Spatio-temporal interaction is inherent to cases of infectious diseases and occurrences of earthquakes, whereas the spread of other events, such as cancer or crime, is less evident. Statistical significance tests of space–time clustering usually assess the correlation between the spatial and temporal (transformed) distances of the events. Although appealing through simplicity, these classical tests do not adjust for the underlying population nor can they account for a distance decay of interaction. We propose to use the framework of an endemic–epidemic point process model to jointly estimate a background event rate explained by seasonal and areal characteristics, as well as a superposed epidemic component representing the hypothesis of interest. We illustrate this new model-based test for space–time interaction by analysing psychiatric inpatient admissions in Zurich, Switzerland (2007–2012). Several socio-economic factors were found to be associated with the admission rate, but there was no evidence of general clustering of the cases.