This work was partially supported by National Science Foundation award NSF ITR #IIS-0331707 and National Institutes of Health award 5 R01 DA012831-05, subaward 918197. I would like to thank Mark Handcock, David Hunter, Hal Stern, and Tom Snijders for their input and advice. Direct correspondence to Carter T. Butts, Department of Sociology and Institute for Mathematical Behavioral Sciences,University of California - Irvine; SSPA 2145, Irvine, CA 92697; (e-mail: firstname.lastname@example.org).
PERMUTATION MODELS FOR RELATIONAL DATA
Version of Record online: 18 MAY 2007
Volume 37, Issue 1, pages 257–281, December 2007
How to Cite
Butts, C. T. (2007), PERMUTATION MODELS FOR RELATIONAL DATA. Sociological Methodology, 37: 257–281. doi: 10.1111/j.1467-9531.2007.00183.x
- Issue online: 18 MAY 2007
- Version of Record online: 18 MAY 2007
A common problem in sociology, psychology, biology, geography, and management science is the comparison of dyadic relational structures (i.e., graphs). Where these structures are formed on a common set of elements, a natural question that arises is whether there is a tendency for elements that are strongly connected in one set of structures to be more—or less—strongly connected within another set. We may ask, for instance, whether there is a correspondence between golf games and business deals, trade and warfare, or spatial proximity and genetic similarity. In each case, the data for such comparisons may be continuous or discrete, and multiple relations may be involved simultaneously (e.g., when comparing multiple measures of international trade volume with multiple types of political interactions). We propose here an exponential family of permutation models that is suitable for inferring the direction and strength of association among dyadic relational structures. A linear-time algorithm is shown for MCMC simulation of model draws, as is the use of simulated draws for maximum likelihood estimation (MCMC-MLE) and/or estimation of Monte Carlo standard errors. We also provide an easily performed maximum pseudo-likelihood estimation procedure for the permutation model family, which provides a reasonable means of generating seed models for the MCMC-MLE procedure. Use of the modeling framework is demonstrated via an application involving relationships among managers in a high-tech firm.