Towards an Encompassing Theory of Network Models

Network models like the Ising model are increasingly used in psychological research. In a recent article published in this journal, Brusco, Steinley, Hoffman, Davis-Stober, and Wasserman (in press) provide a critical assessment of the conditions that underlie the Ising model and the eLasso method that is commonly used to estimate it. In this commentary, we show that their main criticisms are unfounded. First, where Brusco et al. suggest that Ising models have little to do with classical network models such as random graphs, we show that they can be fruitfully connected. Second, if one makes this connection it is immediately evident that Brusco et al.’s second criticism – that the Ising model requires complete population homogeneity and does not allow for individual differences in network structure – is incorrect. In particular, we establish that if every individual has their own topology, and these individual differences instantiate a random graph model, the Ising model will hold in the population. Hence, population homogeneity is sufficient for the Ising model, but it is not necessary, as Brusco et al. suggest. Third, we address Brusco et al.’s criticism regarding the sparsity assumption that is made in common uses of the Ising model. We show that this criticism is misdirected, as it targets a particular estimation algorithm for the Ising model rather than the model itself. We also describe various established and validated approaches for estimating the Ising model for networks that violate the sparsity assumption. Finally, we outline important avenues for future research.