Modern lane centering assistance systems often use the mid-lane as a reference line for tracking. However, human drivers prefer to keep an offset to the mid-lane. Therefore, we have proposed in our previous work a driver model which calculates human-like offset values and enable the path planner to plan human-like paths. The driving data of 15 drivers have been analyzed. It has been revealed that drivers behave differently in left or right curves and choose to drive on either the left or the right side in straight road sections. Therefore, we extend our model to handle these traits. We have shown that the extended model outperforms the previous symmetric model.