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Journal of Data Science


Modeling Dynamic Transport Network with Matrix Factor Models: an Application to International Trade Flow
Volume 21, Issue 3 (2023): Special Issue: Advances in Network Data Science, pp. 490–507
Pub. online: 5 December 2022      Type: Statistical Data Science      Open accessOpen Access
Received
6 April 2022
Accepted
11 September 2022
Published
5 December 2022

Abstract

International trade research plays an important role to inform trade policy and shed light on wider economic issues. With recent advances in information technology, economic agencies distribute an enormous amount of internationally comparable trading data, providing a gold mine for empirical analysis of international trade. International trading data can be viewed as a dynamic transport network because it emphasizes the amount of goods moving across network edges. Most literature on dynamic network analysis concentrates on parametric modeling of the connectivity network that focuses on link formation or deformation rather than the transport moving across the network. We take a different non-parametric perspective from the pervasive node-and-edge-level modeling: the dynamic transport network is modeled as a time series of relational matrices; variants of the matrix factor model of Wang et al. (2019) are applied to provide a specific interpretation for the dynamic transport network. Under the model, the observed surface network is assumed to be driven by a latent dynamic transport network with lower dimensions. Our method is able to unveil the latent dynamic structure and achieves the goal of dimension reduction. We applied the proposed method to a dataset of monthly trading volumes among 24 countries (and regions) from 1982 to 2015. Our findings shed light on trading hubs, centrality, trends, and patterns of international trade and show matching change points to trading policies. The dataset also provides a fertile ground for future research on international trade.

Supplementary material

 Supplementary Material
Supplementary material (Chen and Chen, 2022) contains exploratory analysis of the international trade data used in the present paper and asymmetric export and import analysis from applying Model (2) to the international trade volume data.

References

 
Airoldi EM, Blei DM, Fienberg SE, Xing EP (2008). Mixed membership stochastic blockmodels. Journal of Machine Learning Research, 9(9): 1981–2014.
 
Arroyo J, Athreya A, Cape J, Chen G, Priebe CE, Vogelstein JT (2021). Inference for multiple heterogeneous networks with a common invariant subspace. Journal of Machine Learning Research, 22(142): 1–49.
 
Chen E, Chen R (2022). Supplemental material of “Modeling dynamic transport network with matrix factor models: an application to international trade flow”. Journal of Data Science.
 
Chen R, Xiao H, Yang D (2021). Autoregressive models for matrix-valued time series. Journal of Econometrics, 222(1): 539–560.
 
Durand DE (1953). Country classification. In: International Trade Statistics (RGD Allen, EJ Ely, eds.), 117–129. Wiley.
 
Hafner-Burton EM, Kahler M, Montgomery AH (2009). Network analysis for international relations. International Organization, 63(3): 559–592.
 
Hanneke S, Fu W, Xing EP (2010). Discrete temporal models of social networks. Electronic Journal of Statistics, 4: 585–605.
 
Hoff PD (2011). Hierarchical multilinear models for multiway data. Computational Statistics & Data Analysis, 55(1): 530–543.
 
Huisman M, Snijders TA (2003). Statistical analysis of longitudinal network data with changing composition. Sociological Methods & Research, 32(2): 253–287.
 
IMF (2017). Direction of Trade Statistics, International Monetary Fund.
 
Kaiser HF (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23(3): 187–200.
 
Kim S, Shin EH (2002). A longitudinal analysis of globalization and regionalization in international trade: A social network approach. Social Forces, 81(2): 445–468.
 
Krivitsky PN, Handcock MS (2014). A separable model for dynamic networks. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 76(1): 29–46.
 
Lam C, Yao Q (2012). Factor modeling for high-dimensional time series: Inference for the number of factors. The Annals of Statistics, 40(2): 694–726.
 
Lee DD, Seung HS (2000). Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, 13: 556–562.
 
Linnemann H (1966). An Econometric Study of International Trade Flows, volume 234. North-Holland Publishing Company, Amsterdam.
 
Mahutga MC (2006). The persistence of structural inequality? A network analysis of international trade, 1965–2000. Social Forces, 84(4): 1863–1889.
 
Murtagh F, Legendre P (2014). Ward’s hierarchical agglomerative clustering method: Which algorithms implement ward’s criterion? Journal of Classification, 31(3): 274–295.
 
Sewell DK, Chen Y (2015). Latent space models for dynamic networks. Journal of the American Statistical Association, 110(512): 1646–1657.
 
Sewell DK, Chen Y (2016). Latent space models for dynamic networks with weighted edges. Social Networks, 44: 105–116.
 
Sewell DK, Chen Y (2017). Latent space approaches to community detection in dynamic networks. Bayesian Analysis, 12(2): 351–377.
 
Smith DA, White DR (1992). Structure and dynamics of the global economy: Network analysis of international trade 1965–1980. Social Forces, 70(4): 857–893.
 
Snijders TA (2001). The statistical evaluation of social network dynamics. Sociological Methodology, 31(1): 361–395.
 
Snijders TA (2005). Models for longitudinal network data. In: Models and Methods in Social Network Analysis (PJ Carrington, S John, W Stanley, eds.), 215–247.
 
Snijders TA (2006). Statistical methods for network dynamics. In: Proceedings of the XLIII Scientific Meeting, Italian Statistical Society (S Luchini, ed.), 281–296. CLEUP, Padova.
 
Snijders T, Steglich C, Schweinberger M (2007). Modeling the coevolution of networks and behavior. In: Longitudinal Models in the Behavioral and Related Sciences (K van Montfort, J Oud, A Satorra, eds.), 41–72. Routledge Academic, Mahwah. Chapter 3.
 
Snijders TA, Koskinen J, Schweinberger M (2010a). Maximum likelihood estimation for social network dynamics. Annals of Applied Statistics, 4(2): 567.
 
Snijders TA, Van de Bunt GG, Steglich CE (2010b). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32(1): 44–60.
 
Wang D, Liu X, Chen R (2019). Factor models for matrix-valued high-dimensional time series. Journal of Econometrics, 208(1): 231–248.
 
Westveld AH, Hoff PD (2011). A mixed effects model for longitudinal relational and network data, with applications to international trade and conflict. Annals of Applied Statistics, 5(2A): 843–872.
 
Xing EP, Fu W, Song L (2010). A state-space mixed membership blockmodel for dynamic network tomography. Annals of Applied Statistics, 4(2): 535–566.
 
Xu R, Wunsch D (2005). Survey of clustering algorithms. IEEE Transactions on Neural Networks, 16(3): 645–678.

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Copyright
2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
latent models matrix-variate time series trading hubs weighted relational data

Funding
Elynn Y. was supported in part by NSF Grants DMS-1803241. Rong Chen was supported in part by NSF Grants DMS-1503409, DMS-1737857, DMS-1803241 and IIS-1741390.

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