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Network ANOVA random effects models for node attributes

  • * Corresponding author: Gabriel Montes-Rojas

    * Corresponding author: Gabriel Montes-Rojas 

We are grateful to the Guest Editors, Viktoriya Semeshenko, Gabriel Brida and Andrea Roventini, and to two anonymous referees for helpful comments and suggestions. Matías Pardini and Emilio Sáenz Guillén provided invaluable research assistance. We also thank the Gerencia Principal de Estadísticas Económicas of Banco Central de la República Argentina for the data used in the empirical application.

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  • This paper develops a subgraph network random effects error components structure for network data to perform analysis of variance. In particular, it proposes a model for evaluating the network interdependence of nodes attributes allowing for edge and triangle specific components. The latter serve as a basal model for modeling more general network effects. Consistent estimators of the variance components and Lagrange Multiplier specification tests for evaluating the appropriate model of random components in networks structures is proposed. Monte Carlo simulations show that the tests have good performance in finite samples. The proposed tests is applied to the unsecured (Call) interbank market network in Argentina.

    Mathematics Subject Classification: Primary:05Cxx; Secondary:68R10.

    Citation:

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  • Figure 1.  LM tests for edge effects, $ \sigma_\mu^2=0 $, Erdös-Rényi random graph

    Figure 2.  LM tests for edge effects, $ \sigma_\mu^2=0 $, Queen spatial structure

    Figure 3.  LM tests for triangle effects, $ \sigma_\delta^2=0 $, Erdös-Rényi random graph

    Figure 4.  LM tests for triangle effcts, $ \sigma_\delta^2=0 $, Queen spatial structure

    Figure 5.  Subgraph joint tests for edge and triangle effects and spatial Moran's Ⅰ LM test

    Figure 6.  Subgraph tests for edge and triangle effects

    Figure 7.  Robust subgraph tests for edge and triangle effects

    Table 1.  Empirical size

    N LMµ LMδ LMµ,δ LMµ(δ) LMδ(µ) LMδµ
    Erdös-Rényi random graph
    Size 1%
    100 0.009 0.016 0.0145 0.009 0.0165 0.0115
    225 0.012 0.0115 0.015 0.013 0.012 0.009
    400 0.013 0.012 0.0085 0.0095 0.0075 0.007
    Size 5%
    100 0.043 0.05 0.0465 0.042 0.052 0.041
    225 0.052 0.0485 0.0495 0.052 0.0495 0.041
    400 0.047 0.0475 0.049 0.046 0.046 0.0435
    Size 10%
    100 0.082 0.0885 0.0855 0.089 0.092 0.0765
    225 0.1045 0.092 0.102 0.098 0.0995 0.0875
    400 0.089 0.087 0.093 0.0965 0.099 0.0915
    Spatial queen structure
    Size 1%
    100 0.0115 0.0105 0.0105 0.01 0.011 0.0115
    225 0.0075 0.0065 0.012 0.0145 0.0135 0.014
    400 0.0085 0.0085 0.0095 0.012 0.011 0.011
    Size 5%
    100 0.0475 0.0515 0.047 0.048 0.044 0.046
    225 0.045 0.039 0.0565 0.0595 0.052 0.0525
    400 0.046 0.0465 0.049 0.0535 0.049 0.0505
    Size 10%
    100 0.0965 0.0975 0.0955 0.094 0.09 0.097
    225 0.0965 0.09 0.1 0.1085 0.1115 0.1125
    400 0.0935 0.0965 0.098 0.096 0.0995 0.1015
    Notes: Monte carlo experiments based on 2000 replications.
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