Some properties of structural equivalence measures derived from sociometric choice data

I discuss and illustrate the extent to which different relation measures and pattern similarity measures can be expected to generate different structural equivalence results. Measures of network relations and pattern similarity are reviewed to establish clear comparisons between structural equivalence measures. Using Monte Carlo sociometric choice data drawn from four strategically designed study populations, alternative relation and pattern similarity measures are combined in a factorial design generating six measures of structural equivalence within each study population. I report the magnitudes of differences between structural equivalence measures within populations, compared across populations. Three conclusions are drawn: (1) There is significant reliability across alternative measures. (2) This reliability increases with the clarity of boundaries between statuses in a study population. (3) The noticeable differences between structural equivalence measures that exist under conditions at all weaker than strong equivalence are principally a function of how relations are measured rather than how relation pattern similarities are measured. Two inferences are drawn for applied network analysis: (1) Structural equivalence should be computed from path distance measures of network relations (however normalized) rather than being computed directly from patterns of binary choice data. (2) Renewed methodological attention should shift from how we measure pattern similarity to how we measure relationships.