This paper focuses on the estimation of a driver's psychological characteristics using driving data for driving assistance systems. Driving assistance systems that support drivers by adapting individual psychological characteristics can provide appropriate feedback and prevent traffic accidents. As a first step toward implementing such adaptive assistance systems, this research aims to develop a model to estimate drivers' psychological characteristics, such as cognitive function, psychological driving style, and workload sensitivity, from on-road driving behavioral data using machine learning and deep learning techniques. We also investigated the relationship between driving behavior and various cognitive functions, including the Trail Making Test (TMT) and Useful Field of View (UFOV) test, through regression modeling. The proposed method focuses on road type information and captures various durations of time-series data observed from driving behaviors. First, we segment the driving time-series data into two road types, namely, arterial roads and intersections, to consider driving situations. Second, we further segment data into many sequences of various durations. Third, statistics are calculated from each sequence. Finally, these statistics are used as input features of machine learning models to estimate psychological characteristics. The experimental results show that our model can estimate a driver's cognitive function, namely, the TMT (B) and UFOV test scores, with Pearson correlation coefficients r of 0.579 and 0.708, respectively. Some characteristics, such as psychological driving style and workload sensitivity, are estimated with high accuracy, but whether various duration segmentation improves accuracy depends on the characteristics, and it is not effective for all characteristics. Additionally, we reveal important sensor and road types for the estimation of cognitive function.