Changes in the properties of extreme rainfall events have been observed worldwide. In relation to the discussion of ongoing climatic changes, it is of high importance to attribute these changes to known sources of climate variability. Focusing on spatial and temporal changes in the frequency of extreme rainfall events, a statistical model is tested for this purpose. The model is built on the theory of generalized linear models and uses Poisson regression solved by generalized estimation equations. Spatial and temporal explanatory variables can be included simultaneously, and their relative importance can be assessed. Additionally, the model allows for a spatial correlation between the measurements. Data from a Danish rain gauge network are used as a case study for model evaluation. Focusing on 10 min and 24 h rainfall extremes, it was found that regional variation in the mean annual precipitation could explain a significant part of the spatial variability. Still, this variable was found to be of minor influence in comparison to explanatory variables in the temporal domain. The identified significant temporal variables comprise the East Atlantic pattern, the average summer precipitation, and the average summer temperature. The two latter showed a high relative importance. The established link will be beneficial when predicting future occurrences of precipitation extremes.