Determining the degree to which predation affects prey abundance in natural communities constitutes a key goal of ecological research. Predators can affect prey through both consumptive effects (CEs) and nonconsumptive effects (NCEs), although the contributions of each mechanism to the density of prey populations remain largely hypothetical in most systems. Common statistical methods applied to time series data cannot elucidate the mechanisms responsible for hypothesized predator effects on prey density (e.g., differentiate CEs from NCEs), nor provide parameters for predictive models. State space models (SSMs) applied to time series data offer a way to meet these goals. Here, we employ SSMs to assess effects of an invasive predatory zooplankter, Bythotrephes longimanus, on an important prey species, Daphnia mendotae, in Lake Michigan. We fit mechanistic models in a SSM framework to seasonal time series (1994-2012) using a recently developed, maximum likelihood-based optimization method, iterated filtering, which can overcome challenges in ecological data (e.g. nonlinearities, measurement error, and irregular sampling intervals). Our results indicate that B. longimanus strongly influences D. mendotae dynamics, with mean annual peak densities of B. longimanus observed in Lake Michigan estimated to cause a 61% reduction in D. mendotae population growth rate and a 59% reduction in peak biomass density. Further, the mechanism underlying the B. longimanus effect is most consistent with an NCE via reduced birth rates. The SSM approach also provided estimates for key biological parameters (e.g., demographic rates) and the contribution of dynamic stochasticity and measurement error. Our study therefore highlights the utility of SSMs to enhance inference for species interactions from time series data. In particular, our findings provide evidence derived directly from survey data that the invasive zooplankter B. longimanus is affecting zooplankton demographics and offer parameter estimates needed to inform predictive models that explore the effect of B. longimanus under different scenarios such as climate change.