# 4.3 Bivariate Local Join Count

Bivariate or no-colocation local join count ([2019](https://geodacenter.github.io/workbook/6d_local_discrete/lab6d.html#ref-AnselinLi:18)) only works when two events cannot happen in the same location (e.g., a zoning classification, or a case-control design). It can be used to identify *negative* spatial autocorrelation, i.e., evidence of spatial outliers. For more information, please read [http://geodacenter.github.io/workbook/6a\_local\_auto/lab6a.html](https://geodacenter.github.io/workbook/6d_local_discrete/lab6d.html#bivariate-local-join-count-statistic)

## local\_bijoincount()

{% hint style="info" %}
local\_bijoincount() is a PostgreSQL WINDOW function. Please call it  with an OVER clause.
{% endhint %}

### Synopsis

Short version:

```sql
float[] local_bijoincount(real val1, numeric val2, bytea weights)
```

Full version:

```sql
float[] local_bijoincount(numeric val1, numeric val2, bytea weights,
    integer permutations, 
    character varying permutation_method,
    float significance_cutoff, 
    integer cpu_threads, 
    integer seed)
```

### Arguments

| Name                 | Type              | Description                                                                                                |
| -------------------- | ----------------- | ---------------------------------------------------------------------------------------------------------- |
| val1                 | *numeric*         | the first numeric column that contains the binary values (e.g. 0 and 1) for LISA statistics                |
| val1                 | *numeric*         | the second numeric column that contains the binary values (e.g. 0 and 1) 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 {'local join count',  'pseudo-p value', 'number of neighbors'} |

{% hint style="info" %}
The results do NOT have 'category indicator'.
{% endhint %}

### Examples

Apply bivariate local join count statistics on the variable "death\_*dum" (dummy variable for death incidence, dataset '*[*deaths\_nd\_by*\_house](https://geodacenter.github.io/data-and-lab/snow/)'), and "1 - death\_dum" using distance-based weights "d20" (distance cutoff value = 20 meters):

* Create weights:

```sql
-- add a new column 'd20' first
-- ALTER TABLE deaths_nd_by_house ADD COLUMN d20 bytea
UPDATE deaths_nd_by_house SET d20 = w.distance_weights
FROM (
  SELECT 
    gid, 
    distance_weights(gid, ST_Transform(the_geom, 27700), 20.0) 
  OVER() FROM deaths_nd_by_house
) AS w 
WHERE deaths_nd_by_house.gid = w.gid
```

{% hint style="info" %}
When importing the dataset to PostgresSQL, the projection could be changed (e.g. using EPSG: 4326). In this example, we need to use **ST\_Transform**(geom, srid) to project the points from EPSG 4326 to EPSG 27700 (unit: meter) so that we can create distance weights using 20.0 meters as the cutoff value.
{% endhint %}

* apply local\_bijoincount()

```sql
SELECT local_bijoincount(death_dum, (1-death_dum), d20) OVER() FROM deaths_nd_by_house;

 local_joincount 
-----------------
 {0,-1,11}
 {0,-1,11}
 {0,-1,12}
 {0,-1,12}
 {7,0.009,14}
 {6,0.021,12}
 {7,0.005,13}
 {5,0.079,13}
 ...
```


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