> For the complete documentation index, see [llms.txt](https://xunli.gitbook.io/postgeoda/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://xunli.gitbook.io/postgeoda/3.-lisa/3.5-local-quantile-lisa.md).

# 3.5 Quantile LISA

Quantile LISA ([2019](https://geodacenter.github.io/workbook/6d_local_discrete/lab6d.html#ref-Anselin:19b)) is quantile local spatial autocorrelation that applies local join count statistics to quantiles of a continuous variable by converting the continuous variable to a binary variable that takes the value of 1 for a specific quantile. For more information, please read <https://geodacenter.github.io/workbook/6d_local_discrete/lab6d.html#quantile-lisa>

## quantile\_lisa()

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

### Synopsis

Short version:

```sql
float[] quantile_lisa(integer k, integer q, numeric val,  bytea weights)
```

Full version:

```sql
float[] quantile_lisa(integer k, integer q, numeric val,  bytea weights,
    integer permutations, 
    character varying permutation_method,
    float significance_cutoff, 
    integer cpu_threads, 
    integer seed)
```

### Arguments

| Name                 | Type              | Description                                                                                                |
| -------------------- | ----------------- | ---------------------------------------------------------------------------------------------------------- |
| k                    | integer           | the number of quantiles                                                                                    |
| q                    | integer           | the index of which quantile is used in local join count statistics                                         |
| 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 {'local join count',  'pseudo-p value', 'number of neighbors'} |

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

### Examples

Apply quantile lisa statistics on the variable "hr60" (homicide rate 1960), the 1st quantile of 10 quantiles, using queen contiguity weights "queen\_w":

```sql
SELECT quantile_lisa(10, 1, hr60, queen_w) OVER() FROM natregimes;

 local_quantilelisa 
--------------------
 {0,-1,3}
 {0,-1,3}
 {0,-1,4}
 {0,-1,7}
 {0,-1,4}
 {0,-1,3}
 {0,-1,4}
 {0,-1,9}
 {1,0.492,3}
 {0,-1,3}
 ...
```