Network ANOVA random effects models for node attributes

Gabriel Montes-Rojas; Pedro Elosegui

doi:10.3934/jdg.2020017

Article Contents

2020, Volume 7, Issue 3: 239-252. Doi: 10.3934/jdg.2020017

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Network ANOVA random effects models for node attributes

Gabriel Montes-Rojas^1, , and
Pedro Elosegui^2,

1.
Instituto Interdisciplinario de Economía Política de Buenos Aires, (IIEP-BAIRES-UBA)-CONICET, Facultad de Ciencias Económicas, Universidad de Buenos Aires, Av. Córdoba 2122 2do piso, C1120AAQ, Ciudad Autónoma de Buenos Aires, Argentina
2.
Banco Central de la República Argentina and Universidad Nacional de La Plata

^* 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.

Received: January 31, 2020

Revised: March 31, 2020

Published: July 2020

Abstract Full Text(HTML) Figure(7) / Table(1) Related Papers Cited by

Abstract

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.

Keywords:

Networks,
Nodes,
Links,
Triangles,
Clusters.

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

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

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

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

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

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Figure 6. Subgraph tests for edge and triangle effects

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Figure 7. Robust subgraph tests for edge and triangle effects

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Table 1. Empirical size

N	LM_µ	LM_δ	LM_µ,δ	LM_µ(δ)	LM_δ(µ)	LM_δ−µ
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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