Conformity of two sociometric relations

The problem of comparing two sociometric relations or measurements (A andB) recorded in distinct sociomatrices was originally discussed by Katz and Powell in the early 1950's and Hubert and Baker in the late 1970's. The problem is considered again using a probabilistic model designed specifically for discrete-valued network measurements. The model allows for the presence of various structural tendencies, such as reciprocity and differential popularity. A parameter that isolates the tendency for actors to choose other actors on both relations simultaneously is introduced, and estimated conditional on the presence of other parameters that reflect additional important network properties. The parameter is presented as a symmetric index but is also generalized to the predictive (A onB orB onA) situation. This approach to the problem is illustrated with the same data used by the earlier solutions, and the unique nature of the two relations in the data set (A = received choices,B = perceived choices), as it affects the modeling, is discussed. Significance tests for the parameter and related parameters are described, as well as an extension to more than two relations.Research support provided by National Science Grant #SES84-08626 to the University of Illinois at Urbana-Champaign. I am grateful to Dawn Iacobucci and Sheila Weaver for assistance with the research reported here, and to Carolyn Anderson, James Green, David Holtgrave, and four anonymous referees for comments on the paper.