Latent variable network models that accommodate edge correlations implicitly, by assuming an underlying latent factor, are increasing in popularity. Although, these models are examples of what is a growing body of research, much of the research is focused on proposing new models or extending others. There has been very little work on unifying the models in a single framework. In this paper, we present a complete framework that organizes existing latent variable network models within an integrative generalized additive model. Our framework is called Conditionally Independent Dyad (CID) models, and includes existing network models that assume dyad (or edge) independence conditional on latent variables and other components in the model. We further discuss practical aspects of model fitting such as posterior parameter estimation via MCMC, identifiability of parameters, approaches to handle missing data and model selection via cross-validation, for the proposed additive CID models. Finally, by presenting several data examples, we illustrate the utility of the proposed framework and provide advice on selecting components for building new CID models.

通过假设潜在的潜在因素，隐含地容纳边缘相关性的潜在变量网络模型正日益普及。尽管这些模型只是不断发展的研究实例，但许多研究都集中在提出新模型或扩展其他模型上。在单一框架中统一模型的工作很少。在本文中，我们提出了一个完整的框架，该框架在集成的广义加性模型内组织现有的潜在变量网络模型。我们的框架称为有条件独立Dyad（CID）模型，包括现有网络模型，这些模型假定dyad（或边缘）独立性取决于潜在变量和模型中的其他组件。我们进一步讨论了模型拟合的实际方面，例如通过MCMC进行后参数估计，对于所提出的附加CID模型，参数的可识别性，处理丢失数据的方法以及通过交叉验证的模型选择。最后，通过提供几个数据示例，我们说明了所提出框架的实用性，并为选择用于构建新CID模型的组件提供了建议。