Frequency analysis residuals?

Professional Actuarial Topics Property/Casualty
1

When I think of residuals, I think actual - predicted.

But what’s a residual for a frequency analysis? Because you train models on a binary, 1 or 0, but the predicted result is an expected frequency per unit of exposure…so how would you calculate a “residual” for a frequency analysis?

Severity is much easier, you can calculate actual severity(continuous) - predicted severity(also continuous)

Till all are one,

Epistemus

2

One method that I’ve seen is “bunched” residuals: you bucket the data according to some consistent level (often aggregating to unique values of input variables of the model . . . with some level of grouping for continuous or near-continuous variables) so that the predicted value has very small (or zero) variance within the bin. Then you can do the actual (rate) less the predicted.

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3

Actually, the correct term to search for would be “crunched residuals” . . . this is often available in most statistical packages.

Another method for this is to group the residuals into a fixed number of buckets (e.g., 500 or 10,000 depending on the size of your data) and graph the average residual value.

4

Right…but what, exactly, are the residuals in this context? How would you define it?

5

It’s still going to be some form of “actual - predicted”; but there are some various transformations that you might consider to help with the analysis.

Here is a resource from a google search on “residuals”:
Understanding Deviance Residuals | UVA Library (virginia.edu)

You might also look at chapter 6 of the CAS Monograph #5:
Understanding Deviance Residuals | UVA Library (virginia.edu)

To a large extent, I’ve seen the “deviance residual” used quite a bit in practice; but variations of the Pearson’s residual have appeared in some of the competitive filings I’ve reviewed (but this was about 10 years ago).

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