Chi-square automatic interaction detection: Difference between revisions

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{{Short description|Decision tree learning technique}}

'''Chi-square automatic interaction detection''' ('''CHAID''')<ref name=":1" /> is a [[Decision tree learning|decision tree]] technique based on adjusted significance testing ([[Bonferroni correction]], [[Holm-Bonferroni method|Holm-Bonferroni testing]]).<ref name="kass1980">{{Cite journal |last=Kass |first=G. V. |date=1980 |title=An Exploratory Technique for Investigating Large Quantities of Categorical Data |url=https://www.jstor.org/stable/2986296 |journal=Applied Statistics |volume=29 |issue=2 |pages=119–127 |doi=10.2307/2986296|jstor=2986296 |url-access=subscription }}</ref><ref name=":0">{{Cite journal |last1=Biggs |first1=David |last2=De Ville |first2=Barry |last3=Suen |first3=Ed |date=1991 |title=A method of choosing multiway partitions for classification and decision trees |url=https://www.tandfonline.com/doi/full/10.1080/02664769100000005 |journal=Journal of Applied Statistics |language=en |volume=18 |issue=1 |pages=49–62 |doi=10.1080/02664769100000005 |bibcode=1991JApSt..18...49B |issn=0266-4763|url-access=subscription }}</ref>

==History==

CHAID is based on a formal extension of AID (Automatic Interaction Detection)<ref name="morgan1963">{{Cite journal |last1=Morgan |first1=James N. |last2=Sonquist |first2=John A. |date=1963 |title=Problems in the Analysis of Survey Data, and a Proposal |url=http://www.tandfonline.com/doi/abs/10.1080/01621459.1963.10500855 |journal=Journal of the American Statistical Association |language=en |volume=58 |issue=302 |pages=415–434 |doi=10.1080/01621459.1963.10500855 |issn=0162-1459|url-access=subscription }}</ref> and THAID (THeta Automatic Interaction Detection)<ref name="messenger1972">{{Cite journal |last1=Messenger |first1=Robert |last2=Mandell |first2=Lewis |date=1972 |title=A Modal Search Technique for Predictive Nominal Scale Multivariate Analysis |url=http://www.tandfonline.com/doi/abs/10.1080/01621459.1972.10481290 |journal=Journal of the American Statistical Association |language=en |volume=67 |issue=340 |pages=768–772 |doi=10.1080/01621459.1972.10481290 |issn=0162-1459|url-access=subscription }}</ref><ref name="morgan1973">{{Cite book |last=Morgan |first=James N. |url=https://www.worldcat.org/oclc/666930 |title=THAID, a sequential analysis program for the analysis of nominal scale dependent variables |date=1973 |others=Robert C. Messenger |isbn=0-87944-137-2 |___location=Ann Arbor, Mich. |oclc=666930}}</ref> 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.<ref>{{Cite journal |last=Belson |first=William A. |date=1959 |title=Matching and Prediction on the Principle of Biological Classification |url=https://www.jstor.org/stable/2985543 |journal=Applied Statistics |volume=8 |issue=2 |pages=65–75 |doi=10.2307/2985543|jstor=2985543 |url-access=subscription }}</ref>

In 1975, the CHAID technique itself was developed in South Africa. It was published in 1980 by Gordon V. Kass, who had completed a PhD thesis on the topic.<ref name="kass1980"/>

A history of earlier supervised tree methods can be found in [[Gilbert Ritschard|Ritschard]], including a detailed description of the original CHAID algorithm and the exhaustive CHAID extension by Biggs, De Ville, and Suen.<ref name=":0" /><ref name=":1">{{Cite journal |last=Ritschard |first=Gilbert |title=CHAID and Earlier Supervised Tree Methods |url=https://www.researchgate.net/publication/315476407 |journal=Contemporary Issues in Exploratory Data Mining in the Behavioral Sciences, McArdle, J.J. And G. Ritschard (Eds) |___location=New York |publisher=Routledge |publication-date=2013 |pages=48–74}}</ref>

CHAID was used as the data mining technique. It is a technique based on multiway splitting to create discrete groups and understand their impact on the dependent variable. CHAID was preferred for analysis because of five major criteria:

1. A good proportion of input data was categorical;

2. Its efficiency in large datasets;

3. Its highly visual and ease of interpretation;

4. Ease of implementation/integration of business rules generated from CHAID in business; and

5. Input data quality can be handled efficiently<ref>{{Cite web |last=Behera, Desik |first= |date=Nov 2012 |title=Acquiring Insurance Customer: The CHAID Way |url=https://www.researchgate.net/publication/256038754_Acquiring_Insurance_Customer_The_CHAID_Way |access-date=7 Aug 2025 |website=Research Gate}}</ref><ref>{{Cite web |last=Kotane |first=Inta |date=September 2024 |title=APPLICATION OF CHAID DECISION TREES AND NEURAL NETWORKS METHODS IN FORECASTING THE YIELD OF CEREAL INDUSTRY COMPANIES |url=https://www.researchgate.net/publication/383956028_APPLICATION_OF_CHAID_DECISION_TREES_AND_NEURAL_NETWORKS_METHODS_IN_FORECASTING_THE_YIELD_OF_CEREAL_INDUSTRY_COMPANIES |url-status=live |archive-url= |archive-date= |access-date=7 August 2025 |website=Research Gate |doi=10.17770/het2024.28.8264}}</ref>

==Properties==

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.<ref name="morgan1963"/><ref name="messenger1972"/><ref name="morgan1973"/>

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.{{fact|date=December 2024}}

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.{{fact|date=December 2024}}

One important advantage of CHAID over alternatives such as multiple regression is that it is non-parametric.{{fact|date=December 2024}}

==See also==