spatial-autocorrelation

name

spatial-autocorrelation

description

Builds Moran's I spatial autocorrelation workflows in CARTO. Triggers when the user mentions spatial autocorrelation, Moran's I, spatial dependency, spatial correlation, spatial outliers, HH HL LH LL quadrants, high-high clusters, low-low clusters, spatial weight matrix, "is there clustering", "are values spatially correlated", local indicators of spatial association, LISA, spatial randomness test, or wants to determine whether a variable exhibits spatial clustering, dispersion, or randomness across a gridded dataset. Also relevant when the user needs to classify locations into cluster types (HH, HL, LH, LL) rather than just identifying hotspots and coldspots.

Spatial Autocorrelation with Moran's I

Builds CARTO Workflows that measure spatial autocorrelation using Moran's I, determining whether a variable exhibits clustering, dispersion, or randomness, and classifying each location into HH/HL/LH/LL quadrants.

Prerequisites: Load build-carto-workflow for the full workflow development process, JSON structure, and validation commands.

When to use Moran's I vs Getis-Ord Gi*:

• Moran's I: "Is there clustering?" + classify into cluster types (HH, HL, LH, LL) + identify spatial outliers (HL, LH)
• Getis-Ord Gi*: "Where are the hotspots/coldspots?" + magnitude of clustering (z-scores)

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Instructions

A Moran's I workflow follows this pipeline:

Source Data -> (Filter) -> Spatial Indexing (H3) -> Aggregation -> Moran's I -> (Filter Significant) -> Save

Step 1: Load Source Data

Use native.gettablebyname. The input table typically contains point geometries or pre-indexed grid data.

Success: Node outputs a table with a geometry column (e.g. geom) or an existing spatial index column.

Step 2: Filter (if needed)

Use native.wheresimplified or native.where to narrow the dataset (e.g. filter by category, date range, non-null values).

Success: Output contains only the subset relevant to the analysis.

Step 3: Spatial Indexing

Convert point geometries to H3 cells using native.h3frompoint.

Resolution guidance -- higher resolution = smaller cells = more local patterns:

Resolution	Cell size	Use case
H3 res 7	~5 km edge	District/city-level patterns
H3 res 8	~2 km edge	Neighborhood-level
H3 res 9	~500m edge	Street-level (used in Berlin POI tutorial)

Success: Every row has a spatial index column (e.g. h3).

Step 4: Aggregate per Cell

Use native.groupby to produce one row per cell with a numeric value:

• Group by: the spatial index column (h3)
• Aggregation: geoid,count (or value_col,sum / value_col,avg)

Success: Output has exactly one row per unique cell with a numeric column (e.g. geoid_count).

Step 5: Run Moran's I

Use native.moransi with:

Input	Description	Default
indexcol	Column with H3/Quadbin indexes	h3
valuecol	Numeric column to test for autocorrelation	geoid_count
size	K-ring neighborhood radius (in hops)	3
decay	Distance decay function for spatial weights	uniform

Decay options: uniform, inverse, inverse_square, exponential.

• uniform: Equal weight to all neighbors within the k-ring
• exponential: Weight decreases exponentially with distance (used in Berlin POI tutorial)

K-ring size: Larger = broader neighborhood = smoother global patterns. Smaller = more localized assessment. The choice of neighborhood size significantly affects results.

Success: Output contains INDEX, MORANS_I, P_VALUE, and QUADRANT columns for every cell.

Step 6: Filter Significant Results (recommended)

Use native.where to keep only statistically significant cells. Quadrant classification is only meaningful for significant cells.

Common filters:

• P_VALUE < 0.05 -- all significant cells (95% confidence)
• P_VALUE < 0.05 AND QUADRANT = 'HH' -- high-value clusters only
• P_VALUE < 0.05 AND (QUADRANT = 'HL' OR QUADRANT = 'LH') -- spatial outliers only

Success: Only cells with statistically meaningful spatial patterns remain.

Step 7: Save

Use native.saveastable to persist results. The H3/Quadbin column is directly visualizable in CARTO Builder without geometry conversion.

Success: Validated workflow that can be uploaded via carto workflows create.

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Output Columns

Column	Meaning
INDEX	Spatial index cell ID (H3 or Quadbin)
MORANS_I	Local Moran's I value -- positive = similar neighbors, negative = dissimilar neighbors
P_VALUE	Statistical significance -- lower = more confident
QUADRANT	Cluster classification: HH, HL, LH, or LL

Interpreting Results

Global Moran's I (overall pattern):

• > 0 = spatial clustering (similar values near each other)
• < 0 = spatial dispersion (dissimilar values near each other)
• Near 0 = spatial randomness

Local quadrants (per-cell classification):

Quadrant	Meaning	Interpretation
HH	High value surrounded by high values	Cluster core
LL	Low value surrounded by low values	Low-value cluster
HL	High value surrounded by low values	Spatial outlier (high anomaly)
LH	Low value surrounded by high values	Spatial outlier (low anomaly)

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Gotchas

• The Moran's I component requires the Analytics Toolbox. Always run carto workflows verify --connection <conn> to ensure the AT path is resolved. carto workflows validate is offline and cannot resolve AT location.
• The output column is named INDEX, not H3 or QUADBIN. If you need to join back to original data, rename it (e.g. with native.renamecolumn). This is the same behavior as Getis-Ord.
• The valuecol must be numeric. If you are counting features, the group-by step must produce a count column -- do not pass the raw index column as the value.
• On Snowflake, column names are uppercased. Use H3, GEOID_COUNT, MORANS_I, P_VALUE, QUADRANT in expressions.
• Resolution too high + large area = very many cells, which can be slow or hit memory limits. Start with a moderate resolution and refine.
• Moran's I is sensitive to the definition of neighborhood. Both k-ring size and decay function choice materially affect results. Document your choices and consider testing alternatives.
• Quadrant classification is only meaningful for statistically significant cells. Always filter by P_VALUE before interpreting quadrants -- non-significant cells may show any quadrant label by chance.
• The decay input parameter is named decay (not kernel). Check the component schema if unsure.

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Reference Templates

Resource	Description
BQ Tutorial	Computing spatial autocorrelation of POI locations in Berlin (BigQuery)
SF Tutorial	Same tutorial for Snowflake
Workflow template	"Computing the spatial auto-correlation of point of interest locations" (available in CARTO Workspace)

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Common Variations

Variant	How
Pre-indexed data	Skip Step 3 if data already has H3/Quadbin column
Polygon input instead of points	Use native.h3polyfill instead of native.h3frompoint
Complete grid (no gaps)	Polyfill study area boundary first, then enrich with data (same approach as hotspot analysis)
Combine with Getis-Ord	Run both analyses on the same aggregated grid, then join results for a richer picture
Filter to outliers only	Keep HL and LH quadrants to find anomalous locations