Incidence Getis Ord Hotspots

Compute local Getis–Ord Gi* standardized scores from supplied incidence and self-inclusive spatial weights; caller cutoff is not a multiple-testing correction.

Description

Getis–Ord Gi* describes whether weighted neighboring incidence is unusually high relative to the supplied study-wide mean and variance.

Getis–Ord Gi* describes whether weighted neighboring incidence is unusually high relative to the supplied study-wide mean and variance. Spatial weights define what counts as a neighborhood.

The tool returns giStarZScores (gi star z scores); hotspotIds (hotspot ids). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Incidence Getis Ord Hotspots

Use Incidence Getis Ord Hotspots when you already have siteIds, incidenceValues, spatialWeights, hotspotZCutoff and want giStarZScores, hotspotIds. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Incidence Getis Ord Hotspots and understand its results

Enter siteIds, incidenceValues, spatialWeights, hotspotZCutoff using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read giStarZScores, hotspotIds. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
siteIds	Site ids	list of string	Required
incidenceValues	Incidence values	list of number	Required
spatialWeights	Spatial weights	list of list of number	Required
hotspotZCutoff	Hotspot z cutoff	number	Required

Use distinct site labels, nonnegative incidence and a square nonnegative weight matrix with positive self-weights. Compute each z score and flag values at or above the positive caller cutoff.

Gi* = (Σwᵢⱼxⱼ − mean(x)Σwᵢⱼ) / (populationSD × sqrt((NΣwᵢⱼ² − (Σwᵢⱼ)²)/(N−1)))

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "siteIds": [
      "A",
      "B",
      "C",
      "D"
    ],
    "incidenceValues": [
      0,
      0,
      10,
      10
    ],
    "spatialWeights": [
      [
        1,
        1,
        0,
        0
      ],
      [
        1,
        1,
        0,
        0
      ],
      [
        0,
        0,
        1,
        1
      ],
      [
        0,
        0,
        1,
        1
      ]
    ],
    "hotspotZCutoff": 1.5
  },
  "output": {
    "giStarZScores": [
      -1.7320508075688774,
      -1.7320508075688774,
      1.7320508075688774,
      1.7320508075688774
    ],
    "hotspotIds": [
      "C",
      "D"
    ]
  }
}

Limitations and assumptions

Weights are not built from coordinates. This calculation supplies no multiple-testing correction or causal explanation; degenerate denominators and constant incidence are rejected.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Rainfall Incidence Lag: Find the nonnegative rainfall-to-incidence lag with greatest paired Pearson correlation; not a causal estimate. Climate Envelope Screen: Screen climate observations against a caller-defined suitability envelope, not a transmission prediction.

Methodological background: The analysis of spatial association by use of distance statistics.^[1]

References

The analysis of spatial association by use of distance statistics — Getis and Ord; Geographical Analysis

Similar or alternative tools

Rainfall Incidence Lag
Find the nonnegative rainfall-to-incidence lag with greatest paired Pearson correlation; not a causal estimate.
Climate Envelope Screen
Screen climate observations against a caller-defined suitability envelope, not a transmission prediction.