Statistics and Its Interface

Volume 12 (2019)

Number 3

Dynamic structural equation models for directed cyclic graphs: the structural identifiability problem

Pages: 365 – 375

DOI: https://dx.doi.org/10.4310/18-SII550

Authors

Yulin Wang (School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China)

Yu Luo (School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China)

Hulin Wu (Department of Biostatistics and Data Science, School of Public Health, University of Texas Health Science Center, Houston, Tx., U.S.A.)

Hongyu Miao (Department of Biostatistics and Data Science, School of Public Health, University of Texas Health Science Center, Houston, Tx., U.S.A.)

Abstract

Network systems are commonly encountered and investigated in various disciplines, and network dynamics that refer to collective node state changes over time are one area of particular interests of many researchers. Recently, dynamic structural equation model (DSEM) has been introduced into the field of network dynamics as a powerful statistical inference tool. In this study, in recognition that parameter identifiability is the prerequisite of reliable parameter inference, a general and efficient approach is proposed for the first time to address the structural parameter identifiability problem of linear DSEMs for cyclic networks. The key idea is to transform a DSEM to an equivalent frequency domain representation, then Mason’s gain is employed to deal with feedback loops in cyclic networks when generating identifiability equations. The identifiability result of every unknown parameter is obtained with the identifiability matrix method. The proposed approach is computationally efficient because no symbolic or expensive numerical computations are involved, and can be applicable to a broad range of linear DSEMs. Finally, selected benchmark examples of brain networks, social networks and molecular interaction networks are given to illustrate the potential application of the proposed method, and we compare the results from DSEMs, state-transition models and ordinary differential equation models.

Keywords

cyclic network, dynamic structural equation model, structural identifiability analysis, feedback loop

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Wang was partially supported by Fundamental Research Funds for the Central Universities of China under Grant ZYGX2014J064.

Wu was partially supported by NIH/NIAID grant R01AI087135-08.

Miao was partially supported by NSF grant DMS-1620957.

Received 22 July 2018

Published 4 June 2019