Discriminating causal clustering from inhomogeneity in point processes is of high interest for a variety of applications. We propose a simulation-based test based on the relative likelihood of Hawkes models, Poisson cluster models, and inhomogeneous Poisson models, and compare with the time reversal test of Cordi et al. (2017). Under general conditions, causal clustering can be distinguished from inhomogeneity with high accuracy using these tests, with the test proposed here exhibiting somewhat higher power in simulations. The methods are applied to crime data on reported shootings in Boston from 2015-2021, where strong evidence of retaliatory triggering of events is seen in certain areas.