Chi-square automatic interaction detection explained

Chi-square automatic interaction detection (CHAID)^{[1] [2]} 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)^[3] and THAID (THeta Automatic Interaction Detection)^{[4] [5]} 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.^[6] 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.^[7]

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.

See also

• Chi-squared distribution
• Bonferroni correction
• Latent class model
• Structural equation modeling
• Market segment
• Decision tree learning
• Multiple comparisons

Further reading

• Press, Laurence I.; Rogers, Miles S.; & Shure, Gerald H.; An interactive technique for the analysis of multivariate data, Behavioral Science, Vol. 14 (1969), pp. 364–370
• Hawkins, Douglas M.; and Kass, Gordon V.; Automatic Interaction Detection, in Hawkins, Douglas M. (ed), Topics in Applied Multivariate Analysis, Cambridge University Press, Cambridge, 1982, pp. 269–302
• Hooton, Thomas M.; Haley, Robert W.; Culver, David H.; White, John W.; Morgan, W. Meade; & Carroll, Raymond J.; The Joint Associations of Multiple Risk Factors with the Occurrence of Nosocomial Infections, American Journal of Medicine, Vol. 70, (1981), pp. 960–970
• Brink, Susanne; & Van Schalkwyk, Dirk J.; Serum ferritin and mean corpuscular volume as predictors of bone marrow iron stores, South African Medical Journal, Vol. 61, (1982), pp. 432–434
• McKenzie, Dean P.; McGorry, Patrick D.; Wallace, Chris S.; Low, Lee H.; Copolov, David L.; & Singh, Bruce S.; Constructing a Minimal Diagnostic Decision Tree, Methods of Information in Medicine, Vol. 32 (1993), pp. 161–166
• Magidson, Jay; The CHAID approach to segmentation modeling: chi-squared automatic interaction detection, in Bagozzi, Richard P. (ed); Advanced Methods of Marketing Research, Blackwell, Oxford, GB, 1994, pp. 118–159
• Hawkins, Douglas M.; Young, S. S.; & Rosinko, A.; Analysis of a large structure-activity dataset using recursive partitioning, Quantitative Structure-Activity Relationships, Vol. 16, (1997), pp. 296–302

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.

Notes and References

1. Kass . G. V. . 1980 . An Exploratory Technique for Investigating Large Quantities of Categorical Data . Applied Statistics . 29 . 2 . 119–127 . 10.2307/2986296. 2986296 .
2. Biggs . David . De Ville . Barry . Suen . Ed . 1991 . A method of choosing multiway partitions for classification and decision trees . Journal of Applied Statistics . en . 18 . 1 . 49–62 . 10.1080/02664769100000005 . 0266-4763.
3. Morgan . James N. . Sonquist . John A. . 1963 . Problems in the Analysis of Survey Data, and a Proposal . Journal of the American Statistical Association . en . 58 . 302 . 415–434 . 10.1080/01621459.1963.10500855 . 0162-1459.
4. Messenger . Robert . Mandell . Lewis . 1972 . A Modal Search Technique for Predictive Nominal Scale Multivariate Analysis . Journal of the American Statistical Association . en . 67 . 340 . 768–772 . 10.1080/01621459.1972.10481290 . 0162-1459.
5. Book: Morgan, James N. . THAID, a sequential analysis program for the analysis of nominal scale dependent variables . 1973 . Robert C. Messenger . 0-87944-137-2 . Ann Arbor, Mich. . 666930.
6. Belson . William A. . 1959 . Matching and Prediction on the Principle of Biological Classification . Applied Statistics . 8 . 2 . 65–75 . 10.2307/2985543. 2985543 .
7. Ritschard . Gilbert . CHAID and Earlier Supervised Tree Methods . Contemporary Issues in Exploratory Data Mining in the Behavioral Sciences, McArdle, J.J. And G. Ritschard (Eds) . New York . Routledge . 2013 . 48–74.