Logistic Regression with Network Structure

Zhang, Xu; Pan, Rui; Guan, Guoyu; Zhu, Xuening; Wang, Hansheng

doi:10.5705/ss.202017.0281

Cited by 7 publications

(10 citation statements)

References 29 publications

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“…Hence, it is useful to extend IONI to dynamic network models; see, e.g., Dou et al (2016) and Gao et al (2019). Lastly, based on an anonymous reviewer's suggestion, it is of great interest to generalize IONI to accommodate data with discrete responses (see Zhang et al 2020). We believe each of the above efforts would increase the value of IONI considerably.…”

Section: Discussionmentioning

confidence: 99%

Inward and Outward Network Influence Analysis

Wu,

Lan,

Zou

et al. 2022

Preprint

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Measuring heterogeneous influence across nodes in a network is critical in network analysis. This paper proposes an Inward and Outward Network Influence (IONI) model to assess nodal heterogeneity. Specifically, we allow for two types of influence parameters; one measures the magnitude of influence that each node exerts on others (outward influence), while we introduce a new parameter to quantify the receptivity of each node to being influenced by others (inward influence). Accordingly, these two types of influence measures naturally classify all nodes into four quadrants (high inward and high outward, low inward and high outward, low inward and low outward, high inward and low outward).To demonstrate our four-quadrant clustering method in practice, we apply the quasi-maximum likelihood approach to estimate the influence parameters, and we show the asymptotic properties of the resulting estimators. In addition, score tests are proposed to examine the homogeneity of the two types of influence parameters. To improve the accuracy of inferences about nodal influences, we introduce a Bayesian information criterion that selects the optimal influence model.The usefulness of the IONI model and the four-quadrant clustering method is illustrated via simulation studies and an empirical example involving customer segmentation.

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Section: Discussionmentioning

confidence: 99%

Inward and Outward Network Influence Analysis

Wu,

Lan,

Zou

et al. 2022

Preprint

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“…Predicting the linkage from a new primary node to all secondary nodes, given its connectivity with other primary nodes, is essentially a group label classification problem. In particular, we propose to implement the leave‐one‐out method to construct the classification rule (Zhang et al, 2020). Without loss of generality, given an estimated GRMM, we consider predicting the group membership of a new primary node ( n 1 + 1) by evaluating the conditional probabilities:

\begin{matrix} P false(k_{n_{1} + 1} = k false| A^{12}, \overset{boldk}{true}, \overset{bold-italicψ}{true} false) \propto {\overset{π}{true}}_{k} true \prod_{j = 1}^{n_{2}} ({, {(][, \frac{\exp ()(, {\overset{θ}{true}}_{k} + {\overset{ϕ}{true}}_{j} + \overset{ρ}{true} W_{n_{1} + 1} \overset{Z}{true} \overset{bold-italicθ}{true})}{1 + \exp false({\overset{θ}{true}}_{k} + {\overset{ϕ}{true}}_{j} + \overset{ρ}{true} W_{n_{1} + 1} \overset{Z}{true} \overset{bold-italicθ}{true} false)})}^{A_{false(n_{1} + 1 false) j}^{12}} {(][, \frac{1}{1 + \exp false({\overset{θ}{true}}_{k} + {\overset{ϕ}{true}}_{j} + \overset{ρ}{true} W_{n_{1} + 1} \overset{Z}{true} \overset{bold-italicθ}{true} false)})}^{1 - A_{false(n_{1 ...}}}) \end{matrix}

…”

Section: Test and Prediction Of Grmmmentioning

confidence: 99%

Section: Predictionmentioning

confidence: 99%

Statistical inference on group Rasch mixture network models

Long

Huang

2022

Stat

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In a two-mode network, the nodes are divided into two types (primary nodes and secondary nodes), and connections exist only between nodes of different types. In reality, in such a two-mode network, one-mode network connections may also exist among primary nodes, and these two kinds of networks are usually not independent and coexistent. In this paper, we first propose a group Rasch mixture network model that focuses on the connections between primary nodes and secondary nodes, while incorporating the group structure and linkage information of primary nodes. We then develop a modified expectation-maximization algorithm to estimate the proposed model with a λ-BIC method for selecting the tuning parameter. Additionally, we provide a likelihood-ratio test statistic to examine whether the two kinds of networks are independent and implement the leave-one-out method to construct a network prediction rule. Finally, we establish asymptotic results and demonstrate the numerical performance of the proposed methods using both simulations and the Last.fm dataset.

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“…We first prove (22). To this aim, we use the blocks decomposition introduced by [7] (see also [16]) which will be useful afterwards.…”

Section: Proofsmentioning

confidence: 99%

“…For example, in remote sensing technology or digital geography information, we need somehow to classify spatial data into patterns or images into types. Recently, [22] propose a novel probabilistic model for classification, that incorporates a network's structure into the classical logistic regression model. This model is mostly used to classify data produced by social network analysis taking into account the connection between nodes, but without any influence of the spatial coordinates.…”

mentioning

confidence: 99%

Consistency of the k-Nearest Neighbor Classifier for Spatially Dependent Data

Younso

Kanaya²,

Azhari³

2022

Commun. Math. Stat.

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The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data. Some spatial mixing conditions are considered, and under such spatial structures, the well known k-nearest neighbor rule is suggested to classify spatial data. We established consistency and strong consistency of the classifier under mild assumptions. Our main results extend the consistency result in the i.i.d. case to the spatial case.Analysis of spatial data arises in various areas of research including agricultural field trials, astronomy, econometrics, epidemiology, environmental science, geology, hydrology, image analysis, meteorology, ecology, oceanography and many others in which the data of interest are collected across space. One of the most fundamental issues in spatial analysis is classification and pattern

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Logistic Regression with Network Structure

Cited by 7 publications

References 29 publications

Inward and Outward Network Influence Analysis

Inward and Outward Network Influence Analysis

Statistical inference on group Rasch mixture network models

Consistency of the k-Nearest Neighbor Classifier for Spatially Dependent Data

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