Thanks to the popularity of online experiments, in which the treatment assignment of one unit may influence the outcome of another, the problem of experimental design and analysis under network interference is receiving increasing attention. While experiments with binary outcomes are common in practice, most experimental outcome models proposed in the literature are built for continuous outcomes. In this presentation, we consider a class of binary models to analyze binary network experiments which allows the network effects to be modeled flexibly using nonlinear functions. Based on the model, we define causal quantities and hypothesis tests of interest and demonstrate how estimation and inference can be done via the maximum likelihood framework. Different specifications of the proposed model class are then applied to analyze a real-world agricultural insurance experiment. This example demonstrates the need for nonlinear network effect modeling.