  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.
