A Comparison of Latent and Deterministic Blockmodeling with Application to Binary Substance Use Disorder Data

Substance use disorder data are often collected by asking individuals to endorse (or not endorse) a set of items pertaining to various diagnostic criteria. The result is a bipartite network, which can be represented by a two-mode binary matrix with rows corresponding to the individuals and columns to the items. Two-mode blockmodeling is an exploratory data analysis approach for bipartite networks that establishes partitions of both the individuals and items. Some two-mode blockmodeling methods are deterministic, whereas the latent blockmodel is stochastic and grounded by an underlying statistical model. A simulation study comparing the latent blockmodel and two deterministic blockmodeling methods revealed that the methods often perform comparably with respect to recovery of the true (known) cluster memberships when the number of clusters for both individuals and items is prespecified. However, the results also showed that one of the deterministic methods is unsuitable for sparse bipartite networks. A key advantage of the latent blockmodel method is a principled approach to selection of the number of clusters for individuals and items. We also demonstrate the effectiveness of the latent blockmodel via comparison to deterministic blockmodeling for a multiple-substance use disorder data set from the literature.