56 research outputs found
Maximum likelihood estimation for social network dynamics
A model for network panel data is discussed, based on the assumption that the
observed data are discrete observations of a continuous-time Markov process on
the space of all directed graphs on a given node set, in which changes in tie
variables are independent conditional on the current graph. The model for tie
changes is parametric and designed for applications to social network analysis,
where the network dynamics can be interpreted as being generated by choices
made by the social actors represented by the nodes of the graph. An algorithm
for calculating the Maximum Likelihood estimator is presented, based on data
augmentation and stochastic approximation. An application to an evolving
friendship network is given and a small simulation study is presented which
suggests that for small data sets the Maximum Likelihood estimator is more
efficient than the earlier proposed Method of Moments estimator.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS313 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Socio-Demographic Latent Space Approach to Spatial Data When Geography is Important but Not All-Important
Many models for spatial and spatio-temporal data assume that "near things are
more related than distant things," which is known as the first law of
geography. While geography may be important, it may not be all-important, for
at least two reasons. First, technology helps bridge distance, so that regions
separated by large distances may be more similar than would be expected based
on geographical distance. Second, geographical, political, and social divisions
can make neighboring regions dissimilar. We develop a flexible Bayesian
approach for learning from spatial data which units are close in an unobserved
socio-demographic space and hence which units are similar. As a by-product, the
Bayesian approach helps quantify the relative importance of socio-demographic
space relative to geographical space. To demonstrate the proposed approach, we
present simulations along with an application to county-level data on median
household income in the U.S. state of Florida
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