Research School of Finance, Actuarial Studies & Statistics, Australian National University, Acton, Australia.
Institute for Marine and Antarctic Studies, University of Tasmania, Hobart, Australia.
Biometrics. 2022 Mar;78(1):85-99. doi: 10.1111/biom.13416. Epub 2021 Jan 6.
Multivariate spatial data, where multiple responses are simultaneously recorded across spatially indexed observational units, are routinely collected in a wide variety of disciplines. For example, the Southern Ocean Continuous Plankton Recorder survey collects records of zooplankton communities in the Indian sector of the Southern Ocean, with the aim of identifying and quantifying spatial patterns in biodiversity in response to environmental change. One increasingly popular method for modeling such data is spatial generalized linear latent variable models (GLLVMs), where the correlation across sites is captured by a spatial covariance function in the latent variables. However, little is known about the impact of misspecifying the latent variable correlation structure on inference of various parameters in such models. To address this gap in the literature, we investigate how misspecifying and assuming independence for the latent variables' correlation structure impacts estimation and inference in spatial GLLVMs. Through both theory and numerical studies, we show that performance of maximum likelihood estimation and inference on regression coefficients under misspecification depends on a combination of the response type, the magnitude of true regression coefficient, and the corresponding loadings, and, most importantly, whether the corresponding covariate is (also) spatially correlated. On the other hand, estimation and inference of truly nonzero loadings and prediction of latent variables is consistently not robust to misspecification of the latent variable correlation structure.
多元空间数据是指在空间索引观测单元中同时记录多个响应的数据集，在许多学科中都有常规的收集。例如，南大洋连续浮游生物记录仪调查收集了南大洋印度海域浮游动物群落的记录，目的是确定和量化生物多样性对环境变化的空间模式。目前，一种越来越受欢迎的分析此类数据的方法是空间广义线性潜在变量模型（GLLVM），其中站点之间的相关性通过潜在变量中的空间协方差函数来捕捉。然而，对于在这些模型中指定潜在变量相关结构的影响，人们知之甚少。为了弥补文献中的这一空白，我们研究了在潜在变量相关结构中指定和假设独立性对空间 GLLVM 中各种参数推断的影响。通过理论和数值研究，我们表明，在指定错误的情况下，最大似然估计和对回归系数的推断性能取决于响应类型、真实回归系数的大小以及相应的载荷，最重要的是，相应的协变量是否（也）具有空间相关性。另一方面，潜在变量相关结构指定错误会一致地影响潜在变量的估计和推断以及潜在变量的预测。
