Zero Re-centered Projection: An Alternative Proposal for Modeling Empty Networks in ENA

Making Sense of the Model: Interpreting Epistemic Networks and their Projection Space

“…ENA uses an optimization routine (a least-squares method) to position the nodes of the networks such that for any unit, the centroid of its network graph ("center of mass"; arithmetic mean of the edge weights distributed according to the network projection in space [8,9]) is as close as possible to the location of its plotted point [5]. Goodness of fit, that is, correlation between the plotted points and their centroids on each dimension, is typically measured with Pearson's or Spearman's r; centroids are not represented visually in the model.…”

“…Apart from the plotted points in the two-dimensional space, ENA offers another, coordinated visualization of the data: network graphs. Nodes represent codes and edges represent values in the unit vectors [5]. Node positions are the same for every network in the model; this "fixed node position" facilitates visual comparison [16].…”

“…Node positions are the same for every network in the model; this "fixed node position" facilitates visual comparison [16]. Furthermore, the coordination of network graphs and plotted points means that the positions of the nodes (and the connections they define) can be used to interpret the dimensions forming the projection space and explain the position of plotted points; this is known as coregistration [5].…”

“…Epistemic Network Analysis (ENA) is the most commonly employed QE tool enabling the representation of code interactions. ENA offers two coordinated visualizations of the data: 1) dynamic network graphs where nodes represent codes and edges represent the relative frequency of co-occurrence between unique pairs of codes, and 2) a space in which networks are projected as points [5]. The two visualizations jointly are hereon referred to as an ENA model.…”

“…This may not always be true, as the interpretation of network connectedness is dependent on the content of the codes being modelled, as well as the meaning of their co-occurrence. Congruently, QE researchers have highlighted the connectedness of a single node, or degree centrality 5 , as a driver in identifying points of interest for application or theory [19,23]. In a similar vein, others have noted instances where a particular node solely connects to one or two other nodes in the network and leveraged that sparsity as interpretative power [24].…”