Otolith chemical analyses enable researchers to follow the dispersal pathways of individual fish through time. Given that water masses have spatially or temporally variable chemical signatures (or correlates thereof) and that this variability can be modelled statistically, we have the potential to describe a fish’s dispersal history by examining a temporal transect of elemental concentrations throughout the otolith generated from laser ablation inductively coupled plasma mass spectrometry. Statistical analyses tend to focus on temporal trajectories of individual elements or analyse multiple elements at single points in time. We have developed a customised statistical technique allowing detailed exploration of elemental signatures using maximum likelihood methods. The benefit of this approach is the ability to model chronological series of otolith measurements for all sampled fish and all elements simultaneously, while providing explicit treatment of variability in the data. We used data from a Caribbean fish population to compare traditional analysis techniques with this likelihood-based approach, showing their relative capacities to test among alternative hypotheses regarding the dispersal trajectories of individual fish. By incorporating information specific to the species’ natural history and to the analytical techniques, we can explore more detailed models of fish movement than were possible using pre-existing approaches.