# Spatial Statistics

> >-

- **Type:** Skill
- **Install:** `agentstack add skill-muend-geoai-skills-spatial-statistics`
- **Verified:** Yes — security-reviewed for prompt injection and unsafe behavior
- **Seller:** [muend](https://agentstack.voostack.com/s/muend)
- **Installs:** 0
- **Category:** [Developer Tools](https://agentstack.voostack.com/c/developer-tools)
- **Latest version:** 0.1.0
- **License:** MIT
- **Upstream author:** [muend](https://github.com/muend)
- **Source:** https://github.com/muend/geoai-skills/tree/main/skills/spatial-statistics

## Install

```sh
agentstack add skill-muend-geoai-skills-spatial-statistics
```

Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent.

## About

# Spatial Statistics

Purpose: answer "is it clustered, where, and why" with defensible inference.
The core discipline: spatial data violates independence assumptions, so
standard statistics silently overstate significance — every analysis here
starts with weights design and ends with residual diagnostics.

## Spatial weights (W) — the analysis IS the weights

Every result downstream depends on W; choose it for substantive reasons and
run a sensitivity check with one alternative:

| Weights | Use when |
|---|---|
| Queen/Rook contiguity | Irregular polygons (admin units, parcels) |
| K-nearest neighbors | Points; islands present (contiguity leaves them unconnected) |
| Distance band | Physical process with known range |
| Kernel (distance-decayed) | Smooth influence, GWR-style local models |

```python
from libpysal.weights import Queen

w = Queen.from_dataframe(gdf, use_index=True)
print(f"islands: {w.islands}")   # unconnected units break stats — fix or document
w.transform = "r"                # row-standardize (default for Moran/lag models)
```

Always report: weights type, parameters, number of islands, and whether
results survive an alternative W.

## Global → local workflow

1. **Global Moran's I** (`esda.Moran`, permutation inference ≥999) —
   answers "any clustering at all?" Report I, p_sim, and the permutation
   distribution, not the analytical p.
2. **LISA / local Moran** (`esda.Moran_Local`) — maps WHERE: High-High,
   Low-Low clusters, High-Low/Low-High outliers. Correct for multiple
   testing (FDR at minimum) before coloring a map — uncorrected LISA maps
   overstate clusters and this is the field's most common abuse.
3. **Getis-Ord Gi\*** (`esda.G_Local`, star=True) — hot/cold spots of
   intensity (a distinct question from Moran clusters — Gi* finds
   concentrations of high values, LISA finds similarity structure).
4. Rates, not counts, for population-based phenomena; use Empirical Bayes
   smoothing (`esda.smoothing`) for small-population units before any of
   the above — raw rates in sparse units are noise.

## Point patterns

- Separate first-order intensity (density varies) from second-order
  interaction (points attract/repel) — KDE describes the former, Ripley's
  K/L (`pointpats`) tests the latter.
- Always test against an inhomogeneous null when the study area has obvious
  density gradients (population, roads); CSR against a city is a strawman.
- KDE bandwidth drives the story: report it, justify it (Silverman/CV), and
  show one alternative.

## Spatial regression decision path

Run OLS first, then diagnose — never start with a spatial model:

```python
from spreg import OLS
ols = OLS(y, X, w=w, spat_diag=True, moran=True, name_y="price", name_x=xnames)
```

Decision (Anselin's rule via LM tests): LM-Lag significant & LM-Error not →
**spatial lag (SAR)**; reverse → **spatial error (SEM)**; both → compare
robust LM versions; neither → OLS stands (report that as a finding).
Interpretation caveats: in SAR, coefficients are NOT marginal effects —
report direct/indirect (spillover) effects. In SEM, spatial structure is
nuisance correlation, no spillover story allowed.

**GWR/MGWR** (`mgwr`): when relationships plausibly vary over space.
Bandwidth by AICc search; map local coefficients WITH local t-values masked
for insignificance; MGWR when predictors operate at different scales.
GWR is exploratory — resist causal language on local coefficients.

## Inference honesty

- Permutation p-values over analytical ones wherever available.
- Multiple testing: n local tests = n units; FDR-correct.
- MAUP (modifiable areal unit problem): results can flip with unit
  aggregation — if the aggregation level is a choice, test one alternative
  and disclose.
- Spatial autocorrelation in residuals after modeling = model still wrong;
  report residual Moran's I for every final model.
- Correlation ≠ causation applies doubly here: spatially confounded
  variables (everything correlates with "distance to coast") demand
  explicit identification strategies before causal claims.

## Reporting template

```
## Spatial analysis: 
- Units & n, variable(s), rate smoothing: 
- W: , islands: , sensitivity W: 
- Global: Moran's I = <> (p_perm = <>)
- Local:  significant clusters after FDR; map attached
- Model:  chosen because 
- Residual Moran's I: <> — 
- Caveats: MAUP, W-sensitivity, causal limits
```

## Execution contract

- **Workflow:** define inferential question and unit; inspect distributions and rates; construct and justify spatial weights; run global before local tests; fit models if needed; diagnose residual dependence; report uncertainty.
- **Decision rules:** use spatial statistics for dependence and inference, geostatistics for interpolating sampled continuous surfaces, and predictive ML when out-of-sample prediction is the primary goal.
- **Verification protocol:** test alternative weights and aggregation, use valid permutation or model inference, correct local multiplicity, inspect residual Moran's I, and distinguish association from causation.
- **Failure modes:** withhold inferential claims for arbitrary weights, islands ignored, unstable MAUP results, uncorrected multiple tests, residual autocorrelation, or unsupported causal language.
- **Deliverables:** analysis-ready variables, weights specification, global and local results, corrected significance, diagnostic maps, model and residual checks, sensitivity analysis, and caveats.
- **Source freshness:** consult [the authoritative source registry](references/authoritative-sources.md) before applying version-sensitive statistical APIs or defaults.

## Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

- **Author:** [muend](https://github.com/muend)
- **Source:** [muend/geoai-skills](https://github.com/muend/geoai-skills)
- **License:** MIT

Install and usage instructions live in the source repository linked above.

## Pricing

- **Free** — Free

## Security capabilities

Automated source analysis of v0.1.0 — what this tool can access:

- **Network access:** no
- **Filesystem access:** no
- **Shell / process execution:** no
- **Environment & secrets:** no
- **Dynamic code execution:** no

*"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.*


## Versions

- **0.1.0** — security scan: passed — Imported from the upstream source.

## Links

- Listing page: https://agentstack.voostack.com/l/skill-muend-geoai-skills-spatial-statistics
- Seller: https://agentstack.voostack.com/s/muend
- Browse the marketplace: https://agentstack.voostack.com/browse

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