Method and system for determining the importance of individual variables in a statistical model

• US 20030101080A1
• Filed: 11/28/2001
• Published: 05/29/2003
• Est. Priority Date: 11/28/2001
• Status: Active Grant

• Current Assignee: Deloitte Development LLC
• Original Assignee: Deloitte Development LLC
• Inventors: Stukel, Raymond E., Adamopoulos, Hrisanthi, Peter Wu, Cheng-Sheng, Zizzamia, Frank M.
• Granted Patent: US 8,200,511 B2
• Time in Patent Office: Days
• US Class Current: 705/4
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06Q 40/08 Insurance

Abstract

A method and system for determining the importance of each of the variables that contribute to the overall score of a model for predicting the profitability of an insurance policy. For each variable in the model, an importance is calculated based on the calculated slope and deviance of the predictive variable. Since the score is developed using complex mathematical calculations combining large numbers of parameters with predictive variables, it is often difficult to interpret from the mathematical formula for example, why some policyholders receive low scores while other receive high scores. Such clear communication and interpretation of insurance profitability scores is critical if they are used by the various interested insurance parties including policyholders, agents, underwriters, and regulators.

Claims

1. A system for calculating the contribution of each of a plurality of variables in a statistical model including a scoring formula for generating a score comprising a database for storing values associated with at least some of the plurality of variables, means for calculating a slope for any of the plurality of variables, means for calculating a deviance value for any of the plurality of variables and means for calculating the contribution of any of the plurality of variables based on the calculated slope and deviance values.

2. The system of claim 1 wherein the means for calculating the slope comprises a software module that takes the first derivative of the scoring formula with respect to the variable being analyzed.

3. The system of claim 1 wherein the plurality of variables describe characteristics of at least one of an existing policyholder and potential policyholder and the scoring formula is used to generate a score reflective of the expected loss/premium ratio for an insurance policy.

4. The system of claim 3 wherein the premium for the insurance policy is based on the score.

5. The system of claim 1 further comprising means for ranking the individual variables based on the calculated contribution.

6. The system of claim 1 wherein the means for calculating a deviance value includes a software module that receives inputs for a mean value and a standard deviation value and the deviance value is calculated using the formula:

7. The system of claim 1 wherein the contribution is calculated for any of the plurality of variables by multiplying the slope and deviance values.

8. In a system that employs a statistical model comprised of a scoring formula having a plurality of predictive variables for generating a score that is representative of a risk associated with an insurance policyholder, a method of evaluating the contribution of each of the plurality of predictive variables to the score generated by the model comprising the steps of populating a database associated with the system with a mean value and standard deviation value for each of the plurality of predictive variables, calculating a slope value for each of the plurality of predictive variables, calculating a deviance value based on the mean value and the standard deviation value for each of the plurality of predictive variables, and multiplying the deviance value and slope value for each of the plurality of predictive variables to determine the contribution of each of the plurality of predictive variables to the score.

9. The method of claim 8 further comprising the step of defining at least one assumption for the mean value associated with at least one of the plurality of predictive variables.

10. The method of claim 8 wherein the step of calculating the slope further comprises the step of calculating the first derivative of the scoring formula with respect to the predictive variable of the plurality of predictive variables that is being analyzed.

11. The method of claim 8 wherein the deviance value is calculated as follows:

12. The method of claim 8 further comprising the step of ranking each of the plurality of predictive variables based on the contribution of a predictive variable to the score wherein a predictive variable having a higher calculated contribution value is assumed to have had a greater effect on the score.

13. A method of evaluating the contribution of each of the plurality of variables in a statistical model comprised of a scoring formula having at least one value associated with each of the plurality of variables comprising the steps of obtaining a mean value and a standard deviation value for each of the plurality of variables, calculating a slope value for each of the plurality of variables, calculating a deviance value based on the mean value and the standard deviation value for each of the plurality of variables, and multiplying the deviance value and slope value for each of the plurality of variables to quantify the contribution of each of the plurality of variables to the score.

14. The method of claim 13 further comprising the step of populating a storage means with the mean value and standard deviation values for each of the plurality of variables.

15. The method of claim 13 wherein the statistical model is used to assess the profitability of an insurance policy and each of the plurality of variables is associated with at least one of the policyholder and item to be insured.

16. The method of claim 15 wherein a score generated by the model determines the price for the insurance policy and the contribution is used to identify which variables had the greatest effect on the price.

17. In a system that employs a statistical model comprised of a scoring formula having a plurality of predictive variables for generating a score that is representative of a risk associated with an insurance policyholder and for pricing a particular coverage based on the score, a method of quantifying the contribution of each of the plurality of predictive variables to the score generated by the model comprising the steps of populating a database associated with the system with a mean value and a standard deviation value for each of the plurality of predictive variables, calculating a slope value for each of the plurality of predictive variables, calculating a deviance value based on the mean value and the standard deviation value for each of the plurality of predictive variables, and multiplying the deviance value and slope value for each of the plurality of predictive variables to quantify the contribution of each of the plurality of predictive variables to the score.

18. The method of claim 17 further comprising the step of ranking each of the plurality of variables based on the quantified contribution as calculated for each of the plurality of predictive variables.

19. The method of claim 17 wherein the step of calculating the slope further comprises the step of calculating the first derivative of the scoring formula with respect to a predictive variable of the plurality of predictive variables that is being analyzed.

20. The method of claim 17 wherein the deviance value is calculated as follows: