CHAID Decision Tree: Reverse Mortgage Loan Termination Example

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1 CHAID Decision Tree: Reverse Mortgage Loan Termination Example Business Context 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. market 2. 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 websire 3. 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 of borrowers are used below example to illustrate Decision Tree Building process. CHAID Algorithm 1 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 Step 1: Best Split for a Predictor Variable In this example Age of borrowers are considered as one of the predictor or Independent variable. Age is ordinal variable hence merging of continuous categories are allowed. Ordinal variables (without missing category) are referred as Monotonic Predictors. An ordinal variable with missing category is considered as Floating Predictor. In the floating predictors, floating category can be grouped with any other category. Since Age of borrower does not have any missing category, it is considered as Monotonic Predictor and categories will be compared and merged to the subsequent category only. RamG Data Analytics and Insights Page 1

2 1. Calculate Chi Square Statistics between two of the subsequent categories of the Predictor or Independent variable, Age of the Borrowers. Each value of borrower will be considered as separate category, but for simplicity the below category groups are created. Borrower Age Loan Terminate Low-65 <=70 <=75 <=80 <=85 <=90 <=95 95-High No Yes Total Merge the categories which are the least significantly different In above categories, the categories <=95 and 95-High are least significantly different and will be candidates for merging. Below will be tables after merging. Borrower Age Loan Terminate Low-65 <=70 <=75 <=80 <=85 <=90 90-High No Yes Total Chi-square between subsequent categories will be calculated again to find next least significantly different category group. 3. Continue category merging steps until two categories are left, the process also involve splitting categories of a group which has more than 2 categories. 4. Final Split for the variable, age of borrower Loan Terminate Borrower Age <=69 >69 No Yes Total RamG Data Analytics and Insights Page 2

3 Chi Square Statistics Follow similar steps for other predictor variables. Consider of borrower. is nominal variable; hence any category can be clubbed with any other category. In the original paper, the nominal variables are referred as Free Predictors. Loan Terminate Couple Female Male Not Reported Total No Yes Total First Merge Iteration Loan Terminate Couple Female Male Not Reported Total No Yes Total Chi Square Statistics Chi Square Statistics RamG Data Analytics and Insights Page 3

4 Chi Square Statistics Chi Square Statistics Chi Square Statistics Chi Square Statistics 6.7 Second Merge Iteration Loan Terminate Couple Female Male & Not Reported Total No Yes Total Chi Square Statistics RamG Data Analytics and Insights Page 4

5 Chi Square Statistics Chi Square Statistics 145 Final Split for the predictor variable, of borrower Loan Terminate Couple Male, Female & Not Reported Total No Yes Total Chi Square Statistics 795 Step 2: Selecting Best Predictor Variable for Node split The most discriminate variable based on Chi Square Statistics will be selected to split the parent node to child nodes. In the above example, if Age and of borrowers are only two predictor variables, based on Chi Square Statistics (Age Chi-Square 1162 and Chi-Square 765), age is selected as variable to split the parent node. Main Data Yes % NO % Age of Borrower Age<=69 Age>69 Yes % Yes % NO % NO % RamG Data Analytics and Insights Page 5

6 References 1. G.V.Kass, An exploratory technique for investigating large quantities of categorical data, Applied Statistics 2. Tonja Bowen Bishop, Hui Shan, Reverse Mortgages: A Closer Look at HECM Loans 3. RamG Data Analytics and Insights Page 6