out noise from small populations. RR = 1.5 means 50% above the state average.

Level 1: Data Model

y_i ~ Poisson(E_i · θ_i)

Level 2: Process Model

log(θ_i) = β₀ + Σβ_jx_ij + u_i + v_i   →   exp(·) = RR_i

Symbol	Meaning
β₀	Intercept — statewide baseline supervision rate
Σβjxij	Measured conversion factors (education, income, diabetes…)
ui	Structured spatial effect — collective capabilities shared with neighbors
vi	Unstructured effect — this tract’s unique, unmeasured characteristics
RRi	Relative Risk — combined effect of all components, smoothed for sampling noise

• Coefficients exponentiate to relative risk: exp(β) = 1.5 means 50% higher supervision rate per SD increase.

• Bayesian credible intervals tell policymakers: “We are 95% confident the true effect falls here” — not just whether p < 0.05.

• The spatial random effects (u_i + v_i) capture everything the measured conversion factors miss — and the BYM2 decomposition tells us how much of that residual is spatially structured.

• This model asks a simple question: what makes a tract’s supervision rate higher or lower than expected? It starts with a baseline — the count we’d expect if this tract matched the statewide rate, adjusted for its population. Then three layers explain why it deviates: the measured conversion factors push the rate up or down, the spatial residual captures what neighboring tracts share beyond what we measured, and the local residual captures what’s unique to this tract alone. Exponentiate the total and you get RR — the tract’s estimated risk relative to the state average.

• This slide shows how the model answers a simple question: why are some tracts higher and some lower than expected? We start with a baseline — the number of supervised individuals we’d expect in this tract if it had the statewide average rate, scaled to its population. A tract with 5,000 people gets a higher expected count than one with 500, but the rate is the same. The model then asks: what makes the actual rate deviate from that population-adjusted expectation? It adds three layers. First, the measured conversion factors — education, income, diesel PM, social isolation — observable conditions of a place. Second, the spatial effect uᵢ — neighboring tracts tend to look alike for reasons our variables don’t fully capture, things like shared labor markets or overlapping institutional catchments. That’s the collective capabilities piece. Third, vᵢ — variation unique to a single tract, like the presence of a treatment facility. Combine all four and exponentiate, and you get RRᵢ — the model’s best estimate of how much that tract’s true rate deviates from what we’d expect given its population. An RR of 2.0 means double. The next slide then asks: of the uᵢ + vᵢ portion — everything our conversion factors missed — how much is shared between neighbors and how much is unique? That’s what φ answers.

(Moraga 2020; Rue et al., 2017; Riebler et al., 2016; Simpson et al., 2017)

Ch. 3: BYM2 Decomposition — Do Neighborhoods Matter?

The model specification included uᵢ + vᵢ — but how much of the unexplained variation is shared between neighbors vs. unique to each tract?

φ tells you the balance

φ share → uᵢ

Shared between neighbors — labor markets,
networks, institutions crossing boundaries

+

(1 − φ) share → vᵢ

Unique to this tract — a treatment facility
here, a local employer there

φ = 0.51

After measuring 22 conversion factors, neighboring tracts still look alike — neighborhoods matter

• Ch. 1 theorized collective capabilities. Ch. 2’s SLX showed neighbors matter (RR = 1.440). φ = 0.51 confirms it — and tells policy at what scale to act:

φ → 1

Fix regions

φ = 0.51

Fix both

φ → 0

Fix tracts

Stress tested. Six regional controls added — φ never decreases. Not confounding.

Regions mediated. LHD boundaries significant in raw data but worsen fit when added. Conversion factors explain what jurisdictions cannot.

Better measurement → lower φ. Full: 0.51 → Health-enriched: 0.23 → Composites: 0.86.

φ = 0.51 is the core empirical test of spatial capabilities theory. The dissertation thread: Ch. 1 theorized it, Ch. 2 showed neighbors matter, Ch. 3 quantifies exactly how much.

No new formula — stays with uᵢ and vᵢ from the model specification. φ is just the balance dial between them. The dissertation thread: Ch. 1 theorized it, Ch. 2 showed neighbors matter, Ch. 3 quantifies exactly how much. ~3 min.

After accounting for all 22 measured conversion factors, half the remaining variation still clusters geographically. This is the core empirical test of spatial capabilities theory. φ = 0.51 validates the collective dimension. Addresses committee question: “How do you know φ isn’t just capturing unmodeled regional confounders?” The six-specification stress test + the fact that φ increases with regional controls is the definitive answer. The cross-specification variation (0.23 to 0.86) shows measurement matters — better variables explain spatial structure, they don’t eliminate it. ~2-3 min.

• After all the measured covariates are accounted for, uᵢ models the leftover spatial pattern in the outcome itself.

• INLA-BYM2 looks at what’s left over and asks: do neighboring tracts have similar leftover patterns?

• Small area estimation borrows strength across neighboring areas, stabilizing estimates for tracts with limited observations by leveraging information from similar nearby locations.

Ch. 3: Robust Conversion Factor Effects

Conversion Factor	Direction	Effect Range	Robustness
Educational attainment (bachelor’s)	🛡️	−13.5% to −21.9%	★★★ All 3 specs
Median household income	🛡️	−9.2% to −12.1%	★★★ All 3 specs
Living alone (social isolation)	⬆	+19.5% to +28.4%	★★★ Full + Partial
Diabetes prevalence	⬆	+20.8% to +26.9%	★★★ Full + Partial
Walkability index	⬆	+2.3% to +2.9%	★★
Clean environment (HPI)	🛡️	−26.7%	★★
Social domain (HPI)	🛡️	−24.6%	★★
Transportation (HPI)	🛡️	−11.0%	★★
Limited physical activity	⬆	+45.4%	★

🛡= Protective. Effect ranges = % change in supervision rate per SD. ★★★ = credible in 2+ specifications; ★★ = credible in 1. All shown achieve 95% Bayesian credibility (CI excludes zero).

• Each conversion factor is a policy lever — a specific, addressable community condition

+26.9%

Diabetes — strongest robust risk

Health conditions reflect upstream deficits

+19.5%

Living alone — social fragmentation

Dominant driver in SL urban core

−21.9%

Education — most robust protective

Credible across all 3 specifications

−12.1%

Income — economic conversion factor

Robust across all 3 specifications

• Communities with one standard deviation higher diabetes prevalence have 26.9% higher supervision rates, all else equal.

-Walkability index (+2.3 to +2.9%) — captures residual urban density effects; walkable tracts in Utah are urban cores where supervision also concentrates. This isn’t saying walkable neighborhoods cause supervision. It’s saying our other variables don’t fully capture the urban concentration pattern, and walkability picks up what’s left over. It’s a control variable, not a policy target — nobody should conclude that making neighborhoods less walkable would reduce supervision.

Ch. 3: The Geography of Risk

Risk clusters in both urban cores and rural extraction regions. ➡️ Relative Risk = tract supervision rate relative to statewide average. RR of 2.0 = double expected; 0.5 = half expected.

Urban Core

Salt Lake (46), Weber (13)

Rural Extraction

Carbon (5), Duchesne (4), Uintah (3)

Suburban

Utah County (14)

Region	N	%
Salt Lake	46	46%
Utah	14	14%
Weber	13	13%
Uinta Basin	7	7%
Carbon	5	5%

128 high-risk tracts / 689 (18.6%). P(RR > 1.5) exceeds 80%
Top: RR = 35.85 (SL 1025.02)

⛶ Full screen ↗

• INLA-BYM2 assigns every tract a smoothed relative risk score — ranking all 689 tracts by risk level while accounting for population size and spatial context.

• The SLX tells you that neighbors’ conditions matter as a substantive finding. But The BYM2 uses the neighborhood structure to produce better estimates for every tract — especially the small ones where raw data is unreliable.

Ch. 3: Exceedance Probabilities — Where to Invest?

• The model doesn’t just estimate which tracts are high-risk — it tells us how confident we are. Exceedance integrates both magnitude and confidence (Medina et al. 2022). These tiers group tracts by the probability that their rate truly exceeds double the state average: Tiers translate model uncertainty into actionable 📍 investment categories.

Tier	P(RR>2.0)	Tracts	Population	Supervised	Mean RR	RR Range	Action
🔴 Red	80–100%	59	224,490	14,084	4.68	2.13–35.85	Comprehensive (3.0×)
🟠 Orange	50–79%	10	46,162	1,465	2.09	2.01–2.18	Targeted (2.0×)
🟡 Yellow	20–49%	11	44,348	1,304	1.92	1.86–2.00	Prevention (1.5×)
🟢 Green	<20%	609	2,949,000	~29,000	0.76	0.10–1.88	Maintain (1.0×)

P(RR > 2.0) = how confident is the model that this tract’s rate is at least double the state average?

This gives us a spatially precise framework for policy investment ➡️ Ch. 4

County	Tracts	Profile
Salt Lake	34	Social isolation, poverty, diesel PM
Weber	10	Post-industrial — education deficits
Carbon	5	100% Red — post-extraction collapse
Duchesne	4	Uinta Basin — rural + industrial

Dual concentration confirmed. Red tracts cluster in Salt Lake’s urban core (social isolation pathway) and rural extraction counties (education deficit pathway). Same tier, different interventions.

Carbon County: 100% of tracts Red — a county-wide capability deficit from post-extraction economic collapse.

Why exceedance? A tract with RR = 2.1 but wide uncertainty differs from RR = 2.0 with narrow uncertainty. Exceedance integrates both magnitude and confidence.

• The model doesn’t just estimate which tracts are high-risk — it tells us how confident we are.

• These tiers group tracts by the probability that their rate truly exceeds double the state average: 59 Red Zone tracts where we’re at least 80% certain, down to 609 Green Zone tracts at or below expectation.

• This gives us a framework for policy investment

• The Red Zone splits into two distinct geographies — Salt Lake’s urban core driven by social isolation, and rural extraction counties driven by education deficits — same confidence level, but they’d need completely different interventions.

CHAPTER 4

From Punishing Places to Capability-Enabling Places

A Policy Framework for Organized Spatial Investment

Ch. 3 → Ch. 4: The Policy Translation 🧭

What Chapters 1–3 Established

• Punishment concentrates in places where conversion factors constrain what residents can achieve — where education is depleted, health infrastructure is absent, social connections are fractured, and environmental burdens accumulate.

These are modifiable features of the built and social environment — not fixed characteristics of the people who live there.

INLA provides targeted policy guidance: tract-specific diagnoses of which conversion factors drive risk where — not just that disadvantage matters, but that education matters most in Carbon County while social isolation matters most in Salt Lake’s urban core.

Chapter 4 Addresses

Where to invest

Exceedance probability tiers rank 689 tracts by confidence-weighted risk → 59 Red, 10 Orange, 11 Yellow

What to target

Coefficient contributions decompose each tract’s risk into specific conversion factors → different tracts, different interventions

How to deliver

Intervention archetypes matched to local conversion factor profiles → no one-size-fits-all

At what scale

φ = 0.51 means both tract-level targeting and regional coordination — neither alone is sufficient

With what protections

Care/control safeguards ensure place-based investment doesn’t become place-based surveillance

Ch. 4: Coefficient Contribution Analysis

Two tracts can have the same overall risk but need completely different interventions.

How It Works

For each tract, multiply the statewide coefficient by that tract’s local value:

Contribution_ij = β_j × x_ij

β_j

Statewide effect
of factor j

×

x_ij

This tract’s
local value

=

RR_ij

How much this
factor adds here

RR tells you where to invest. Contributions tell you what to invest in. Together they are the direct input for Ch. 4’s targeting framework.

Same Tier, Different Interventions

Salt Lake Tract 1025.02 (RR = 35.85)

Living alone

social isolation

Walkability

urban density

Treatment ctr

facility siting

Policy: Social infrastructure — community centers, third places, peer support networks

Weber Tract 2018 (RR = 20.08)

Diabetes

health deficit

Education

bachelor’s gap

Walkability

built environment

Policy: Health + education — community health workers, workforce development, food access

This is targeted public policy. Generic “invest in disadvantaged communities” cannot distinguish between these two tracts. Contribution analysis can. ➡️ Policy Chapter 4

Live Demo: Risk Factor Decomposition

If iframe doesn’t load, open utah-spatial-maps.netlify.app/policy_risk_driver_map in a new tab.

Policy Relevance: Already in Practice

📍️ Utah is already using place-based targeting for juvenile justice — the same framework this dissertation develops for adult supervision.

KUER 90.1 | Feb 6, 2026

Ogden hopes a successful Magna program can reduce youth crime in Weber County

The parallel: Utah CCJJ identified 100 neighborhoods as priorities for juvenile justice intervention — based on where youth live, not where crimes occur. Four of the top six hotspots are in Ogden — the same Weber County tracts this dissertation flags as Red Zone.

What this dissertation adds: The CCJJ analysis identifies where. Spatial capabilities theory explains why and prescribes what — matching specific conversion factor deficits to targeted interventions.

🔗 Read full article ↗

Conclusion: The Policy Choice

Path A: $130M

768 new prison beds

(Utah 2026 proposal — Baird, 2026)

⚠️ Manages consequences of community disinvestment

Path B: $195M RHTP

Community conditions that prevent CJ contact

(RHTP alignment — federal funding)

✅ Addresses conversion factor deficits at their source

What distinguishes this framework from prior place-based proposals is that every recommendation is grounded in empirical evidence and anchored in a theoretical framework. The analysis mapped 689 tracts, identified 128 as high-risk, and regional analysis that are calibrated to the specific conversion-factor deficits documented by the spatial models. This is a precise specification of which communities need what investments and why.

SYNTHESIS

Contributions & Future Directions

Three Contributions

1. Theoretical: Place Matters

• Criminal justice outcomes aren’t just shaped by who lives somewhere — they’re shaped by what the place provides. Spatial capabilities theory reframes disadvantaged communities as places where conversion factors constrain what residents can achieve.

2. Empirical: First Spatial Bayesian Analysis of Supervision & in Utah

• Utah is the first non-metropolitan state analyzed with INLA-BYM2 for correctional supervision. Key findings: 128 high-risk tracts identified, φ = 0.51 confirms collective capabilities are real, and the dual concentration pattern (urban cores + rural extraction regions) challenges the assumption that punishment is an urban phenomenon.

3. Actionable Policy: Precise Targeting

• Coefficient contribution analysis tells policymakers not just where to invest but what to invest in — tract by tract. Two tracts in the same Red Zone can need completely different interventions. This is policy tool to navigate investment decisions and deeper investigation in high-risk communities.

Limitations

Every empirical finding in this dissertation should be interpreted within these boundaries:

Cross-sectional design

All findings are associations, not causal claims. We cannot test whether improving conversion factors actually reduces supervision — that requires longitudinal data.

Ecological inference

Tract-level patterns do not describe individuals. However, the spatial capabilities framework argues the ecological level is the appropriate unit — we are studying what places provide, not what individuals do.

Proxy measures

Collective efficacy — central to the theoretical framework — is proxied through voting and census participation rather than directly measured.

Utah specificity

Demographic context (LDS influence, low racial diversity, vast rural geography) limits direct transferability. The framework generalizes; the specific coefficients may not.

Incomplete geographic coverage

Health metrics available for only 450 of 716 tracts. The partial coverage model achieves best fit but cannot represent the full state — hence three specifications rather than one.

Reverse causality

Holaday, Simes & Wang (2025) show supervision concentrations worsen community health — meaning cross-sectional health estimates likely understate true protective effects.

Future Research

Causal Identification

RHTP phased rollout as natural experiment

Staggered implementation across tiers enables difference-in-differences design — the first causal test of whether improving conversion factors reduces supervision concentration.

Natural experiments

Medicaid expansion and extractive industry shocks (mine closures, oil price collapses) provide exogenous variation to test whether healthcare access and economic disruption causally affect supervision rates.

Multi-state extension

Replicate across states with different demographic and institutional contexts to test whether the spatial capabilities framework — and φ’s balanced finding — generalizes beyond Utah.

Community Validation

Participatory qualitative research

Models identify deficits but cannot capture lived experience. Community members in Red Zone tracts should validate whether the conversion factors identified match what they experience as barriers. ➡️ In Progress

UDC research partnerships

Richer outcome data — recidivism, employment post-supervision, program completion — would test whether place-based interventions improve individual trajectories, not just area-level rates. ➡️ Currently being implemented

These quantitative frameworks are empirically informed starting points — community voice must validate and guide implementation of policy priorities.

From Punishing Places to Capability-Enabling Places

🏡 The conversion factors driving correctional supervision concentration are modifiable features of the built and social environment.

Punishing Places

128 tracts where conversion
factors constrain capabilities

→

Diagnose

Tract-specific deficits
identified by coefficient analysis

→

Transform 🤝🏽

Place-based investment matched
to conversion factor needs

“Where people live shapes what people can become. This dissertation provides the empirical architecture, but the communities themselves must determine which freedoms matter most and which investments would most effectively convert formal opportunities into the real capabilities that constitute human flourishing.”

Thank you. Questions?

utah-spatial-maps.netlify.app · 📧 sheena.yoon@utah.edu

BACKUP SLIDES

Theoretical Lineage: Key Sources

The Framework’s Intellectual Architecture

Tradition	Key Author(s)	Core Concept	Dissertation Application
Capabilities approach	Sen (1999), Nussbaum (2011)	Resources ≠ capabilities without conversion factors	Place as multidimensional conversion factor
Neighborhood effects	Sampson (2012), Wilson (1987)	Durable spatial differentiation	Collective efficacy as collective spatial capability
Punishment geography	Simes (2021), Eason (2017)	Spatial concentration of incarceration	Utah replication & rural extension
Stratification economics	Darity (2022), McKay & Darity (2024)	Intergroup competition produces inequality	Conversion factor deficits are structured, not random
Feminist economics	Folbre (2001), Braman (2004)	Care labor as foundational economic activity	Incarceration destroys care infrastructure
Critical geography	Gilmore (2007), Harvey (2009)	Organized abandonment / spatial fix	Punishing places as produced, therefore transformable
Environmental justice	Manduca & Sampson (2019, 2021)	Pollution → developmental harm → incarceration	Diesel PM as conversion factor deficit
Heterodox labor economics	Myers & Sabol (1987), McGahey (1986)	Structural unemployment → CJ involvement	RBPE critique of rational choice

What Spatial Capabilities Theory Adds

The original contribution is integrating these traditions through the capabilities framework — treating place not as a background variable but as the mechanism that converts (or fails to convert) resources into real freedoms. No existing framework connects all six literatures; this dissertation does.

The Spatial Capabilities Framework

• The person returning from incarceration to a community with robust transportation, accessible healthcare, and strong collective efficacy faces a fundamentally different capability set than one returning to institutional withdrawal, environmental degradation, and violence exposure.

The Spatial Capabilities Framework v.2

Why Not Rational Choice?

The Inter-Disciplinary Critique

• Becker (1968): Crime as rational cost-benefit calculation under certainty. Predicts that increasing punishment severity reduces crime.

• Empirical problems: Doleac (2019) reviews the evidence and finds that most deterrence-based interventions show limited or null effects. Severity of punishment has little deterrent effect; certainty of punishment matters more, but even this operates through spatial mechanisms (police presence varies by neighborhood).

• Simes & Jahn (2022): Medicaid expansion — a health policy, not a criminal justice intervention — reduced arrests by 20–32%. This is the largest effect in the criminal justice RCT literature. The conversion factor approach explains why: healthcare access enables capability formation that deterrence-based approaches cannot.

• Myers & Sabol (1987): Radical Black Political Economy challenges the assumption that criminal justice involvement reflects individual choice, arguing instead that labor market segmentation and structural unemployment produce patterns of involvement that rational choice models cannot explain.

• McGahey (1986, 1987): Demonstrates that local labor market conditions — not individual human capital — determine employment and offending patterns. The “crime-unemployment” relationship operates through spatial mechanisms.

The Causal Inversion

• Neoclassical: Individual deficits → criminal behavior → incarceration → spatial concentration

• Spatial capabilities: Community conditions → constrained capability sets → inability to avoid CJ system → concentrated punishment reinforces conditions

Data Pipeline

Geocoding

• 86,734 raw records → 44,650 geocoded addresses (51.5% match rate). Multi-stage process: primary geocoding through Census Bureau, secondary matching through ArcGIS for addresses that failed initial geocoding. 709 census tracts as unit of analysis (2020 boundaries).
  

Key Difference from Simes

• Simes measures prison admissions — the deepest end of the CJ system. This dissertation measures community supervision (probation and parole) — the broadest reach. Utah’s 5.6M supervision population dwarfs the ~1.9M incarcerated population nationally. Finding comparable spatial concentration at the probation stage implies the spatial trap operates before imprisonment’s additional deprivations.

PCA & Concentrated Disadvantage Index Detail

Factor Structure Comparison

Component	MA Loading	UT (5-var) Loading	UT (4-var) Loading
% Poverty	>0.60	Strong	Strong
% Unemployment	>0.60	Strong	Strong
% Female-headed HH	>0.60	Moderate	Moderate
% No HS degree	>0.60	Moderate	Moderate
% Public assistance	>0.60	0.31 (weak)	Excluded
Eigenvalue	>3.0	1.68	1.86
Variance explained	>60%	33.6%	46.5%

Why Public Assistance Loads Weakly in Utah

• LDS Church welfare programs substitute for government assistance; rural access barriers require hours of travel to county offices; stricter TANF eligibility and shorter benefit durations; cultural norms discouraging government assistance. Hager (2021, ProPublica) documents how “Utah makes welfare so hard to get, some feel they must join the LDS Church to get aid.”

Sensitivity Analysis

• 5-variable / 4-variable correlation: r = 0.979. PCA / simple summation correlation: r = 0.995. Substantive findings are invariant to reasonable alternative specifications. The 4-variable index is the primary specification.

Theoretical Significance

• The weaker factor structure is substantively meaningful, not a methodological problem. It demonstrates that concentrated disadvantage manifests differently in non-metropolitan Western contexts — disadvantage still clusters, but indicators don’t march in lockstep the way they do in segregated Northeastern cities.

Ch. 2 Demographic Controls Detail

Model A: Five Demographic Composition Variables

Variable	IRR	p-value	Interpretation
% Non-Hispanic Black	1.033	0.013	Significant positive
% Hispanic	1.016	<0.001	Significant positive
% Non-Hispanic Asian	0.981	0.178	Not significant
% Foreign Born	0.996	0.781	Not significant
% New Residents	1.014	<0.001	Significant — coercive mobility
Treatment Center	1.615	<0.001	Institutional control

How the SLX Reframes Race

In every model (A–D), Hispanic and Black population shares significantly predict higher supervision rates. Once neighbors’ disadvantage enters the model (Model E):

• Hispanic effect disappears entirely (IRR drops to 1.007, n.s.)

• Black effect declines to marginal significance

• This suggests racial composition partly proxies for the broader spatial context of compounding regional disadvantage. Racial stratification and economic disadvantage are not independent predictors but interlocking mechanisms through which place constrains capability formation.

Residential Mobility

• Remains significant even in the SLX model (IRR = 1.010, p < 0.001), consistent with Clear’s (2007) “coercive mobility” framework — the constant churning of people through jails, prisons, and supervision destabilizes neighborhoods.

Simes Comparison Detail

Full Model Results Comparison

Model	Coeff.	SE	RR	95% CI	Moran’s I
A: Simes 4-Region	0.251	0.031	1.285	[1.210, 1.365]	0.326
B: LHD	0.207	0.033	1.229	[1.152, 1.311]	0.287
C: RUCA	0.247	0.031	1.280	[1.204, 1.360]	0.313
D: Full Model	0.245	0.031	1.277	[1.202, 1.357]	0.320
E: SLX (own)	0.179	0.033	1.196	[1.122, 1.275]	0.335
E: SLX (neighbors)	0.365	0.053	1.440	[1.299, 1.597]	—

• Key divergence: Utah’s concentrated disadvantage effect (19.6%–28.5%) converges with Simes’ Massachusetts finding (~31%), confirming the universality of the relationship. Utah’s Moran’s I (0.287–0.335) closely parallels Simes’ MA benchmark (0.30). The SLX model yields the highest Moran’s I (0.335) despite explicitly modeling neighbors — spatial dependency operates through mechanisms beyond disadvantage clustering.

Regional Classification Effects

• Simes’ 4-region classification fails significance in Utah (p = 0.056). LHD boundaries outperform all classifications (ΔAIC = 24.3 over Model A). RUCA urbanicity achieves metropolitan significance only after demographic controls — demographic composition suppresses the metropolitan-rural difference.

San Juan County: The Jurisdictional Exception

Highest Disadvantage, Lowest Supervision

• San Juan County, home to the Navajo Nation, presents a notable exception: despite having the highest concentrated disadvantage scores in the state, it exhibits the lowest LHD-level supervision rate (RR = 1.202, not statistically significant).

Why This Matters

• This apparent paradox likely reflects jurisdictional complexity — tribal justice systems operate independently of state correctional authority. The Navajo Nation maintains its own courts, police, and corrections system. Residents subject to tribal jurisdiction would not appear in state supervision data.

Theoretical Implication

• San Juan illustrates how institutional structure mediates the disadvantage-punishment relationship. The same level of disadvantage produces different correctional outcomes depending on which justice system has jurisdiction. This validates the spatial capabilities framework’s emphasis on institutional infrastructure as a conversion factor.

Backup: A.3 Variable Definitions by Source

A.3.1 Utah Healthy Places Index & Composite Variables

Variable	Definition	Source
automobile	% occupied housing units with vehicle access	ACS 2015-2019
bachelorsed	% population 25+ with bachelor’s degree or higher	ACS 2015-2019
bikeaccess	Miles of bike lanes and paths per capita	Utah Geospatial Resource Center
censusresponse	2020 Census cumulative self-response rate (proxy for collective efficacy)	2020 Census
dieselpm	Diesel particulate matter concentration (μg/m³)	EPA EJSCREEN
employed	% civilian population 16+ employed	ACS 2015-2019
homeownership	% occupied housing units owner-occupied	ACS 2015-2019
houserepair	% occupied units lacking complete plumbing or kitchen	ACS 2015-2019
insured	% civilian noninstitutionalized population with health insurance	ACS 2015-2019
ozone	Mean summer ozone concentration (ppb)	EPA EJSCREEN
parkaccess	% population within 0.5 miles of a park	Utah Geospatial Resource Center
pm25	Annual mean PM2.5 concentration (μg/m³)	EPA EJSCREEN
treecanopy	% land area covered by tree canopy	NLCD 2019
uncrowded	% occupied housing units with ≤1 occupant per room	ACS 2015-2019
voting	Voter turnout rate in most recent general election	Utah Lt. Governor
walkability	National Walkability Index score	EPA Smart Location Database
transit	% workers commuting by public transit	ACS 2015-2019
retail	Retail employment accessibility index	Utah HPI
supermkts	% population beyond 1 mi (rural) / 0.5 mi (urban) from supermarket	USDA Food Access Research Atlas
libraryaccess	Avg distance to nearest public library (pop-weighted)	Utah Geospatial Resource Center
HTA	Housing + transportation costs as % of income	CNT.org H+T Index
LIHTC_HU	Low-Income Housing Tax Credit units per 1,000 housing units	HUD LIHTC Database
LEB	Life expectancy at birth (years)	CDC USALEEP 2015

HPI Composite Domain Scores

Variable	Definition	Source
education	Education domain composite score	Utah HPI
economic	Economic domain composite score	Utah HPI
social	Social domain composite score	Utah HPI
transportation	Transportation domain composite score	Utah HPI
neighborhood	Neighborhood domain composite score	Utah HPI
housing	Housing domain composite score	Utah HPI
healthcare	Healthcare Access domain composite score	Utah HPI
clean_enviro	Clean Environment domain composite score	Utah HPI

A.3.3 Census ACS Variables

Variable	Definition	Source
punemp	Unemployment rate (% civilian labor force)	ACS 2015-2019
ppov	Poverty rate (% population below poverty line)	ACS 2015-2019
pfemhh	% households headed by females with children	ACS 2015-2019
pchldrn	% population under age 18	ACS 2015-2019
MedinAg	Median age of population	ACS 2015-2019
MHI	Median household income (dollars)	ACS 2015-2019
GiniCff	Gini coefficient of income inequality (0–1)	ACS 2015-2019
phisp	% population Hispanic/Latino	ACS 2015-2019
ppa	% population receiving public assistance	ACS 2015-2019
labor_participation	Labor force participation rate	ACS 2015-2019
job_availability	Jobs per working-age population within commuting distance	LEHD/LODES
ownsevere	% owner-occupied units with severe cost burden (>50% income)	ACS 2015-2019
rentsevere	% renter-occupied units with severe cost burden (>50% income)	ACS 2015-2019
VacantP	Housing vacancy rate (%)	ACS 2015-2019
NoIntP	% households without internet access	ACS 2015-2019
inhghsc	% population 25+ with high school diploma or equivalent	ACS 2015-2019
inprsch	School enrollment rate for population 3+ years	ACS 2015-2019

A.3.4 Categorical Classification Variables

Variable	Definition	Source
UrbanType	Urban-rural classification: Urban Area, Urban Cluster, or Rural	Census Urban Area Definitions
Rurality	Urban Influence Code categories (1–12 collapsed)	USDA ERS
NeighbTyp	Neighborhood typology classification (1–6 types)	GeoDaCenter/HPI Composite

A.3.5 Outcome & Derived Variables

Variable	Definition	Source
corr_pop	Count of individuals under correctional supervision in tract	Utah DOC
corr_rate	Correctional supervision rate per 1,000 adult population	Calculated (UDC + ACS)
corr_pp	Correctional supervision proportion (% adult population)	Calculated (UDC + ACS)
expected	Expected count based on statewide rate × tract population (offset)	Calculated
treatment_center	Binary indicator (0/1) for residential treatment facility in tract	Utah DOC

A.4.1 BMA Variable Evidence Summary

Variable	Capabilities Domain	Evidence Tier	PIP
dieselpm	Environmental Justice	Strong	0.95
censusresponse	Collective Efficacy	Strong	0.90
automobile	Transportation Access	Strong	0.85
insured	Healthcare Access	Strong	0.80
bachelorsed	Educational Attainment	Strong	0.80
NeighbTyp_5	Neighborhood Typology	Strong	0.85
employed	Economic Opportunity	Moderate	0.60–0.75
houserepair	Housing Quality	Moderate	0.55–0.70
homeownership	Economic Stability	Moderate	0.50–0.65
HTA	Housing + Transportation	Moderate	0.50–0.65
punemp	Economic Distress	Suggestive	0.40–0.55
ppov	Economic Distress	Suggestive	0.35–0.50
voting	Civic Engagement	Suggestive	0.30–0.45
traffic	Environmental Exposure	Suggestive	0.25–0.40

PIP = Posterior Inclusion Probability from Bayesian Model Averaging (50K iterations, Zellner-Siow priors). Strong ≥ 0.75; Moderate ≥ 0.50; Suggestive ≥ 0.25. All continuous variables z-standardized prior to analysis.

BMA Variable Selection Detail

Evidence Tiers from Posterior Inclusion Probabilities

Tier	PIP Range	Variables	Examples
Strong	> 0.75	8	Education, income, homeownership
Moderate	0.50–0.75	5	Unemployment, poverty, female HH
Suggestive	0.25–0.50	9	Diesel PM, transit, insurance
Theoretical	< 0.25	11	Retained for policy relevance

Two-Stage Spatial Filtering

• Stage 1: Spatial lag regression residuals remove autocorrelation — Moran’s I: 0.44 → −0.06
• BMA on spatially-filtered residuals: 50,000 iterations, Zellner-Siow null priors, uniform model priors
• Applied separately to 3 datasets: full (689 tracts, 50 predictors), partial (450 tracts, 60 predictors), HPI (689 tracts, 10 indices)

Why Retain Theoretical Variables?

Environmental justice indicators, healthcare access, and transportation had PIPs below 0.25 but were retained because excluding them would be a theoretical decision masquerading as a statistical one. The BMA selects for predictive power; the spatial capabilities framework requires testing specific theoretical claims about conversion factor domains.

INLA-BYM2 Model Specifications

Dataset	Model	N Tracts	Predictors	DIC	WAIC	φ
Full	full_suggestive	689	22	5,247	5,129	0.51
Full	full_moderate	689	15	5,259	5,141	0.54
Full	full_strong	689	8	5,272	5,148	0.58
Partial	partial_suggestive	450	39	3,460	3,382	0.23
Partial	partial_moderate	450	18	3,471	3,393	0.29
Partial	partial_strong	450	11	3,482	3,401	0.35
HPI	hpi_full	689	9	5,271	5,145	0.86
HPI	hpi_selected	689	6	5,283	5,157	0.88
HPI	hpi_domains_only	689	8	5,278	5,151	0.84

Prior specs: PC priors P(σ > 0.5) = 0.01, neutral mixing P(φ < 0.5) = 0.5, Zellner-Siow on fixed effects. Queen’s contiguity adjacency matrix following Simes.

Model Selection Rationale

Full_suggestive selected as primary: maximizes geographic coverage (689 tracts, 96.2%), achieves best DIC/WAIC among full-coverage models, retains policy-relevant suggestive-tier variables. The partial model has superior fit but covers only 450 tracts (63%) — insufficient for a framework claiming statewide applicability.

Regional Sensitivity Analysis

Six Regional Classification Tests

Classification	Regional Dummies	ΔDIC	Δφ	Core Coefficients
None (baseline)	0	ref	ref	Stable
RUCA 4-category	3	−0.8	+0.012	Stable
Simes 4-region	3	−1.1	+0.018	Stable
9-region detailed	8	−2.4	+0.021	Stable
Local Health District	12	−1.3	+0.028	Stable
Urban Influence Code	4	−0.6	+0.015	Stable
County (29)	28	−5.1	+0.034	Stable

Three Key Findings

1. Conversion factors fully mediate regional effects. LHD dummies produce significant raw differentiation (F = 2.95, p < 0.001), yet adding them worsens model fit (ΔDIC = −1.3). What appears to be “jurisdictional effects” is entirely explained by place-based conversion factors.

2. φ is genuine, not confounded. Across all six specifications, φ increases slightly (+0.012 to +0.034) rather than decreasing when regional controls are added. If spatial effects were confounded by regional characteristics, adding dummies would absorb this structure.

3. Dual concentration is not an artifact. Elevated correctional rates persist in both urban disadvantaged and rural extraction regions across all specifications.

Partial Coverage Model: Health Metrics

Additional Effects from GeoDaCenter Data (n = 450)

Variable	β	RR	% Effect	Direction
Limited physical activity	0.374	1.454	+45.4%	⬆ Risk
Living alone	0.250	1.284	+28.4%	⬆ Risk
Diabetes prevalence	0.189	1.208	+20.8%	⬆ Risk
Obesity prevalence	0.122	1.130	+13.0%	⬆ Risk
Poor physical health	−0.472	0.624	−37.6%	↓ Counterintuitive
Bachelor’s degree	−0.184	0.832	−16.8%	🛡️ Protective
Life expectancy	−0.062	0.940	−6.0%	🛡️ Protective
MHI	−0.126	0.882	−11.8%	🛡️ Protective

Counterintuitive Finding: Poor Physical Health (−37.6%)

Communities with higher poor physical health have lower supervision rates. Mechanisms: (1) older/disabled populations reflecting the age-crime curve; (2) healthcare system engagement — communities where residents report health problems may have better provider access; (3) compositional vs. contextual — poor health reflects who lives there, not what places provide.

Why φ Drops to 0.23

The partial model’s richer variable set captures more of the substantive drivers of geographic variation, leaving residual effects that are predominantly local and idiosyncratic. More variables → more explained spatial structure → lower φ. This confirms that what cruder models attribute to mysterious “neighborhood effects,” disaggregated measures explain.

Conversion Factor vs. Functioning Distinction

Operationalizing the Theoretical Framework

Category	Examples	Behavior Under Sensitivity	Interpretation
Robust conversion factors	Education (−20.6%), Income (−12.5%), Homeownership (−9.3%), Social isolation (+18.7%)	Stable across all specs and all 6 regional tests	What places provide — genuine environmental, social, and economic conditions
Specification-sensitive functionings	Diabetes (+26.9%/+20.8%), Physical activity (+45.4%), Diesel PM (+9.6%)	Sensitive to regional controls or dataset	What characterizes who lives there — compositional differences reflecting health status or selective migration

Why This Matters for Policy

Robust conversion factors are the actionable policy targets — they capture modifiable features of the built and social environment that operate regardless of regional location. Specification-sensitive functionings are upstream indicators — they signal that conversion factor deficits are producing poor health outcomes, but the intervention should target the underlying conversion factors (food environment, recreational infrastructure, emissions enforcement), not the health outcomes themselves.

The HPI Model Confirms This

The HPI model uses composite domain scores (φ = 0.86, σ = 0.457) — most variation is attributed to “neighborhood effects.” The full model uses disaggregated indicators (φ = 0.51, σ = 0.216) — those effects are explained by specific conversion factors. Composite measures obscure the mechanisms policy must address.

Ch. 4: Interactive Policy Maps

🗺️ utah-spatial-maps.netlify.app

Policy Targeting Maps

1. Priority Neighborhoods by Region — Top 100 by relative risk

2. Risk Factor Decomposition — Which specific factor drives risk in each priority tract

Convergent Evidence

3. Where Evidence Converges — Multi-model, multi-variable convergence → highest-confidence targets

4. Tract Risk Profile Dashboard — All 689 tracts × 17 predictors × 3 models

SWITCH TO BROWSER. Walk through the maps: (1) Regional distribution; (2) Risk factor decomposition; (3) Convergent evidence tracts.