# Statistical Inference in a Directed Network Model With Covariates

@article{Yan2018StatisticalII, title={Statistical Inference in a Directed Network Model With Covariates}, author={Ting Yan and Binyan Jiang and Stephen E. Fienberg and Chenlei Leng}, journal={Journal of the American Statistical Association}, year={2018}, volume={114}, pages={857 - 868} }

ABSTRACT Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this article, we rigorously study a directed network model that captures the former via node-specific parameterization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each…

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## References

SHOWING 1-10 OF 125 REFERENCES

Semiparametric Analysis of Network Formation

- Mathematics, Computer Science
- 2016

A statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes is considered, which is shown to have desirable asymptotic properties under sequences of growing networks.

Null models for network data

- Mathematics, Computer ScienceArXiv
- 2012

This work shows how the logistic-linear model and the implicit log- linear model may be viewed as instances of a broader class of null models, with the property that all members of this class give rise to essentially the same likelihood-based estimates of link probabilities in sparse graph regimes.

Analysis of Partially Observed Networks via Exponential- family Random Network Models

- Mathematics, Computer Science
- 2013

A theory of inference for ERN models when only part of the network is observed is developed, as well as specific methodology for missing data, including non-ignorable mechanisms for network-based sampling designs and for latent class models.

An Econometric Model of Network Formation With Degree Heterogeneity

- Mathematics
- 2017

I formulate and study a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent level heterogeneity…

Stochastic Blockmodels for Directed Graphs

- Mathematics
- 1987

Abstract Holland and Leinhardt (1981) proposed the p 1 model for the analysis of binary directed graph data in network studies. Such a model provides information about the “attractiveness” and…

An Econometric Model of Link Formation with Degree Heterogeneity

- Mathematics
- 2014

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent level heterogeneity in link…

An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity

- MathematicsReview of Economics and Statistics
- 2019

I study a dyadic linking model in which agents form directed links that exhibit homophily and reciprocity. A fixed-effect approach accounts for unobserved sources of degree heterogeneity. I consider…

Exponential-family Random Network Models

- Computer Science, Mathematics
- 2012

This work develops a theory of inference for ERNM when only part of the net- work is observed, as well as specific methodology for missing data, including non- ignorable mechanisms for network-based sampling designs and for latent class models.

Degree-based network models

- Mathematics, Computer Science
- 2012

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network…

Assessing Degeneracy in Statistical Models of Social Networks

- 2003

This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and…