We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Applications to a growth curve model (Gelfand, Hills, Racine-Poon, and Smith 1990) and a complex hierarchical model for opinion data (Bradlow 1994) are described. Our focus on case influence on parameters is complementary to other work which measures influence by distances between posterior or predictive...