CHAID

CHAID stands for Chi-squared Automatic Interaction Detection. It is a statistical decision tree technique used for classification and segmentation, primarily with a categorical dependent variable. It identifies relationships between a target variable and a set of predictors by testing associations with chi-square statistics. Continuous predictors can be accommodated by binning into categories, while categorical predictors are used directly.

Algorithm: For each predictor, CHAID evaluates the association with the target across the observed categories using a chi-square test. It may merge neighboring categories of a predictor that do not differ significantly in their relation to the target. After these merges, the predictor with the strongest association (the smallest p-value) is chosen for the split. The split can be multiway, creating more than two branches. The procedure applies a multiplicity correction (often Bonferroni) to control type I error across tests. Splitting continues recursively until stopping criteria are met, such as a significance threshold, minimum node size, or a maximum tree depth.

Output and interpretation: The resulting tree partitions the data according to predictor categories, with leaves representing the distribution of the target variable in that segment. CHAID trees are often used to estimate class probabilities and to identify interactions among predictors that influence the target.

Strengths and limitations: CHAID is nonparametric and handles nonlinear relationships and interactions without specifying a model form. It tends to perform well on survey and market research data and can handle missing values through separate categories or imputation in some implementations. Limitations include sensitivity to sample size and to the chosen significance level, potential overfitting for small samples or very large category counts, and reliance on chi-square approximations when expected counts are low.

Applications and implementations: Widely used for customer segmentation, market research, and exploratory data analysis. Implementations exist in several software packages, including SAS, SPSS, and various R and Python libraries, each with its own options for pruning, minimum node sizes, and significance criteria.

History: CHAID was introduced by Gordon Kass in the 1980s as a method for automatic interaction detection using chi-square tests.