Jemain, “Handling Overdispersion with Negative Binomial and Generalized Poisson Regression Models,” CAS Winter Forum including the Ratemaking Call Papers
Bibliographic record
Abstract
In actuarial hteramre, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In particular, the Poisson regression model, which is also known as the Generahzed Linear Model (GLM) with Poisson error structure, has been x~adely used in the recent years. However, it is also recognized that the count or frequency data m insurance practice often display overdispersion, i.e., a situation where the variance of the response variable exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standard errors and overstate the sigruficance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This paper suggests the Negative Binomial and Generalized Poisson regression models as ahemafives for handling overdispersion. If the Negative Binomial and Generahzed Poisson regression models are fitted by the maximum likelihood method, the models are considered to be convenient and practical; they handle overdispersion, they allow the likelihood ratio and other standard maximum likelihood tests to be implemented, they have good properties, and they permit the fitting procedure to be carried out by using the herative Weighted I_,east Squares OWLS) regression similar to those of the Poisson. In this paper, two types of regression model will be discussed and applied; multiplicative and additive. The multiplicative and additive regression models for Poisson, Negative Binomial and Generalized Poisson will be fitted, tested and compared on three different sets of claim frequency data; Malaysian private motor third part T property ' damage data, ship damage incident data from McCuUagh and Nelder, and data from Bailey and Simon on Canadian private automobile liabili~,.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.071 | 0.169 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.005 | 0.009 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".