GAMLSS for Longitudinal Multivariate Claim Count Models
Bibliographic record
Abstract
By generalizing traditional regression frameworks, generalized additive models for location, scale, and shape (GAMLSSs) allow parametric or semiparametric modeling of one or more parameters of distributions that are not members of the linear exponential family. Consequently, these GAMLSS approaches offer an interesting theoretical framework to allow the use of several potentially helpful distributions in actuarial science. GAMLSS theory is coupled with longitudinal approaches for counting data because these approaches are essential to predictive pricing models. Indeed, they are mainly known for modeling the dependence between the number of claims from the contracts of the same insured over time. Considering that the models’ cross-sectional counterparts have been successfully applied in actuarial work and the importance of longitudinal models, we show that the proposed approach allows one to quickly implement multivariate longitudinal models with nonparametric terms for ratemaking. This semiparametric modeling is illustrated using a dataset from a major insurance company in Canada. An analysis is then conducted on the improvement of predictive power that the use of historical data and nonparametric terms in the modeling allows. In addition, we found that the weight of past experience in bonus–malus predictive premiums analysis is reduced in comparison with a parametric model and that this method could help for continuous covariate segmentation. Our approach differs from previous studies because it does not use any simplifying assumptions as to the value of the a priori explanatory variables and because we have carried out a predictive pricing integrating nonparametric terms within the framework of the GAMLSS in an explicit way, which makes it possible to reproduce the same type of study using other distributions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.010 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.015 | 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".