Reconstructing ties between archaeological contexts may contribute to explain and describe a variety of past social phenomena. Several models have been formulated to infer the structure of such archaeological networks. The underlying propositions about mechanisms regulating the formation of ties in the past are often articulated on a dyadic basis and therefore rarely account for dependencies among ties. Here, we present a general framework in which we combine exponential random graph models with archaeological substantiations of mechanisms that may be responsible for network formation to account for tie dependence. We use data collected over a set of sites in the Caribbean during the period AD 100 - 400 to illustrate the steps to obtain a network reconstruction.