# Decision Tree: CHAID

There a number of different Decision Tree building algorithm available for both Regression and Classification problems. One of the great advantage with Decision Tree algorithm is that the output can be easily explained to business users.

Some of the decision tree building algorithms are

In this blog, the focus will be to explain Chi-squared Automatic Interaction Detection (CHAID) based decision tree building.

## CHAID Decision Tree: Reverse Mortgage Loan Termination Example

Reverse Mortgage Loan (RML) enables Senior Citizens to avail of periodical payments from a lender against the mortgage of his/her house to supplement their income while remaining the owner and occupying the house. Interest on the payments availed will be accumulated. One of the types of Reverse mortgage is Home Equity Conversion Mortgage (HECM), insured by the Federal Housing Administration (FHA) and constituting over 90% of all reverse mortgage loans originated in the U.S. market2 .

“A HECM loan is terminated when the borrower dies or permanently moves out the house. Understanding termination outcomes of HECM loans is essential for the FHA insurance program and the long-term viability of the HECM program”2 The data is downloaded from HUD.GOV websire3 .

All loans originated in 2003 and 2004 are considered for below example. If the termination date is populated, the HECM loan is considered as close. Age and Gender of borrowers are used below example to illustrate Decision Tree Building process.

CHAID Algorithm1

Process Steps

Step 1: Find best split for each Predictor or Independent Variable by merging categories of the Predictor variable

Step 2: Compare Predicator Variables and select the best variable for the node and split the node into two child nodes

Step 3: Continue Step 1 and Step 2 for each of the new nodes until satisfy the stopping criteria.

Detailed work out example of Decision Tree building using CHAID