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Testing network autocorrelation without replicates

Author

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  • Kwun Chuen Gary Chan
  • Jinhui Han
  • Adrian Patrick Kennedy
  • Sheung Chi Phillip Yam

Abstract

In this paper, we propose a portmanteau test for whether a graph-structured network dataset without replicates exhibits autocorrelation across units connected by edges. Specifically, the well known Ljung-Box test for serial autocorrelation of time series data is generalized to the network setting using a specially derived central limit theorem for a weakly stationary random field. The asymptotic distribution of the test statistic under the null hypothesis of no autocorrelation is shown to be chi-squared, yielding a simple and easy-to-implement procedure for testing graph-structured autocorrelation, including spatial and spatial-temporal autocorrelation as special cases. Numerical simulations are carried out to demonstrate and confirm the derived asymptotic results. Convergence is found to occur quickly depending on the number of lags included in the test statistic, and a significant increase in statistical power is also observed relative to some recently proposed permutation tests. An example application is presented by fitting spatial autoregressive models to the distribution of COVID-19 cases across counties in New York state.

Suggested Citation

  • Kwun Chuen Gary Chan & Jinhui Han & Adrian Patrick Kennedy & Sheung Chi Phillip Yam, 2022. "Testing network autocorrelation without replicates," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-18, November.
    • Handle: RePEc:plo:pone00:0275532
    DOI: 10.1371/journal.pone.0275532
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    1. Thomas De Graaff & Raymond J.C.M. Florax & Peter Nijkamp & Aura Reggiani, 2001. "A General Misspecification Test for Spatial Regression Models: Dependence, Heterogeneity, and Nonlinearity," Journal of Regional Science, Wiley Blackwell, vol. 41(2), pages 255-276, May.
    2. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    3. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    4. Jianqing Fan, 2004. "Generalised likelihood ratio tests for spectral density," Biometrika, Biometrika Trust, vol. 91(1), pages 195-209, March.
    5. Bo Fu, 2002. "Testing model adequacy for dynamic panel data with intercorrelation," Biometrika, Biometrika Trust, vol. 89(3), pages 591-602, August.
    6. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    7. Bent Nielsen, 2006. "Correlograms for non‐stationary autoregressions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 707-720, September.
    8. Youjin Lee & Elizabeth L. Ogburn, 2021. "Network Dependence Can Lead to Spurious Associations and Invalid Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1060-1074, July.
    9. Robinson, Peter, 2008. "Correlation testing in time series, spatial and cross-sectional data," LSE Research Online Documents on Economics 25470, London School of Economics and Political Science, LSE Library.
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