Discussion of "A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks" by Pavel N. Krivitsky, Pietro Coletti, and Niel Hens.

This article explores the challenges of making accurate inferences about populations based on samples in settings where the data is dependent, such as network, spatial, and temporal data. It emphasizes the need for statistical research that is both driven by real-world applications and adheres to statistical principles. The article discusses the assumption of local dependence and suggests the possibility of relaxing this assumption to account for overlapping social circles. It also discusses regression-type diagnostic tools based on residuals and score tests for goodness-of-fit. The authors propose using residuals to test whether an additional network feature should be added to a model and suggest using a score test to test the composite null hypothesis. These diagnostics are applicable to an augmented exponential family with canonical parameter vector and sufficient statistic vector. The article also highlights the importance of out-of-sample assessments and scalable inference methods in network analysis. [Extracted from the article]