Log-linear modelling is advanced as a procedure to identify factors that underlie the relative frequency of occurrence of various characteristics. The purpose of this study is to present a modelling effort using log-linear models to estimate the relationships between driver's fault and carelessness and the traffic variables such as gender, accident severity, and accident time. The study was conducted in four different districts in Ankara, the capital of Turkey. There were 1,325 people selected for the study; and they were asked whether they had been in an accident. Four hundred and forty-eight of them answered that they had been involved in an accident. As drivers, 276 out of 448 people, namely 61.6%, had traffic accidents. The data on the variables, namely gender, driver's fault and carelessness, accident severity and accident time, were collected through a questionnaire survey. Detailed information has been created based on this information. The analysis showed that the best-fit model regarding these variables was the log-linear model. Furthermore, the odds ratio between these variables, the associations of the factors with the accident severity and the contributions of various factors, and the multiple interactions between these variables were assessed. The obtained results provide valuable information in regard to preventing undesired consequences of traffic accidents.