Research Questions
Three research questions guiding the dissertation — from spatial description to explanation to policy application
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1. Theoretical Framework: Spatial Capabilities Approach

The core conceptual model integrates the capabilities approach (Sen, 1993) with spatial analysis to understand how geographic context shapes the translation of resources into actual opportunities. This dissertation extends the capabilities framework by developing spatial capabilities theory, an original contribution that formalizes the spatial dimensions of capability formation. Spatial capabilities are geographically embedded opportunities for human flourishing that emerge through the interaction of individual characteristics, community resources, and place-based conversion factors. This definition extends traditional capabilities theory by incorporating spatial dimensions — capabilities are not merely individual attributes but opportunities constituted by the places in which individuals are embedded. A person's capability set depends fundamentally on where they live. As Robeyns (2017) emphasizes, each list in the capabilities space is context-dependent, where the context is both the geographical area to which it applies and the sort of evaluation that is to be done.

The first diagram below shows how the Spatial Environment feeds conversion factors into the Capability Process, which in turn produces Community Outcomes. The second diagram expands this into the full five-tier hierarchy with cross-cutting connections.

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Capability Process Resources converted by Conversion Factors enable Capabilities achieve Functionings Spatial Environment Physical Infrastructure Institutional Infrastructure Social Infrastructure shapes enables supports Conversion Factors Community Outcomes Crime Reduction Community Integration Supervision Success influences supports enables

This framework illustrates how the Functional Assessment Rating Scale (FARS)1 connects individual-level clinical assessment, used by correctional agencies, to the spatial capabilities model developed in this dissertation. The FARS's 18 domains — organized here into biological, psychological, and social clusters — capture functioning outcomes that, while measured at the individual level, are substantially shaped by place-based conversion factors operating at the community level. Robeyns' (2017) tripartite classification of personal, social, and environmental conversion factors mediates how available resources translate into actual capability sets, which in turn determine the functionings individuals can achieve.

The critical insight is that a returning citizen's FARS scores in domains like Work/School, Depression, or Substance Use are not simply reflections of individual deficits but manifestations of spatially embedded capability deprivations — the same person released to a tract with robust healthcare access, transportation infrastructure, and social connectedness would be expected to achieve markedly different functioning outcomes than one returning to a tract characterized by environmental hazard exposure and institutional scarcity. This reconceptualization grounds the dissertation's empirical finding that environmental and structural conversion factors — including diesel particulate matter exposure and transportation access — operate through these capability pathways to produce the dramatic geographic concentration of correctional supervision outcomes observed across Utah's census tracts.

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SPATIALLY EMBEDDED CAPABILITY FORMATION FARS assessment domains are shaped by place-based conversion factors operating at the community level FARS ASSESSMENT DOMAINS Biological Domains Depression Medical/Physical Substance Use Cognitive Performance Psychological Domains Anxiety Traumatic Stress Interpersonal Skills Family Relations Social Domains Work/School Legal Status Security/Management Social Support CONVERSION FACTORS Robeyns (2017) tripartite classification — policy-alterable Personal Conversion Skills & cognitive abilities Health status & disability Trauma history Literacy & education level Social Conversion Collective efficacy & trust Social networks & isolation Community organizations Stigma & power relations Environmental Conversion Air quality & toxic exposure Transportation infrastructure Healthcare access & providers Built environment & housing CAPABILITY SETS Social Capabilities Community Integration Cultural Connection Civic Participation Economic Capabilities Employment Access Skill Development Financial Stability Health Capabilities Treatment Access Wellness Management Healthcare Navigation ACHIEVED FUNCTIONINGS Social Functionings Family Relations Community Roles Social Networks Economic Functionings Employment Status Income Level Housing Stability Health Functionings Physical Health Mental Wellbeing Recovery Status Criminal Justice Outcomes: Supervision Success Community Integration Reduced Recidivism ASSESSMENT CONVERSION CAPABILITIES FUNCTIONINGS OUTCOMES Figure 2: FARS-to-Spatial Capabilities Hierarchy — Connecting Individual Assessment to Place-Based Capability Formation
1  Note on FARS
The FARS is a clinical assessment tool originally developed in Florida in the mid-1990s that evaluates individuals across 18 functional domains, including depression, anxiety, traumatic stress, substance use, interpersonal relationships, family environment, socio-legal functioning, work/school performance, danger to self, and danger to others. It was designed to standardize clinical impressions from mental status evaluations using cognitive, social, and role functioning as its focus.
Three Fundamental Elements

1. Conversion Factors

The mechanisms that translate resources into actual capabilities:

  • Personal: Skills, health status, trauma history, decision-making capacity
  • Social: Community norms, social networks, cultural context, power relations
  • Environmental: Infrastructure, institutions, geographic location, environmental conditions

2. Capability Sets

The actual freedoms and opportunities available to individuals:

  • Social Capabilities: Community integration, cultural connection, civic participation
  • Economic Capabilities: Employment access, skill development, financial stability
  • Health Capabilities: Treatment access, wellness management, healthcare navigation

3. Spatial Embedding

How capabilities develop and cluster geographically:

  • Collective capabilities that emerge through community-level processes
  • Cross-boundary spillovers between neighboring communities
  • Place-based constraints and opportunities
2. Neighborhood Effects and Spatial Processes
Neighborhood Effects Framework
Figure 2: Neighborhood Effects Framework — How Place Shapes Capabilities

The neighborhood effects framework illustrates how residential segregation by race/ethnicity and socioeconomic status creates differential access to capability-enhancing resources. This process operates through three pathways:

2.1 Physical Environment Pathways

  • Environmental exposures — air quality, pollution, hazards
  • Food and recreational resources — access to healthy options, safe spaces
  • Built environment quality — housing, infrastructure, transportation
  • Aesthetic quality and natural spaces — parks, green space, community appearance

2.2 Social Environment Pathways

  • Safety and violence — community safety, exposure to trauma
  • Social connections and cohesion — collective efficacy, social capital
  • Local institutions — schools, healthcare, community organizations
  • Culture and norms — community values, expectations, social control

2.3 Individual and Behavioral Mediators

The pathway from neighborhood conditions to outcomes operates through stress and behavioral mediators, highlighting how environmental conditions get "under the skin" to affect individual functioning and decision-making.

3. Methodological Integration: INLA and Capabilities

The Integrated Nested Laplace Approximation (INLA) methodology aligns with spatial capabilities theory across three dimensions:

1. Multiple Conversion Factors

  • INLA handles multiple covariates simultaneously
  • Accounts for interaction effects between factors
  • Models spatial dependencies and hierarchical relationships
  • Captures the complex interplay of personal, social, and environmental factors

2. Spatial Embedding of Capabilities

  • Models neighborhood effects as collective capabilities
  • Accounts for spatial clustering of opportunities and constraints
  • Captures spillover impacts between communities
  • Reflects how capabilities develop collectively within geographic space

3. Uncertainty Recognition

  • Provides full posterior distributions rather than point estimates
  • Offers credible intervals essential for policy risk assessment
  • Quantifies uncertainty in capability measurements
  • Supports evidence-based decision making under uncertainty

Mathematical Framework

The INLA-BYM2 model operationalizes spatial capabilities theory:

yi ~ Poisson(μi)

log(μi) = log(Ei) + α + Σ βj xij + ui + vi

Components Map to Theory

  • yi — Observed count in tract i (functioning outcome)
  • Ei — Expected count controlling for population (standardization)
  • Xij — Capability measures and conversion factors
  • ui — Structured spatial effect (collective capabilities)
  • vi — Unstructured random effect (individual variation)
  • βj — Fixed effects measuring conversion factor impacts

Spatial Random Effects Decomposition

ui = (1 / √τu) × [ √φ · zi + √(1 − φ) · εi ]
  • φ — Mixing parameter: spatial clustering vs. individual factors
  • zi — Spatially structured component (collective capabilities)
  • εi — Unstructured component (individual variation)

Collective Capabilities (ui)

  • Identify capability clusters across geographic space
  • Map resource distribution and service accessibility
  • Locate gaps in community infrastructure
  • Target place-based interventions

Conversion Factors (φ)

  • Assess how strongly place matters for outcomes
  • Evaluate barriers to capability development
  • Guide geographic targeting of resources
  • Plan coordination between neighboring areas

Individual Effects (βj)

  • Measure direct impacts of specific conversion factors
  • Identify which capabilities matter most
  • Prioritize intervention components
  • Design individual-level support services
4. Full Dissertation Framework: Spatial Capabilities Model

The comprehensive diagram below synthesizes the full theoretical architecture of the dissertation, integrating Sen's (1993) capability chain, Robeyns' (2017) modular framework and tripartite conversion factor classification, the four place-based conversion factor domains developed in Section 1.3.4, and the three scales of spatial capability introduced as an original contribution in Section 1.3.3. The INLA-BYM2 methodology at the bottom shows how each theoretical component maps to an empirical parameter, with the policy implication that conversion factors are policy-alterable — grounding the Chapter 4 framework for place-based investment in capability enhancement.

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SPATIALLY EMBEDDED CAPABILITY FORMATION "A person's capability set depends fundamentally on where they live" — Robeyns (2017) CORE CHAIN PLACE-BASED DOMAINS SPATIAL SCALES FOUR CONVERSION FACTOR DOMAINS Each domain specifies mechanisms linking place to criminal justice outcomes (§1.3.4) THREE SCALES OF SPATIAL CAPABILITY Original contribution: formalizing the spatial dimensions of capability formation (§1.3.3) MODULE A Resources Income · Housing · Education Healthcare · Infrastructure mediated by MODULE B Conversion Factors Personal · Social · Environmental Robeyns (2017) tripartite classification — policy-alterable enable MODULE C Capability Sets Real freedoms to achieve valued functionings achieve Achieved Functionings Employment · Health Social participation · Stability Criminal Justice Outcomes Supervision success Community integration Reduced recidivism ⟲ SPATIAL TRAP FEEDBACK Supervision degrades the conversion factors that produced system involvement Economic Conversion Factors ▸ Job accessibility & labor markets ▸ Educational infrastructure ▸ Homeownership → residential stability ▸ Income → consumption capacity "Education enables civic participation that Sen identifies as foundational" Social Conversion Factors ▸ Collective efficacy (Sampson 2012) ▸ Institutional density & nonprofits ▸ Social isolation ↔ network erosion ▸ Community organizations (Sharkey 2017) "Mass incarceration systematically weakens social conversion factors" Healthcare Conversion Factors ▸ Provider access & density ▸ Mental health & SUD treatment ▸ Insurance coverage & access ▸ Life expectancy as outcome proxy "Bidirectional: health deficits ↑ CJ contact; CJ contact ↑ health deficits" Environmental Conversion Factors ▸ Air pollution & toxic exposure ▸ Environmental hazard exposure ▸ Built environment quality ▸ Transportation infrastructure "Systematic capability deprivation, not merely a health risk" ⟷ DOMAINS REINFORCE ONE ANOTHER: "The same structural processes that degrade one conversion factor typically degrade others" — creating concentrated disadvantage ⊙ Individual Spatial Capabilities Personal mobility and spatial agency — the ability to access opportunities across geographic space. In rural Utah, limited public transportation severely constrains these capabilities; in urban SLC, poverty constrains other conversion factors. ⊕ Collective Spatial Capabilities Community-level capacities achieved only through coordinated action: collective efficacy, mutual trust, resource mobilization. Non-metro contexts: churches, community organizations, non-profits, and mutual aid. INLA φ=0.51 → ~50% is spatial spillover. ⊗ Cross-Boundary Capabilities Residents reaching beyond their community for essential resources: transportation networks, regional services, coordination. Rural Utahns traveling 2 hours to Wasatch Front for SUD treatment. When connections are absent → geographic isolation = deprivation. EMPIRICAL OPERATIONALIZATION INLA-BYM2: log(θᵢ) = α + Σβⱼxᵢⱼ + uᵢ + vᵢ βⱼ → conversion factor effects uᵢ → collective capabilities (spatial) φ = 0.51 → half of variation is neighborhood spillovers P(RR > 1.5) → policy targeting POLICY IMPLICATION Conversion factors are policy-alterable (Robeyns 2017) → place-based investment in capability enhancement → Chapter 4 framework → Ch. 4 Figure 1: Spatial Capabilities Conceptual Model — Integrating Sen (1993), Robeyns (2017), and INLA-BYM2 Methodology

References

Riebler, A., Sørbye, S. H., Simpson, D., & Rue, H. (2016). An intuitive Bayesian spatial model for disease mapping that accounts for scaling. Statistical Methods in Medical Research, 25(4), 1145–1165.

Robeyns, I. (2017). Wellbeing, Freedom and Social Justice: The Capability Approach Re-Examined. Open Book Publishers.

Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B, 71(2), 319–392.

Sen, A. (1993). Capability and well-being. In M. Nussbaum & A. Sen (Eds.), The Quality of Life. Oxford: Clarendon Press.

Simpson, D., Rue, H., Riebler, A., Martins, T. G., & Sørbye, S. H. (2017). Penalising model component complexity: A principled, practical approach to constructing priors. Statistical Science, 32(1), 1–28.

Ward, J. C., Jr., Dow, M. G., Penner, K., Saunders, T., & Halls, S. (2006). Manual for using the Functional Assessment Rating Scale (FARS) (Text revisions 2004, 2005, 2006). Department of Mental Health Law and Policy, Louis de la Parte Florida Mental Health Institute, University of South Florida. http://outcomes.fmhi.usf.edu/_assets/docs/FARSUserManual2006.pdf