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Varying Responses to Common Shocks and Complex Cross-Sectional Dependence: Dynamic Multilevel Modeling with Multifactor Error Structures for Time-Series Cross-Sectional Data

Published online by Cambridge University Press:  04 January 2017

Xun Pang*
School of Social Sciences, Tsinghua University, 314 Minzhai Hall, Haidian District, Beijing 100084, China. e-mail:


Multifactor error structures utilize factor analysis to deal with complex cross-sectional dependence in Time-Series Cross-Sectional data caused by cross-level interactions. The multifactor error structure specification is a generalization of the fixed-effects model. This article extends the existing multifactor error models from panel econometrics to multilevel modeling, from linear setups to generalized linear models with the probit and logistic links, and from assuming serial independence to modeling the error dynamics with an autoregressive process. I develop Markov Chain Monte Carlo algorithms mixed with a rejection sampling scheme to estimate the multilevel multifactor error structure model with a pth-order autoregressive process in linear, probit, and logistic specifications. I conduct several Monte Carlo studies to compare the performance of alternative specifications and approaches with varying degrees of data complication and different sample sizes. The Monte Carlo studies provide guidance on when and how to apply the proposed model. An empirical application sovereign default demonstrates how the proposed approach can accommodate a complex pattern of cross-sectional dependence and helps answer research questions related to units' sensitivity or vulnerability to systemic shocks.

Research Article
Copyright © The Author 2014. Published by Oxford University Press on behalf of the Society for Political Methodology 

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