Direct Analysis of Pre-Adjusted Loss Cost, Frequency or Severity in Tweedie Models

Response data (loss cost, claim frequency or claim severity) are often pre-adjusted with known factors and directly analyzed with generalized linear models (GLM). This paper shows that the exposure weights should also be adjusted if the Tweedie distribution with log link is used in such direct analysis. An advantage of the direct analysis over GLM offsetting is that the structure of the original dataset may be simplified significantly after removing the known factors. Direct analysis is a convenient tool for directly modeling loss ratio and for removing known territory factors from the dataset. Implementation in EMBLEM and SAS is discussed, and a computationally efficient SAS macro is provided for Tweedie models.

Keywords: Predictive Modeling; GLM offset; Ratemaking; Tweedie Model; EMBLEM; SAS.