carto-spatial-autocorrelation

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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.

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Sourcecartodb/agent-skills

Added on2026-05-26

NPX Install

npx skill4agent add cartodb/agent-skills carto-spatial-autocorrelation

SKILL.md Content

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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:

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. (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

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`

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

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)

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