Does structure find structure?: A critique of Burt's use of distance as a measure of structural equivalence

It is shown that use of distance as a measure of similarity without proper attention to appropriate standardization procedures confounds information on differences between means and differences between variances with information on the similarity of the patterns between pairs of individuals.

Abstract

This paper examines some of the assumptions and consequences of the use of distance as a measure of structural equivalence, as implemented in Burt's STRUCTURE program. We take the general perspective that for a measure to be useful it should not confound separate types of information which are theoretically and mathematically independent. The mathematical relationship between distance and the Pearson product moment correlation coefficient is presented. We show that use of distance as a measure of similarity without proper attention to appropriate standardization procedures confounds information on differences between means and differences between variances with information on the similarity of the patterns between pairs of individuals, e.g. correlation. A detailed examination of Burt and Bittner's analysis of Bernard, Killworth and Sailer's Ham radio operator group is presented, and it is demonstrated that use of distance as a measure of structural equivalence led to nonsensical results.