We first give a mathematical definition of multimode data this includes directed multimode data. Most 2-mode data is undirected but it is possible to have directed data, this would require both modes to have some degree of agency. We give some examples of directed two-mode data and suggest techniques for analyzing and representing such data. We examine standard methods but also look at projections and core-periphery models including the dual projection approach.

Interventions in networks is becoming an increasingly more important topic in public health, business, and public policy more widely concerned with opinion change and online networks. Yet, network research suffers a lack of viable causal frameworks and the choice of targets of interventions are typically based on heuristics. Optimal design theory has long been established as a statistical technique for designing experiments, interventions, etc, but has thus far rarely been applied to networks. A notable exception is Parker, Gilmour, and Schormans (2017), who proposed optimal designs for networks but only for a linear model, i.e, with independent (SIC!) outcomes. We explore designs for network effects and network autocorrelation models, and how these are affected by increasing network autocorrelation and social influence - whom to do treat if potential targets have the capacity to influence others? We derive the local D-optimal design for a specific illustrative example. However, this design is not unique, and highly sensitive to the strength of network autocorrelation. In terms of designs, network models suffer from similar limitations as standard non-linear models but, in addition, determination requires that the network is fixed and known. We suggest that a way forward is to consider designs that are optimal in expectation, either with respect to an a priori network model such as the ERGM or autocorrelation coefficient.

The preferential attachment model is often suggested to be the underlying mechanism of a network’s growth, largely due to that the degree distribution often follows the power law, albeit approximately and partially. While such attribution can be made in the absence of the network’s evolution history, it is more sensible to directly model the evolution when such data is available. This is the case in this work, where the incremental changes of the dependency network of R packages are available. Not only do we fit a generalised linear model based on preferential attachment, we also incorporate a preference function that is realistic for the tail heaviness of the resulting degree distribution. Results suggest that the influence of packages grows superlinearly initially and linearly above a threshold.

Exponential-Family Random Graph Models (ERGMs) are foundational in social network analysis. More recently, their application has extended beyond traditional static and panel networks to diverse data types. Notable extensions include Exponential Random Network Models (ERNMs), which jointly model networks and outcomes; the Generalized Location System (GLS), used for occupational stratification and residential settlement patterns; and the Autologistic Actor Attribute Model (ALAAM), an influence model that captures outcomes through motif-based structures.

In this paper, we introduce a novel application of the ERGM framework for analyzing complex, interrelated binary outcomes beyond conventional network data. Specifically, we propose modeling jointly-distributed health conditions to examine how multiple diseases may be interdependent. Using an empirical panel dataset, we construct a model that moves beyond assumptions of independence between health outcomes. Looking at the data as a bipartite network where individuals are mapped to various health conditions, our approach conceptualizes diseases as a complex system, where the presence or absence of one condition is characterized by sufficient statistics featuring other conditions.

Our analysis leverages the R package defm, which facilitates the estimation of these models. By providing both a methodological extension and a practical implementation, we demonstrate the potential of the ERGM framework in capturing interdependencies in health and other domains with complex binary data structures.