This dissertation begins by demonstrating that publication bias can depend on factors other than statistical significance, including study characteristics like social preferences and source of funding. After providing an empirical example of differing bias patterns, the dissertation presents a weight-function model that is capable of accommodating moderators of publication bias. Subsequent chapters describe a version of the model designed for sensitivity analyses, a Bayesian version, and an R package for implementing the model. Throughout the dissertation, the performance of each version of the model is assessed via simulation. Overall, the model outperforms competing models across simulation cells, and appears to be an effective tool in cases where study characteristics affect publication bias.