Least squares estimation of spatial autoregressive models for large-scale social networks

Huang, Danyang; Lan, Wei; Zhang, Hao Helen; Wang, Hansheng

doi:10.1214/19-ejs1549

Cited by 16 publications

(15 citation statements)

References 39 publications

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“…Conditions (C2.1) and (C2.2) are two separate assumptions regarding the overall network structure. Condition (C2.1) is similar to those in other studies [20,46]. Condition (C2.1) requires certain connectivity for the network structure.…”

Section: The Other Related Matrices and Vectors Are Expressed Assupporting

confidence: 70%

“…However, as Taylor expansion is conducted, this method requires the autocorrelation coefficient to approach zero, which can hardly be satisfied in all cases. Furthermore, Huang et al [20] proposed the LSE estimator for the classical univariate SAR model with no covariates and discussed a simple sampled case. However, the required sample size and corresponding proof were not discussed in [20].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, Huang et al [20] proposed the LSE estimator for the classical univariate SAR model with no covariates and discussed a simple sampled case. However, the required sample size and corresponding proof were not discussed in [20]. This served as the inspiration for the current work.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, focusing on the MSAR model in large-scale networks, we propose the crawling subsampling (CS) method for a general framework. The proposed approach is an extension of the sampling method in [20]. First, we design a general three-step CS scheme.…”

Section: Introductionmentioning

confidence: 99%

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Crawling subsampling for multivariate spatial autoregression model in large-scale networks

Huang

Jing

et al. 2021

Electron. J. Statist.

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In network data analysis, multivariate spatial autoregression (MSAR) models may be used to analyze the autocorrelation among multiple responses. With large-scale networks, the estimation for MSAR on the entire network is computationally expensive. In this case, the subsampling method could be adopted. This approach selects a sample of nodes and then uses the estimate based on the sample to approximate the estimate on the full data. However, traditional sampling methods cannot obtain unbiased parameter estimates. Considering the second-order friend information of sampled nodes, we propose the crawling subsampling (CS) method for a general framework. Thereafter, based on the sampled data only, we construct the least-squares objective function. Under certain conditions, the computational complexity of optimizing the objective function is linear with the sample size ns. The identification condition for the parameters on the sampled network is theoretically provided. The sample size order requirement is provided, and the asymptotic properties of the least-squares estimators are investigated. The numerical results for the simulated and real data are presented to demonstrate the performance of the proposed CS method and least-squares estimator for the MSAR model.

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Section: The Other Related Matrices and Vectors Are Expressed Assupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Crawling subsampling for multivariate spatial autoregression model in large-scale networks

Huang

Jing

et al. 2021

Electron. J. Statist.

Self Cite

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“…The second avenue is using the screening or regularization method to obtain the sparse solution for constructing n influence indices λ i (e.g., see Zhu et al 2019a) or to develop the test statistic for testing a subset of λ i s being equal. The third avenue is proposing a computationally feasible estimation approach (e.g., the least squares method in Huang et al 2019 andZhu et al 2019b), to overcome the computational challenge of QMLE under large scale networks (see numerical illustrations in Section S.4 of the Supplementary Material). The fourth avenue is motivated by an anonymous referee's comment, which extends the adaptive SAR model (1.2) to Y i = ∑ n j=1 λ ij Y j + ε i so that the closeness between node i and node j can be characterized via the influence parameter λ ij .…”

Section: Discussionmentioning

confidence: 99%

Network Influence Analysis

Zou¹,

Luo²,

Lan³

et al. 2021

STAT SINICA

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Due to the rapid development of social networking sites, the spatial autoregressive (SAR) model has played an important role in social network studies. However, the underlying structure of SAR implicitly assumes that all nodes (or actors or users) within the network have the same influential power measured by the common autocorrelation parameter. Hence, the classical SAR is unable to identify influential nodes. This paper proposes the adaptive SAR model by introducing the network influence index, which includes the classical SAR model as a special case. Using this proposed model without imposing any specific error distribution, we apply Lee's (2004) quasi-maximum likelihood approach to estimate the unknown parameters of the index, which can then be used to characterize the influential power of each node. The asymptotic properties of parameter estimates are established and three test statistics for assessing the homogeneity of the network influence indices are presented. The usefulness of the adaptive SAR model and its associated network index are illustrated via simulation studies and an empirical investigation of the spillover effects in Chinese mutual fund cash

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A combined moment equation approach for spatial autoregressive models

Liu

et al. 2023

Can J Statistics

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Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing.

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Least squares estimation of spatial autoregressive models for large-scale social networks

Cited by 16 publications

References 39 publications

Crawling subsampling for multivariate spatial autoregression model in large-scale networks

Crawling subsampling for multivariate spatial autoregression model in large-scale networks

Network Influence Analysis

A combined moment equation approach for spatial autoregressive models

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