A General Monte Carlo Method for Sample Size Analysis in the Context of Network Models

Abstract

We introduce a general method for sample size computations in the context of cross-sectional network models. The method takes the form of an automated Monte Carlo algorithm, designed to find an optimal sample size while iteratively concentrating the computations on the sample sizes that seem most relevant. The method requires three inputs: (1) a hypothesized network structure or desired characteristics of that structure, (2) an estimation performance measure and its corresponding target value (e.g., a sensitivity of 0.6), and (3) a statistic and its corresponding target value that determines how the target value for the performance measure be reached (e.g., reaching a sensitivity of 0.6 with a probability of 0.8). The method consists of a Monte Carlo simulation step for computing the performance measure and the statistic for several sample sizes selected from an initial candidate sample size range, a curve-fitting step for interpolating the statistic across the entire candidate range, and a stratified bootstrapping step to quantify the uncertainty around the recommendation provided.We evaluated the performance of the method for the Gaussian Graphical Model, but it can easily extend to other models. The method displayed good performance, providing sample size recommendations that were, on average, within three observations of a benchmark sample size, with the highest standard deviation of 25.87 observations. The method discussed is implemented in the form of an R package called powerly, available on GitHub and CRAN.