The class of p₂ models is suitable for modeling binary relation data in social network analysis. A p₂ model is essentially a regression model for bivariate binary responses, featuring within‐dyad dependence and correlated crossed random effects to represent heterogeneity of actors. Despite some desirable properties, these models are used less frequently in empirical applications than other models for network data. A possible reason for this is due to the limited possibilities for this model for accounting for (and explicitly modeling) structural dependence beyond the dyad as can be done in exponential random graph models. Another motive, however, may lie in the computational difficulties existing to estimate such models by means of the methods proposed in the literature, such as joint maximization methods and Bayesian methods. The aim of this article is to investigate maximum likelihood estimation based on the Laplace approximation approach, that can be refined by importance sampling. Practical implementation of such methods can be performed in an efficient manner, and the article provides details on a software implementation using R. Numerical examples and simulation studies illustrate the methodology.

中文翻译：

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基于Laplace近似的p2网络回归模型的最大似然估计

p ₂模型的类别适用于对社交网络分析中的二进制关系数据进行建模。甲p ₂模型本质上是用于双变量二元响应的回归模型，其特征在于二分体内依赖性和相关的交叉随机效应，以表示参与者的异质性。尽管具有某些理想的属性，但与其他网络数据模型相比，这些模型在经验应用中的使用频率较低。造成这种情况的可能原因是，该模型用于解释（和显式建模）超出对偶的结构依赖性的可能性有限，这可以在指数随机图模型中完成。然而，另一个动机可能在于通过文献中提出的方法（例如联合最大化方法和贝叶斯方法）来估计此类模型所存在的计算困难。本文的目的是研究基于拉普拉斯近似方法的最大似然估计，可以通过重要性抽样加以完善。可以有效地执行此类方法的实际实现，并且本文提供了有关使用[R 。数值例子和仿真研究说明了该方法。