Assessing the use of the moving window approaches when monitoring social networks using a degree corrected stochastic block model

Abeer A Zaki,Mahmoud A Mahmoud,Nesma A Saleh

doi:10.1108/reps-08-2020-0125

Abstract

PurposeThis study aims to assess the effect of updating the Phase I data – to enhance the parameters' estimates – on the control charts' detection power designed to monitor social networks.Design/methodology/approachA dynamic version of the degree corrected stochastic block model (DCSBM) is used to model the network. Both the Shewhart and exponentially weighted moving average (EWMA) control charts are used to monitor the model parameters. A performance comparison is conducted for each chart when designed using both fixed and moving windows of networks.FindingsOur results show that continuously updating the parameters' estimates during the monitoring phase delays the Shewhart chart's detection of networks' anomalies; as compared to the fixed window approach. While the EWMA chart performance is either indifferent or worse, based on the updating technique, as compared to the fixed window approach. Generally, the EWMA chart performs uniformly better than the Shewhart chart for all shift sizes. We recommend the use of the EWMA chart when monitoring networks modeled with the DCSBM, with sufficiently small to moderate fixed window size to estimate the unknown model parameters.Originality/valueThis study shows that the excessive recommendations in literature regarding the continuous updating of Phase I data during the monitoring phase to enhance the control chart performance cannot generally be extended to social network monitoring; especially when using the DCSBM. That is to say, the effect of continuously updating the parameters' estimates highly depends on the nature of the process being monitored.

Highlights

Statistical process control (SPC) is a set of statistical techniques used to achieve process stability through reducing its variability to the extent possible
In all of the out-of-control scenarios considered, the Shewhart control chart performs significantly better when its control limits are estimated using a fixed window of networks than when estimated using any of the moving window approaches
As for the exponentially weighted moving average (EWMA) chart, the simulation results indicate that its performance is indifferent whether the fixed window or the fixed-sized moving window of networks is used in estimating its control limits

Summary

Introduction

Statistical process control (SPC) is a set of statistical techniques used to achieve process stability through reducing its variability to the extent possible. Wilson et al (2019) integrated an SPC technique with a parametric random graph model to monitor dynamic networks in order to detect significant structural anomalies They applied the Shewhart control chart to monitor the parameters of a dynamic version of the DCSBM. 3. Monitoring the DCSBM using quality control charts As previously illustrated, the main objective of network surveillance is to detect any influential change in the communication level between the network nodes. If the chart statistic exceeds one of the control limits, there is a possible structural change in the network As previously mentioned, both the Shewhart and EWMA charts are used to monitor the maximum likelihood estimators of the DCSBM parameters defined in Equation (2). If one is interested in detecting small shifts in the process parameters, small weights (λ) are given to the recent observations

Performance assessment

Findings

Conclusion