**CHAID (Chi-squared Automatic Interaction Detector)** is an algorithm used for building decision trees, in particular for splitting variables based on their interactions with target variables. Unlike traditional decision trees, which rely primarily on the Gini index or entropy to choose splits, CHAID uses chi-square tests to automatically determine optimal splits.

## The CHAID algorithm

Here’s how the CHAID algorithm works:

**Selecting the target variable**: Start by selecting the target variable, i.e. the variable you want to predict or rank.**Predictor variable selection**: Choose a set of predictor variables (independent variables) that are likely to influence the target variable. These variables can be either categorical or numeric.**Initial Split**: Begin by splitting the dataset by the predictor variable that has the greatest association with the target variable. This initial split creates the first two nodes of the tree**.****Chi-square test calculation**: For each node created, calculate the chi-square test between the target variable and each remaining predictor variable. This test measures the relationship between variables and indicates whether the predictor variable has a significant association with the target variable.**Splitting based on chi-square**: If the chi-square test passes a predefined significance threshold, the predictor variable is used to further split the current node into sub-nodes. This splitting continues until a stop condition is reached.**Stop conditions**: The CHAID algorithm stops in several cases:- When a predefined maximum depth in the tree is reached.
- When the number of observations in a node is less than a predefined threshold.
- When the chi-square test is not significant for any remaining predictor variable.

**Tree creation**: The tree is created based on the splits made. Each node in the tree represents a category or range of a variable. The leaves of the tree represent the final classifications or predictions.**Pruning (Pruning)**: After creating the tree, you can perform a pruning to simplify it by removing the branches that could cause overfitting.

Remember that CHAID is especially useful when you have categorical variables and want to capture the complex interactions between them. However, it is advisable to do more research and testing to determine if CHAID is the best choice for your specific problem.

## The Chi-square test

The CHAID (Chi-squared Automatic Interaction Detection) algorithm is a method of creating decision trees based on chi-square tests for categorical variables. Its mathematical formulation primarily involves calculating the chi-square test to determine the significance of potential splits in the data.

The chi-square test is commonly used to evaluate the association between two categorical variables. The chi-square test formula is:

Where:

is the actual observation in cell (i, j) of the contingency table.

is the theoretical expectation in cell (i, j) calculated as where is the sum of the observations in row i and is the sum of the observations in column j, and (N) is the total of observations.

The CHAID algorithm uses this test to determine the significance of potential splits in the dataset with respect to the target variable. The process involves iterations to find the splits that maximize the significance of the chi-square test.

The key idea is to recursively partition the data so that the new partitions are homogeneous with respect to the target variable. The significance of the subdivisions is assessed through the chi-square test, and the subdivisions are made only when the resulting p-value exceeds a certain pre-established threshold (for example, 0.05).

Remember that while the logic and principles of CHAID involve statistical testing, the i

## A bit of history

The Chi-squared Automatic Interaction Detection (CHAID) algorithm was developed by Gordon Kass in 1980. Kass, a psychologist and statistician, created CHAID as a method for statistical analysis and the discovery of relationships between categorical variables.

The history of the CHAID algorithm is linked to the need to address the analysis of categorical data, where the variables are represented by categories or levels. While traditional decision trees were primarily based on methods such as the Gini index or entropy, CHAID has introduced a new approach using the chi-square test to evaluate the association between variables.

CHAID’s methodology has proven particularly effective for discovering complex interactions between categorical variables, making it suitable for problems where the relationships between variables are non-linear and where possible interactions between variables need to be explored to obtain accurate predictions .

The philosophy behind CHAID is to build a decision tree iteratively, starting with the target variable and splitting by predictor variables with a meaningful chi-squared test. This process of splitting and testing helps reveal complex relationships between categorical variables, allowing for a deeper understanding of the data.

In the years since its introduction, the CHAID algorithm has been used in a variety of fields, including social research, psychology, marketing data analytics, and more. While other techniques and algorithms for analyzing categorical data have emerged in recent years, CHAID remains a relevant and valuable technique for analyzing and discovering complex relationships between categorical variables.

## Where to find CHAID

Unfortunately, this algorithm is not available in Python.

CHAID, an acronym for Chi-squared Automatic Interaction Detection, can be implemented in various programming languages, but is best known for being used in a **SAS (Statistical Analysis System) **environment. This is a statistical software suite that includes the implementation of the CHAID algorithm as part of its analytical capabilities. In SAS, the CHAID algorithm is used for creating decision trees when analyzing data that includes categorical variables. SAS offers a comprehensive environment for statistical analysis and data exploration, and the CHAID algorithm is one of the options available for building decision trees alongside other methods.