Vehicles with driver assistance and even autonomous driving capabilities have become widely spread on the roads in the last decades. Replacing human drivers even partially is a complex issue, as these driving systems must be safe and reliable under various conditions. The complexity is increased further by the fact that driving systems must interact with human participants of the traffic: the driver and passengers of the given vehicle as well as drivers in other vehicles or pedestrians. The market trends show that even though more and more driving assistance solutions are available, the vehicle users often refuse to use them as the behavior of these systems feels unnatural. Therefore, manufacturers have initiated the development of personalized driving assistance which motivates research in driver modeling and driving style classification. One of the most controversial assistance function is lane keeping. In our paper, we propose various different model structures that are able to capture the lane offset selection behavior of human drivers. It is shown that a static linear regression model provides reasonable accuracy and robustness in modeling the lane offset. While Gaussian Process models offer more accuracy, their training time is more demanding. It is shown, that a combination of linear and polynomial third-order basis functions offers a good tradeoff to efficiently describe the lane offset selection of human drivers. Our observations are based on studying real driving data from 41 drivers, whose behavior is modeled with the considered model structures. Then, using the corresponding model parameters, drivers are clustered into two driving style groups. Using the collective data of these groups the models are fitted to all data records in the two driver groups. Any new driver can be classified into one of these groups, and the aggregated models can be further personalized to to increase user satisfaction with the lane keeping systems.