The objective of this research is to explore the relation between personal characteristics of pedestrians and their crossing behaviour in front of an automated vehicle (AV). For this purpose, a simulation experiment was developed using Agent-Based Modelling (ABM) techniques. Sixty participants were asked to cross the road in a virtual environment displayed on a computer screen, allowing to record their crossing behaviour when in the presence of AVs and conventional vehicles (CVs). In some experimental configurations, the AVs communicated their intention to continue or not to continue their trajectories through the use of lights. The ABM allowed controlling the behaviour of the vehicles when interacting with the simulated avatar of the respondents. The subjects of the experiment were also asked to fill in a questionnaire about usual behaviour in traffic, as well as attitudes and risk perceptions toward crossing roads. The questionnaire data were used to estimate individual specific behavioural latent variables by means of principal component analysis which resulted in three main factors named: violations, lapses, and trust in AVs. The results of generalized linear mixed models applied to the data showed that besides the distance from the approaching vehicle and existence of a zebra crossing, pedestrians' crossing decisions are significantly affected by the participants' age, familiarity with AVs, the communication between the AV and the pedestrian, and whether the approaching vehicle is an AV. Moreover, the introduction of the latent factors as explanatory variables into the regression models indicated that individual specific characteristics like willingness to take risks and violate traffic rules, and trust in AVs can have additional explanatory power in the crossing decisions.