Chi-square automatic interaction detection

Chi-square automatic interaction detection (CHAID) is a decision tree technique based on adjusted significance testing (Bonferroni correction, Holm-Bonferroni testing). The technique was developed in South Africa in 1975 and was published in 1980 by Gordon V. Kass, who had completed a PhD thesis on this topic. CHAID can be used for prediction (in a similar fashion to regression analysis, this version of CHAID being originally known as XAID) as well as classification, and for detection of interaction between variables. CHAID is based on a formal extension of AID (Automatic Interaction Detection) and THAID (THeta Automatic Interaction Detection) procedures of the 1960s and 1970s, which in turn were extensions of earlier research, including that performed by Belson in the UK in the 1950s. A history of earlier supervised tree methods together with a detailed description of the original CHAID algorithm and the exhaustive CHAID extension by Biggs, De Ville, and Suen, can be found in Ritschard.

In practice, CHAID is often used in the context of direct marketing to select groups of consumers to predict how their responses to some variables affect other variables, although other early applications were in the fields of medical and psychiatric research.

Like other decision trees, CHAID's advantages are that its output is highly visual and easy to interpret. Because it uses multiway splits by default, it needs rather large sample sizes to work effectively, since with small sample sizes the respondent groups can quickly become too small for reliable analysis.

One important advantage of CHAID over alternatives such as multiple regression is that it is non-parametric.

Software

 * Luchman, J.N.; CHAID: Stata module to conduct chi-square automated interaction detection, Available for free download, or type within Stata: ssc install chaid.
 * Luchman, J.N.; CHAIDFOREST: Stata module to conduct random forest ensemble classification based on chi-square automated interaction detection (CHAID) as base learner, Available for free download, or type within Stata: ssc install chaidforest.
 * IBM SPSS Decision Trees grows exhaustive CHAID trees as well as a few other types of trees such as CART.
 * An R package CHAID is available on R-Forge.