carto-spatial-autocorrelation

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 carto-create-workflow for the development process, JSON structure, and validation commands — it covers both access paths (the MCP server's workflow tools such as create_workflow, validate_workflow, and run_workflow when attached; the carto workflows CLI otherwise; routing signals in carto-basics/references/access-paths.md).

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)

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:

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:

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. (See the Provider casing note in Gotchas — Snowflake surfaces these UPPERCASE.)

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 create_workflow (MCP) or carto workflows create (CLI).

Output Columns

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):

Gotchas

• Provider casing & SQL dialect. This skill documents columns in lowercase (BigQuery / Databricks / Postgres / Redshift convention). On Snowflake, unquoted identifiers surface UPPERCASE — reference H3, INDEX, MORANS_I, P_VALUE, QUADRANT, GEOID_COUNT in expressions. See carto-create-workflow/references/providers/<provider>.md for casing rules and SQL dialect equivalents.
• The Moran's I component requires the Analytics Toolbox. Offline validation can't resolve the AT location — confirm it with a remote verify before running: validate_workflow method: verify over MCP, or carto workflows verify-remote --connection <conn> on the CLI.
• 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).
• 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.
• 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.

Reference Templates

Common Variations