%0 Journal Article %1 citeulike:606488 %A Hoff, Peter D. %A Raftery, Adrian E. %A Handcock, Mark S. %D 2002 %J Journal of the American Statistical Association %K community sna %P 1090+ %T Latent space approaches to social network analysis %U http://www.stat.washington.edu/raftery/Research/PDF/hoff2002.pdf %V 97 %X Social network data typically consist of a set of n actors and a relational tie y.sub.i,j, measured on each ordered pair of actors i, j = 1,..., n. This framework has many applications in the social and behavioral sciences including, for example, the behavior of epidemics, the interconnectedness of the World Wide Web, and telephone calling patterns. Quantitative research on social networks has a long history, going back at least to Moreno (1934). The development of log-linear statistical models by Holland and Leinhardt (1981); Fienberg, Meyer, and Wasserman (1985); Wang and Wong (1987); and others represent major advances. In the simplest cases, y.sub.i,j is a dichotomous variable indicating the presence or absence of some relation of interest, such as friendship, collaboration, transmission of information or disease, and so forth. The data are often represented by an n x n sociomatrix Y. In the case of binary relations, the data can also be thought of as a graph in which the nodes are actors and the edge set is (i, j) : y.sub.i, j = 1. If (i, j) is in the edge set, then we write i right arrow j. If ties are undirected, in that y.sub.i,j = y.sub.j, i for all i not equal to j by logical necessity, then we write i ~ j if y.sub.i,j = 1. However, even in the case of directed relations, ties often tend to be reciprocal (y.sub.i, j = y.sub.j, i with high probability) and transitive (i right arrow j, j right arrow k right arrow i right arrow k with high probability). As such, probabilistic models of network relations have typically allowed for some sort of dependence between ties. For example, the p.sub.1 model of Holla nd and Leinhardt (1981) includes parameters for the propensity of ties to be reciprocal, as well as parameters for the number of ties and individual tendencies to give or receive ties. However, these models are restrictive, as they assume the (MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII) dyads (y.sub.i, j, y.sub.j, i) to be independent.

@article{citeulike:606488, abstract = {Social network data typically consist of a set of n actors and a relational tie [y.sub.i,j], measured on each ordered pair of actors i, j = 1,..., n. This framework has many applications in the social and behavioral sciences including, for example, the behavior of epidemics, the interconnectedness of the World Wide Web, and telephone calling patterns. Quantitative research on social networks has a long history, going back at least to Moreno (1934). The development of log-linear statistical models by Holland and Leinhardt (1981); Fienberg, Meyer, and Wasserman (1985); Wang and Wong (1987); and others represent major advances. In the simplest cases, [y.sub.i,j] is a dichotomous variable indicating the presence or absence of some relation of interest, such as friendship, collaboration, transmission of information or disease, and so forth. The data are often represented by an n x n sociomatrix Y. In the case of binary relations, the data can also be thought of as a graph in which the nodes are actors and the edge set is {(i, j) : [y.sub.i, j] = 1}. If (i, j) is in the edge set, then we write i [right arrow] j. If ties are undirected, in that [y.sub.i,j ] = [y.sub.j, i] for all i [not equal to] j by logical necessity, then we write i ~ j if [y.sub.i,j ] = 1. However, even in the case of directed relations, ties often tend to be reciprocal ([y.sub.i, j] = [y.sub.j, i] with high probability) and transitive (i [right arrow] j, j [right arrow] k [right arrow] i [right arrow] k with high probability). As such, probabilistic models of network relations have typically allowed for some sort of dependence between ties. For example, the [p.sub.1] model of Holla nd and Leinhardt (1981) includes parameters for the propensity of ties to be reciprocal, as well as parameters for the number of ties and individual tendencies to give or receive ties. However, these models are restrictive, as they assume the ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) dyads ([y.sub.i, j], [y.sub.j, i]) to be independent.}, added-at = {2006-09-25T12:54:00.000+0200}, author = {Hoff, Peter D. and Raftery, Adrian E. and Handcock, Mark S.}, biburl = {https://www.bibsonomy.org/bibtex/25cd3bc4a94426bc09ab9ea619d48cb52/grahl}, citeulike-article-id = {606488}, interhash = {9055bbc097d7a7d00b105dff52b1c496}, intrahash = {5cd3bc4a94426bc09ab9ea619d48cb52}, journal = {Journal of the American Statistical Association}, keywords = {community sna}, month = {December}, pages = {1090+}, priority = {2}, timestamp = {2007-07-25T11:36:55.000+0200}, title = {Latent space approaches to social network analysis}, url = {http://www.stat.washington.edu/raftery/Research/PDF/hoff2002.pdf}, volume = 97, year = 2002 }