Finding roles in sparse economic hierarchies: Going beyond regular equivalence

• Advocating pre-specifications for examining role structures of networks.
• Exploring the effect of generalized equivalences on alternative specifications.
• Creating the important distinction between model-induced inconsistencies and errors.
• Identifying and examining model-induced inconsistencies to produce substantively valid blockmodels.
• Proposing a general method for identifying the configuration of commodity chains.

We examine mapping latent roles to reveal meaningful structures of social relations with a focus on substance. Equivalence types are discussed in relation to data and the match (or not) between them. An argument for considering row-regular blocks when studying sparse economic networks is provided. A clear distinction is made between the concepts of inconsistencies and errors when assessing fitted blockmodels. A case is made for examining the patterns of inconsistencies for discerning empirical block types. Three empirical economic networks are considered. Two are rice trading networks in Vietnam with the third being a network of foreign direct investments between countries. Attention is focused on formulating and testing three rival blockmodels for the rice trading networks. Established blockmodels have clear substantive interpretations. The analysis of the investment network is more tentative but extends the idea of examining inconsistencies to two-mode networks. Some implications for blockmodeling by using substantive and empirical knowledge are discussed.