This paper estimates the determinants of decision time for different types of decision maker in the context of an experimental investigation of multiple prior models of behaviour under ambiguity. Four models are considered: Expected Utility, Smooth, Rank Dependent Expected Utility and Alpha model. The results of a mixture model which assigns subjects to types enable us to distinguish the factors influencing the decision time of each of these four types. We find that the different types are influenced by different factors. In general, the Rank Dependent type takes more time, followed by the Smooth, the Expected Utility and finally the Alpha type, whose decision time is always the lowest. Our results reflect the relative complexity of the preference functionals used by the different types. Consequently, the importance of looking at the process of pairwise choices rather than simply at the choice made is raised to the attention of theorists and analysts.