arXiv subjects

Peter Hoff

Publications and source records attributed to Peter Hoff.

23 records · Page 2Linked to original sources

arXiv2012

Likelihoods for fixed rank nomination networks

Many studies that gather social network data use survey methods that lead to censored, missing or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare parameter estimates obtained from a likelihood for complete binary networks to those from a likelihood that is derived from the FRN scheme, and therefore recognizes the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, at least for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

stat.ME↗

arXiv2012

Bayesian sandwich posteriors for pseudo-true parameters

Under model misspecification, the MLE generally converges to the pseudo-true parameter, the parameter corresponding to the distribution within the model that is closest to the distribution from which the data are sampled. In many problems, the pseudo-true parameter corresponds to a population parameter of interest, and so a misspecified model can provide consistent estimation for this parameter. Furthermore, the well-known sandwich variance formula of Huber(1967) provides an asymptotically accurate sampling distribution for the MLE, even under model misspecification. However, confidence intervals based on a sandwich variance estimate may behave poorly for low sample sizes, partly due to the use of a plug-in estimate of the variance. From a Bayesian perspective, plug-in estimates of nuisance parameters generally underrepresent uncertainty in the unknown parameters, and averaging over such parameters is expected to give better performance. With this in mind, we present a Bayesian sandwich posterior distribution, whose likelihood is based on the sandwich sampling distribution of the MLE. This Bayesian approach allows for the incorporation of prior information about the parameter of interest, averages over uncertainty in the nuisance parameter and is asymptotically robust to model misspecification. In a small simulation study on estimating a regression parameter under heteroscedasticity, the addition of accurate prior information and the averaging over the nuisance parameter are both seen to improve the accuracy and calibration of confidence intervals for the parameter of interest.

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arXiv2010

Hierarchical multilinear models for multiway data

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a model-based version of such a decomposition, extending the scope of reduced rank methods to accommodate a variety of data types such as longitudinal social networks and continuous multivariate data that are cross-classified by categorical variables. The proposed model-based approach is hierarchical, in that the latent factors corresponding to a given dimension of the array are not {\it a priori} independent, but exchangeable. Such a hierarchical approach allows more flexibility in the types of patterns that can be represented.

stat.ME↗

arXiv2008

A hierarchical eigenmodel for pooled covariance estimation

While a set of covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most groups, while the correlation between other pairs may be consistently negative. In such cases much of the similarity across covariance matrices can be described by similarities in their principal axes, the axes defined by the eigenvectors of the covariance matrices. Estimating the degree of across-population eigenvector heterogeneity can be helpful for a variety of estimation tasks. Eigenvector matrices can be pooled to form a central set of principal axes, and to the extent that the axes are similar, covariance estimates for populations having small sample sizes can be stabilized by shrinking their principal axes towards the across-population center. To this end, this article develops a hierarchical model and estimation procedure for pooling principal axes across several populations. The model for the across-group heterogeneity is based on a matrix-valued antipodally symmetric Bingham distribution that can flexibly describe notions of ``center'' and ``spread'' for a population of orthonormal matrices.

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arXiv2007

Simulation of the matrix Bingham-von Mises-Fisher distribution, with applications to multivariate and relational data

Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that includes linear and quadratic terms, and arises as a posterior distribution in latent factor models for multivariate and relational data. This article describes rejection and Gibbs sampling algorithms for sampling from this family of distributions, and illustrates their use in the analysis of a protein-protein interaction network.

stat.CO↗