Network models like the Ising model are increasingly used in psychological research. In a recent article published in this journal, Brusco et al. (2019) 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. (2019) 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 (2019) 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. (2019) suggest. Third, we address Brusco et al.’s (2019) 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.

中文翻译：

---

走向包容性的网络模型理论：回复 Brusco、Steinley、Hoffman、Davis-Stober 和 Wasserman (2019)。

像伊辛模型这样的网络模型越来越多地用于心理学研究。在该杂志最近发表的一篇文章中，Brusco 等人。(2019) 对 Ising 模型和通常用于估计该模型的 eLasso 方法的条件进行了严格评估。在这篇评论中，我们表明他们的主要批评是没有根据的。首先，布鲁斯科等人。（2019）表明 Ising 模型与随机图等经典网络模型关系不大，我们证明它们可以有效地连接。其次，如果有人建立这种联系，那么很明显，Brusco 等人 (2019) 的第二个批评——伊辛模型需要完全的群体同质性，并且不允许网络结构中的个体差异——是不正确的。特别是，我们确定，如果每个个体都有自己的拓扑，并且这些个体差异实例化随机图模型，则伊辛模型将在群体中成立。因此，群体同质性对于伊辛模型来说是足够的，但并不是必需的，正如 Brusco 等人所言。（2019）建议。第三，我们解决了 Brusco 等人（2019）对伊辛模型常见使用中的稀疏性假设的批评。我们表明这种批评是错误的，因为它针对的是伊辛模型的特定估计算法，而不是模型本身。我们还描述了各种已建立且经过验证的方法，用于估计违反稀疏性假设的网络的 Ising 模型。最后，我们概述了未来研究的重要途径。