It has long been understood that an individual's characteristics play a role in the formation of their social network. For example, friendship networks are often characterized by ties among people with similar attributes. More recently the converse phenomenon has been studied, in which an individual's social network may affect their personal characteristics. For example: teenagers may change their alcohol or smoking behavior to more closely match those of their friends. More generally, an individual's network is likely to play a role in determining their status for a communicable disease. Such results indicate that, rather than think of individual-level attributes as fixed quantities which impact a network, the attributes might vary along with or as a result of the social network. However, there has been very little development of statistical methodology for the joint analysis of network and nodal attribute data. In typical data analyses, either the network or the nodal attribute data is chosen as the """"""""outcome variable."""""""" But analyses that treat the attribute data as the outcome variable generally fail to properly account for statistical dependencies due to social network effects, leading to inflated claims of statistical significance. Analyses in which the network is the outcome run into problems when there is incomplete or missing attribute data: common practice is to delete cases for which the data are incomplete. Such ad hoc data reductions discard valuable information and can result in biased parameter estimates and statistical inferences. The goal of this research project is to remedy these problems by developing statistical methods and software for the joint analysis of networks and nodal attribute data. The methods will be based on extensions of well-studied and familiar data analysis methods such as factor analysis, linear regression and probit models. This project will provide 7statistical methods for the joint analysis of social network and individual-level data;7analysis of Adolescent health datasets;7methods for the analysis of longitudinal network data;7open source data analysis tools for researchers.
Several public health studies have shown evidence of interactions between people's characteristics and their social networks. For example, teenagers may preferentially form friendships with others having similar characteristics, or conversely, they may adjust their smoking or drinking behaviors to more closely match those of their friends. The proposed research project will develop statistical data analysis methods that allow for the quantification and detection of relationships between social networks and individual level characteristics, as well as provide for predictions of individual-level behavior from social network information.
| Hoff, Peter D (2015) MULTILINEAR TENSOR REGRESSION FOR LONGITUDINAL RELATIONAL DATA. Ann Appl Stat 9:1169-1193 |
| Gerard, David; Hoff, Peter (2015) Equivariant minimax dominators of the MLE in the array normal model. J Multivar Anal 137:32-49 |
| Fosdick, Bailey K; Hoff, Peter D (2015) Testing and Modeling Dependencies Between a Network and Nodal Attributes. J Am Stat Assoc 110:1047-1056 |
| Kessler, David C; Hoff, Peter D; Dunson, David B (2015) Marginally specified priors for non-parametric Bayesian estimation. J R Stat Soc Series B Stat Methodol 77:35-58 |
| Volfovsky, Alexander; Hoff, Peter D (2015) Testing for nodal dependence in relational data matrices. J Am Stat Assoc 110:1037-1046 |
| Volfovsky, Alexander; Hoff, Peter D (2014) HIERARCHICAL ARRAY PRIORS FOR ANOVA DECOMPOSITIONS OF CROSS-CLASSIFIED DATA. Ann Appl Stat 8:19-47 |
| Fosdick, Bailey K; Hoff, Peter D (2014) SEPARABLE FACTOR ANALYSIS WITH APPLICATIONS TO MORTALITY DATA. Ann Appl Stat 8:120-147 |
| Hoff, Peter D; Niu, Xiaoyue; Wellner, Jon A (2014) Information bounds for Gaussian copulas. Bernoulli (Andover) 20:604-622 |
| Hoff, Peter; Fosdick, Bailey; Volfovsky, Alex et al. (2013) Likelihoods for fixed rank nomination networks. Netw Sci (Camb Univ Press) 1:253-277 |
