Embedding Network Autoregression for time series analysis and causal peer effect inference
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嵌入网络自回归：时间序列分析与因果同伴效应推断
- 研究问题
- 如何从网络中估计潜变量以处理同质性选择，并分别支持多变量网络时间序列预测和有限期纵向数据中的因果同伴效应估计？
- 方法与思路
- 作者先依据观测网络估计潜变量，再用最小二乘估计含潜变量加性效应的网络自回归模型，并研究潜在维度选择。
- 材料陈述的贡献
- 摘要称，在不同时间维度设定下建立动量与同伴参数的一致性和渐近正态性，允许潜在维度增长，并提供不低选的维度准则。
- 阅读关注点
- 应分别核对增长期与有限期设定中的识别、潜变量限制和增长率，以及网络嵌入误差、维度选择对参数推断的影响。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未给出具体增长率，统一模型并不意味着两个问题共享同一保证。
原文摘要
We propose an Embedding Network Autoregressive Model for multivariate networked longitudinal data. We assume the network is generated from a latent variable model, and these unobserved variables are included in a structural peer effect model or a time series network autoregressive model as additive effects. This approach takes a unified view of two related yet fundamentally different problems: (1) modeling and predicting multivariate networked time series data and (2) causal peer influence estimation in the presence of homophily from finite time longitudinal data. Our estimation strategy comprises estimating latent variables from the observed network followed by least squares estimation of the network autoregressive model. We show that the estimated momentum and peer effect parameters are consistent and asymptotically normally distributed in setups with a growing number of network vertices (N) while considering both a growing number of time points T (for the time series problem) and finite T cases (for the peer effect problem). We allow the number of latent vectors K to grow at appropriate rates, which improves upon existing rates when such results are available for related models. Our theoretical results encompass cases both when the network is modeled with the random dot product graph model (ENAR) and a more general latent space model with both additive and multiplicative effects (AMNAR). We also develop a selection criterion when K is unknown that provably does not under-select and show that the theoretical guarantees hold with the selected number for K as well. Interestingly, even though we propose a unified model, our theoretical results find that different growth rates and restrictions on the latent vectors are needed to induce omitted variable bias in the peer effect problem and to ensure consistent estimation in the time series problem.