> ## Documentation Index
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> Use this file to discover all available pages before exploring further.

> Calculates the value of `(P(tag = 1) - P(tag = 0))(log(P(tag = 1)) - log(P(tag = 0)))` for each category.

# categoricalInformationValue

<h2 id="categoricalInformationValue">
  categoricalInformationValue
</h2>

Introduced in: v20.1.0

Calculates the information value (IV) for categorical features in relation to a binary target variable.

For each category, the function computes: `(P(tag = 1) - P(tag = 0)) × (log(P(tag = 1)) - log(P(tag = 0)))`

where:

* P(tag = 1) is the probability that the target equals 1 for the given category
* P(tag = 0) is the probability that the target equals 0 for the given category

Information Value is a statistic used to measure the strength of a categorical feature's relationship with a binary target variable in predictive modeling.
Higher absolute values indicate stronger predictive power.

The result indicates how much each discrete (categorical) feature `[category1, category2, ...]` contributes to a learning model which predicts the value of `tag`.

**Syntax**

```sql theme={null}
categoricalInformationValue(category1[, category2, ...,]tag)
```

**Arguments**

* `category1, category2, ...` — One or more categorical features to analyze. Each category should contain discrete values. [`UInt8`](/reference/data-types/int-uint)
* `tag` — Binary target variable for prediction. Should contain values 0 and 1. [`UInt8`](/reference/data-types/int-uint)

**Returned value**

Returns an array of Float64 values representing the information value for each unique combination of categories. Each value indicates the predictive strength of that category combination for the target variable. [`Array(Float64)`](/reference/data-types/array)

**Examples**

**Basic usage analyzing age groups vs mobile usage**

```sql title=Query theme={null}
CREATE TABLE visits (is_young UInt8, is_female UInt8, is_mobile UInt8) ENGINE = Memory;

-- 80 of the 100 young visitors browse on a mobile device, and only 20 of the 100 older ones do,
-- while the sex of a visitor says nothing about the device.
INSERT INTO visits SELECT 1, number % 2, number < 80 FROM numbers(100);
INSERT INTO visits SELECT 0, number % 2, number < 20 FROM numbers(100);

SELECT round(categoricalInformationValue(is_young, is_mobile)[1], 4) AS iv FROM visits;
```

```response title=Response theme={null}
┌─────iv─┐
│ 0.8318 │
└────────┘
```

**Multiple categorical features with user demographics**

```sql title=Query theme={null}
-- The age of a visitor predicts the device, the sex of a visitor does not.
SELECT arrayMap(x -> round(x, 4), categoricalInformationValue(is_young, is_female, is_mobile)) AS iv
FROM visits;
```

```response title=Response theme={null}
┌─iv─────────┐
│ [0.8318,0] │
└────────────┘
```