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.

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 carto workflows create.

Output Columns

The engine declares these lowercase. See the Provider casing note in Gotchas for Snowflake.

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) |

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. Always run carto workflows verify-remote --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.
• 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