Hyperparameter optimisation of generalised linear models in vehicle insurance pricing

Abstract

Predictive modelling is increasingly important in data-driven decision-making, yet traditional statistical approaches such as the Generalised Linear Model (GLM) with a Gamma distribution often exhibit limited accuracy when applied to complex datasets. This study compared the performance of the standard GLM with an optimised iterative hybrid approach employing machine learning algorithms, including XGBoost, RF, Gradient Boosting GBM), and Artificial Neural Networks (ANN). Models were trained and tested on the same dataset, and performance was assessed using three metrics: coefficient of determination (R²), root mean squared error (RMSE) and mean absolute error (MAE). Hypothesis testing was conducted using t-tests and F-tests at a 5% significance level. Results showed that the GLM baseline achieved modest explanatory power (training R² = 0.23; test R² = 0.19) and comparatively high prediction errors (RMSE ≈ 83,992–84,789; MAE ≈ 56,943–60,897). In contrast, hybrid machine learning models performed substantially better, with XGBoost, RF, and ANN each achieving R² = 0.42 on the test set, RMSE values around 81,200, and competitive MAE scores. Statistical testing confirmed significant improvements in R² and RMSE, while MAE differences were less conclusive under unequal variance assumptions. These findings highlight the limitations of conventional GLMs and the enhanced generalisability of hybrid methods. In conclusion, the optimised iterative hybrid approach offers a more reliable and accurate predictive framework. It is recommended that organisations adopt hybrid models, particularly XGBoost and ANN, for predictive tasks requiring high levels of accuracy, while future research should investigate issues of interpretability, computational efficiency, and scalability in applied context.