This is the accepted version of the following article: Pirotta, E, Edwards, EWJ, New, L & Thompson, P 2018, 'Central place foragers and moving stimuli: a hidden-state model to discriminate the processes affecting movement' Journal of Animal Ecology, vol 87, no. 4, pp. 1116-1125. , which has been published in final form at https://doi.org/10.1111/1365-2656.12830. This article may be used for non-commercial purposes in accordance with the Wiley Self Archiving Policy [https://authorservices.wiley.com/author-resources/JournalAuthors/licensing-open-access/open-access/self-archiving.html].