Social actors are often embedded in multiple social networks, and there is a growing interest in studying social systems from a multiplex network perspective. In this paper, we propose a mixed-effects model for cross-sectional multiplex network data that assumes dyads to be conditionally independent. Building on the uniplex $p_2$ model, we incorporate dependencies between different network layers via cross-layer dyadic effects and actor random effects. These cross-layer effects model the tendencies for ties between two actors and the ties to and from the same actor to be dependent across different relational dimensions. The model can also study the effect of actor and dyad covariates. As simulation-based goodness-of-fit analyses are common practice in applied network studies, we here propose goodness-of-fit measures for multiplex network analyses. We evaluate our choice of priors and the computational faithfulness and inferential properties of the proposed method through simulation. We illustrate the utility of the multiplex $p_2$ model in a replication study of a toxic chemical policy network. An original study that reflects on gossip as perceived by gossip senders and gossip targets, and their differences in perspectives, based on data from 34 Hungarian elementary school classes, highlights the applicability of the proposed method.

翻译：社会行动者通常嵌入于多重社会网络之中，从多重网络视角研究社会系统的兴趣日益增长。本文提出了一种面向横截面多重网络数据的混合效应模型，该模型假设二元组在条件上相互独立。基于单重p₂模型，我们通过跨层二元组效应与行动者随机效应，引入了不同网络层之间的依赖性。这些跨层效应能够建模以下趋势：两个行动者之间的联结，以及同一行动者发出与接收的联结，在不同关系维度上存在依赖性。该模型亦可研究行动者与二元组协变量的影响。由于基于模拟的拟合优度分析在应用网络研究中已成为常见做法，本文提出了适用于多重网络分析的拟合优度度量方法。我们通过模拟实验评估了先验分布的选择、所提方法的计算保真度与推断性质。在一项有毒化学品政策网络的复制研究中，我们展示了多重p₂模型的实用性。一项基于34个匈牙利小学班级数据的原创研究，通过分析八卦传播者与接收者对八卦的感知及其视角差异，进一步凸显了所提方法的适用性。