A new method for constructing networks from binary data

Claudia D van Borkulo, Denny Borsboom, Sacha Epskamp, Tessa F Blanken, Lynn Boschloo, Robert A Schoevers, Lourens J Waldorp, Claudia D van Borkulo, Denny Borsboom, Sacha Epskamp, Tessa F Blanken, Lynn Boschloo, Robert A Schoevers, Lourens J Waldorp

Abstract

Network analysis is entering fields where network structures are unknown, such as psychology and the educational sciences. A crucial step in the application of network models lies in the assessment of network structure. Current methods either have serious drawbacks or are only suitable for Gaussian data. In the present paper, we present a method for assessing network structures from binary data. Although models for binary data are infamous for their computational intractability, we present a computationally efficient model for estimating network structures. The approach, which is based on Ising models as used in physics, combines logistic regression with model selection based on a Goodness-of-Fit measure to identify relevant relationships between variables that define connections in a network. A validation study shows that this method succeeds in revealing the most relevant features of a network for realistic sample sizes. We apply our proposed method to estimate the network of depression and anxiety symptoms from symptom scores of 1108 subjects. Possible extensions of the model are discussed.

Figures

Figure 1. Examples of networks with 30…
Figure 1. Examples of networks with 30 nodes in the simulation study.
(a) Generated networks. From left to right: random network (probability of an extra connection is 0.1), scale-free network (power of preferential attachment is 1) and small world network (rewiring probability is 0.1). (b) Weighted versions of (a) that are used to generate data (true networks). (c) Estimated networks.
Figure 2. Mean correlations (vertical axes) of…
Figure 2. Mean correlations (vertical axes) of the upper triangles of the weighted adjacency matrices of true and estimated networks of 100 simulations with random, scale-free, and small world networks for sample sizes ssize = 100, 500, 1000, and 2000, with number of nodes nnodes = 10, 20, 30, and 100.
We used three levels of connectivity (random networks: probability of an extra connection Pconn = .1, .2, and .3; scale-free networks: power of preferential attachment Pattach = 1, 2, and 3; small world networks: rewiring probability of Prewire = .1, .5, and 1). For the condition with 100 nodes, we used different levels of connectivity for random and scale-free networks in order to obtain more realistic networks (random networks: Pconn = .05, .1, and .15; scale-free networks: Pattach = 1, 1.25, and 1.5).
Figure 3. Application of eLasso to real…
Figure 3. Application of eLasso to real data.
The resulting network structure of a group of healthy controls and people with a current or history of depressive disorder (N = 1108). Cognitive symptoms are displayed as ○ and thicker edges (connections) represent stronger associations.
Figure 4. Three centrality measures of the…
Figure 4. Three centrality measures of the nodes in the network based on real data.
From left to right: node strength, betweenness, and clustering coefficient. “Hypersomnia” (hyp) has no clustering coefficient, since it has only one neighbour.
Figure 5. Community structure of the network…
Figure 5. Community structure of the network based on real data, detected by the Walktrap algorithm.

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