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Redefining the deviance objective for generalised linear models

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  • Lovick, A. C.
  • Lee, P. K. W.

Abstract

This paper defines the ‘Case Deleted’ Deviance - a new objective function for evaluating Generalised Linear Models, and applies this to a number of practical examples in the pricing of general insurance. The paper details practical approximations to enable the efficient calculation of the objective, and derives modifications to the standard Generalised Linear Modelling algorithm to allow the derivation of scaled parameters from this measure to reduce potential over fitting to historical data. These scaled parameters improve the predictiveness of the model when applied to previously unseen data points, the most likely being related to future business written. The potential for over fitting has increased due to number of factors now used, particularly in pricing personal lines business and the advent of price comparison sites which has increased the penalties of mis-estimation. New material in this paper has been included in a UK patent application No. 1020091.3.

Suggested Citation

  • Lovick, A. C. & Lee, P. K. W., 2012. "Redefining the deviance objective for generalised linear models," British Actuarial Journal, Cambridge University Press, vol. 17(3), pages 491-509, September.
    • Handle: RePEc:cup:bracjl:v:17:y:2012:i:03:p:491-509_00
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