# Multilevel Hierarchical Bayesian Modeling of Cross-National Factors in Vehicle Sales
## 1 Introduction  
SUVs (sport utility vehicles), as a car segment, have become a foundation within the automotive industry due to their versatility. Initially designed for challenging terrains and poor road conditions, today's SUVs cater to a broad spectrum of needs, offering models that range from compact urban crossovers to full-sized luxury cars. Their adaptability makes them perfect for families requiring extra space, outdoor enthusiasts in need of toughness, and those looking for a symbol of status and sophistication. The SUV market continues to grow, with manufacturers extending their current range of new models or engine versions to better suit customer needs. Following North America in the last decade, the trend can likewise be seen in Europe. A great example of this is Poland, where, despite the end of the pandemic, galloping inflation and the ever-increasing cost of living, SUV sales continue to grow by the year. In 2022, they accounted for as much as 46.4% of all new car registrations [1]. Based on Figure 1, which uses the previous year's data, seven of the top ten best-selling passenger cars were SUVs. Furthermore, this type of car is usually considerably more expensive to buy than the other classic body types, which further prompts a consideration of what factors might have influenced purchasers' decisions for these types of cars. Their rising popularity and utility drove our focus on SUVs. The problem we focused on investigating was the impact of economic and geographical factors on SUV sales, and we generated a model that predicts these sales. We chose to study whether aspects such as the quality of infrastructure, geographical location and a country's welfare do, in fact, determine whether this type of car is sold more or less often. There are many ways to predict car sales, but very few of them focus on SUVs. Indian scientists, in an article, discussed the development of a machine learning model to predict whether a customer would buy an SUV based on data collected from banks [3]. The model applies logistic regression to analyse data on customer age and estimated salary to forecast their purchasing behaviour. In addition, they explored various machine learning and data mining techniques used to handle the chosen issue. It was the only article we found that focused on the creation of an SUV sales prediction model. Another interesting and popular approach to general car purchase prediction is the reliance on sentiment analysis. The main difference between them is the sources of analysed data. Some individuals base their analysis on information collected from car review websites and social media [4], whereas others additionally incorporate data derived from Google Trends [5]. In view of the possible approaches, we chose to use Bayesian inference. It is a statistical technique that combines prior knowledge with new data to make forecasts about uncertain events, based on [PERSON]'s rule. We rely on it to update the likelihood of an event in the case of getting more information about it [6]. This approach not only offers an estimate but also quantifies the uncertainty around it, providing a full probability distribution for the parameters being studied. The key advantage of this approach lies in its adaptability, which comes from its ability to incorporate various levels of randomness and merge information from different sources while considering all plausible sources of uncertainty in inferential summaries. Bayesian methods tend to create smoothed estimates in complex data structures, which improves their capacity to deliver more accurate responses that reflect real-world situations. Moreover, Bayesian inferences depend on probability models that inevitably include simplifications when attempting to depict complex real-world interactions and relationships. If Bayesian responses significantly vary based on scientifically sound assumptions that cannot be disputed based on the data, then the range of potential conclusions should be recognised as valid [7].