A.6. Using Multi-Dimensional Credibility to Estimate Class Frequency Vectors in Work Comp

Question 1

Couret & Venter’s main insight

Answer 1

Couret & Venter observe that the physical circumstances underlying various injury types are correlated, and they use those correlations to gain additional information in estimating credibility weighted claim frequencies by injury type.

Question 2

How Couret & Venter’s use of injury type compares

to Robertson

Answer 2

The NCCI estimates excess ratios for each injury type

separately, and does not use information about correlations between injury types.

Question 3

3 methods for estimating injury type ratios for a class

Answer 3

1. The hazard group injury type ratios (i.e., Vh)
2. The raw sample data injury type ratios (i.e., Vi)
3. The injury type ratios resulting from the credibility
   procedure (i.e., vi est)

Question 4

Describe a Holdout Sample and why it is used

Answer 4

A Holdout Sample is used to test the predictive ability of a model built on data excluding the holdout sample data. If the model does not do a good job of predicting the holdout sample results, it is likely that the model has been overfit to the sample data used in building the model (or that the model has poor predictive power in general)

Question 5

Two unbiased options for producing a holdout

sample

Answer 5

1. Split data by even and odd years.

2. Split risks randomly between the modeling dataset and the holdout dataset.

Question 6

Reasons Couret & Venter give why initial SSE test

didn’t show much improvement for their procedure

Answer 6

1. Estimators derived from the even year data are designed to fit that data.
2. Class data by year is volatile

Question 7

Quintiles Test steps

Answer 7

1. Sort the injury type relativities produced by the credibility procedure for all classes in increasing order (i.e., the vi est).
2. Group the classes into 5 groups (quintiles) based on the sorted relativities. The size of the quintiles should be set so that each quintile has about the same number of TT claims.
3. Calculate the weighted average injury type relativity across all classes within each quintile and within the hazard group. Do this step for each of the 3 methods and for the holdout sample using their respective relativities.
4. Use the results from step 3 to calculate the SSE for each of the 3 methods.
5. The method that produces the lowest SSE is deemed best, and you would use this method’s injury type ratio for that particular injury type and all classes in that hazard group.

Question 8

Reason that Couret & Venter give why their procedure

doesn’t show an improvement for Hazard Group A

Answer 8

Couret & Venter claim that this is due to the classes in hazard group A being very homogeneous, so they wouldn’t expect the injury type ratios to vary much within that hazard group