3.3 Local Getis-Ord G

The local Getis-Ord statistic is a ratio of the weighted average of the values in the neighboring locations to the sum of all values. It is called local g or local g*, when not including the value at the location. In local g/g*, a value larger than the mean (or, a positive value for a standardized z-value) suggests a High-High cluster or hot spot, a value smaller than the mean (or, negative for a z-value) indicates a Low-Low cluster or cold spot. For more information, please read: https://geodacenter.github.io/workbook/6b_local_adv/lab6b.html#getis-ord-statistics

In contrast to the Local Moran and Local Geary statistics, the Getis-Ord approach does not consider spatial outliers.

CONTENTS

1. local_g() and local_gstar()

local_g(), local_gstar()

local_g() or local_gstar() is a PostgreSQL WINDOW function. Please call it with an OVER clause.

Synopsis

Short version:

float[] local_g(numeric val,  bytea weights)

float[] local_gstar(numeric val,  bytea weights)

Full version:

float[] local_g(numeric val,  bytea weights,
    integer permutations, 
    character varying permutation_method,
    float significance_cutoff, 
    integer cpu_threads, 
    integer seed)

float[] local_gstar(numeric val,  bytea weights,
    integer permutations, 
    character varying permutation_method,
    float significance_cutoff, 
    integer cpu_threads, 
    integer seed)

Arguments

Name	Type	Description
val	numeric	the numeric column that contains the values for LISA statistics
weights	bytea	the bytea column that stores the spatial weights information
permutations	integer	the number of permutations for the LISA computation. Default: 999.
permutation_method	character varying	the permutation method used for the LISA computation. Options are 'complete', 'lookup'. Default: 'lookup'.
significance_cutoff	float	the cutoff value for significance p-values to filter not-significant clusters. Default: 0.05.
cpu_threads	integer	the number of CPU threads used for parallel LISA computation. Default: 6.
seed	integer	the seed for random number generator used in LISA statistics. Default: 123456789.

Return

Type	Description
float[]	an array contains 3 values, which are {'lisa value', 'pseudo-p value' and 'cluster indicator'}

Examples

Apply local_g on the variable "hr60" (homicide rate 1960 in natregimes dataset) using queen contiguity weights "queen_w":

Please see chapter 'Contiguity Based Weights' for how to create a Queen contiguity weights.

SELECT local_g(hr60, queen_w) OVER() FROM natregimes;

            local_g             
--------------------------------
 {6.82727000829049e-05,0.086,0}
 {0.000180615019894871,0.289,0}
 {0.00010018844366193,0.075,0}
 ...

One can specify the arguments of local g using the full version of local_g() function. For example, apply local moran statistics using 9,999 permutations, significance cutoff value 0.01:

SELECT local_g(
    hr60, queen_w, 9999, 'lookup', 0.01, 6, 123456789
) OVER() FROM natregimes;

             local_g             
---------------------------------
 {6.82727000829049e-05,0.0868,0}
 {0.000180615019894871,0.2858,0}
 {0.00010018844366193,0.0843,0}
 ...

Cluster Indicators

The predefined values of the cluster indicators of local g/g* are:

Cluster indicator value	Description	Color
0	Not significant	#eeeeee
1	High-High	#ff0000
2	Low-Low	#0000ff
3	Undefined Value	#464646
4	Isolated	#999999

One can extract the cluster indicators and make a local g/g* cluster map using the 'Color" values in the table above:

SELECT tmp.local_g[3] FROM (
    SELECT local_g(hr60, queen_w) OVER() FROM natregimes
) AS tmp;

Or by extracting the pseudo-p values to make a significance map:

SELECT tmp.local_g[2] FROM (
    SELECT local_g(hr60, queen_w) OVER() FROM natregimes
) AS tmp;