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Social network data often contain missing values because of the sensitive nature of the information collected and the dependency among the network actors. As a response, network imputation methods including simple ones constructed from network structural characteristics and more complicated model-based ones have been developed. Although past studies have explored the influence of missing data on social networks and the effectiveness of imputation procedures in many missing data conditions, the current study aims to evaluate a more extensive set of eight network imputation techniques (i.e., null-tie, Reconstruction, Preferential Attachment, Constrained Random Dot Product Graph, Multiple Imputation by Bayesian Exponential Random Graph Models or BERGMs, k-Nearest Neighbors, Random Forest, and Multiple Imputation by Chained Equations) under more practical conditions through comprehensive simulation. A factorial design for missing data conditions is adopted with factors including missing data types, missing data mechanisms, and missing data proportions, which are applied to generated social networks with varying numbers of actors based on 4 different sets of coefficients in ERGMs. Results show that the effectiveness of imputation methods differs by missing data types, missing data mechanisms, the evaluation criteria used, and the complexity of the social networks. More complex methods such as the BERGMs have consistently good performances in recovering missing edges that should have been present. While simpler methods like Reconstruction work better in recovering network statistics when the missing proportion of present edges is low, the BERGMs work better when more present edges are missing. The BERGMs also work well in recovering ERGM coefficients when the networks are complex and the missing data type is actor non-response. In conclusion, researchers analyzing social networks with incomplete data should identify the network structures of interest and the potential missing data types before selecting appropriate imputation methods. [ABSTRACT FROM AUTHOR]

The brain can be modelled as a network with nodes and edges derived from a range of imaging modalities: the nodes correspond to spatially distinct regions and the edges to the interactions between them. Whole-brain connectivity studies typically seek to determine how network properties change with a given categorical phenotype such as age-group, disease condition or mental state. To do so reliably, it is necessary to determine the features of the connectivity structure that are common across a group of brain scans. Given the complex interdependencies inherent in network data, this is not a straightforward task. Some studies construct a group-representative network (GRN), ignoring individual differences, while other studies analyse networks for each individual independently, ignoring information that is shared across individuals. We propose a Bayesian framework based on exponential random graph models (ERGM) extended to multiple networks to characterise the distribution of an entire population of networks. Using resting-state fMRI data from the Cam-CAN project, a study on healthy ageing, we demonstrate how our method can be used to characterise and compare the brain’s functional connectivity structure across a group of young individuals and a group of old individuals.

• Compares state of the art missing network data treatment methods. • Evaluation on descriptive statistics, link reconstruction, and model parameters. • Tested on simulated networks varying in structure and size. • Multiple imputation outperforms simpler methods. • Multiple imputation with Bayesian ERGMs overall performed best. This paper compares several missing data treatment methods for missing network data on a diverse set of simulated networks under several missing data mechanisms. We focus the comparison on three different outcomes: descriptive statistics, link reconstruction, and model parameters. The results indicate that the often used methods (analysis of available cases and null-tie imputation) lead to considerable bias on descriptive statistics with moderate or large proportions of missing data. Multiple imputation using sophisticated imputation models based on exponential random graph models (ERGMs) lead to acceptable biases in descriptive statistics and model parameters even under large amounts of missing data. For link reconstruction multiple imputation by simple ERGM performed well on small data sets, while missing data was more accurately imputed in larger data sets with multiple imputation by complex Bayesian ERGMs (BERGMs). [ABSTRACT FROM AUTHOR]

• Exponential random graph models (ERGMs) are a flexible class of network models. • We develop a novel ERGM-based Bayesian multilevel model for groups of brain networks. • Fitting networks simultaneously yields more precise estimates for model parameters. • Our method can also assess differences in network properties between multiple groups. • We demonstrate our method on resting-state fMRI data from Cam-CAN, an ageing study. The brain can be modelled as a network with nodes and edges derived from a range of imaging modalities: the nodes correspond to spatially distinct regions and the edges to the interactions between them. Whole-brain connectivity studies typically seek to determine how network properties change with a given categorical phenotype such as age-group, disease condition or mental state. To do so reliably, it is necessary to determine the features of the connectivity structure that are common across a group of brain scans. Given the complex interdependencies inherent in network data, this is not a straightforward task. Some studies construct a group-representative network (GRN), ignoring individual differences, while other studies analyse networks for each individual independently, ignoring information that is shared across individuals. We propose a Bayesian framework based on exponential random graph models (ERGM) extended to multiple networks to characterise the distribution of an entire population of networks. Using resting-state fMRI data from the Cam-CAN project, a study on healthy ageing, we demonstrate how our method can be used to characterise and compare the brain's functional connectivity structure across a group of young individuals and a group of old individuals. [ABSTRACT FROM AUTHOR]