An Investigative Comparison of Bayesian and Classical Logistic Regression in Modeling Motor Insurance Preferences

Abstract

This study illustrates the importance of investigative analysis (IA) in a statistical modeling activity. Wrong inferences are inevitable when a thorough investigation of the model variables is missing. The concept could be considered exploratory data analysis (EDA) but labeled as investigative analysis to portray the focus: investigating the particular specification of the model variables that leads to the correct inference. Logistic regression analysis was carried out to investigate factors influencing motor insurance subscription preferences, explicitly focusing on third-party and comprehensive insurance policies, using both Bayesian and classical approaches. The dataset of 59 subscribers includes variables such as type of policy, age, sex, profession, and area of residence. The dependent variable is the type of motor insurance policy subscribed to (third-party or comprehensive).Akaike Information criteria (AIC), Residual Deviance (RD), and area under the curve (AUC) showed that the final specification of the model (AUC = 79.46, RD = 67.46, AUC = 0.7417) was better than the first (AUC = 88.643, RD = 66.643, AUC = 0.7292).The analysis identified profession as a significant factor influencing the choice between thirdparty and comprehensive insurance, implying that individuals in certain professions are more likely to opt for comprehensive coverage. In contrast, others would prefer the third-party type and suggest the need for targeted strategies that consider specific professional groups. More importantly, the result revealed that, while profession plays a crucial role in motor insurance subscription decisions in the dataset, some other variable specifications had a contradicting result. The research underscores the significance of investigative analysis in drawing out the information in a dataset under study. Careful exploration and analysis would ensure the elicitation of vital information.