We introduce a Bayesian approach to conduct inferential analyses on dyadic data while accounting for interdependencies between observations through a set of additive and multiplicative effects (AME). The AME model is built on a generalized linear modeling framework and is thus flexible enough to be applied to a variety of contexts. We contrast the AME model to two prominent approaches in the literature: the latent space model (LSM) and the exponential random graph model (ERGM). Relative to these approaches, we show that the AME approach is (a) to be easy to implement; (b) interpretable in a general linear model framework; (c) computationally straightforward; (d) not prone to degeneracy; (e) captures first-, second-, and third-order network dependencies; and (f) notably outperforms ERGMs and LSMs on a variety of metrics and in an out-of-sample context. In summary, AME offers a straightforward way to undertake nuanced, principled inferential network analysis for a wide range of social science questions.