Human speakers generally find it easy to refer to entities in such a way that their hearers can determine who or what is being talked about. In an attempt to model this behaviour, researchers in computational linguistics have explored the development of algorithms that operate in a deliberate manner, choosing attributes of an intended referent on the basis of their ability to distinguish that entity from its distractors. Psycholinguistic models, on the other hand, suggest that speakers align their referring expressions at several linguistic levels with those used previously in the discourse. This implies more subconscious reuse, and less deliberate choice, than is found in computational models of referring expression generation. Which of these is a more accurate characterisation of what people do? Do both models capture aspects of human referring behaviour? In this paper, we use a machine-learning approach to explore these questions. In our first study, we examine how underlying factors of the psycholinguistic and the computational models impact on the production of reference in dialogue. In our second study, we explore the psychological validity of another crucial aspect of some computational approaches to reference production: their serial dependency characteristic, whereby attributes are included in a referring expression based on which other attributes have already been chosen. The results of both studies suggest that the assumptions underpinning computational algorithms do not play a large role in people's referring behaviour.