Likelihood-Based Inference for Stochastic Models of Sexual Network Formation Mark S. Handcock Center for Statistics and the Social Sciences Department of Statistics University of Washington, Seattle, WA James Holland Jones1 Center for Studies in Demography and Ecology Center for Statistics and the Social Sciences Center for AIDS and Sexually Transmitted Diseases University of Washington, Seattle, WA 29 January 2003 Working Paper #29 Center for Statistics and the Social Sciences University of Washington Box 354322 Seattle, WA 98195-4322, USA 1Corresponding Author: Center for Statistics and the Social Sciences, Box 354320, Seattle, WA 98195- 4320, email:
[email protected], Phone: 206-221-6874, Fax: 206-221-6873 Abstract Sexually-Transmitted Diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a pop- ulation. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women’s network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results sug- gest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions.