A doubly multivariate model for statistical analysis of spatio-temporal environmental data
A doubly multivariate model for statistical analysis of spatio-temporal environmental data
复制标题
时空环境数据统计分析的双多元模型
DOI：
10.1002/(sici)1099-095x(199611)7:6
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发表时间：
1996
期刊：
影响因子：
1.7
通讯作者：
B. Pinel‐Alloul
中科院分区：
文献类型：
--
作者：
P. Dutilleul;B. Pinel‐Alloul
本文提出了一种双多元统计模型，称为矩阵正态模型，因为它能够考虑到时空自相关、异方差和平均值的非平稳性。它唯一的基本假设是理论自协方差函数的时空可分性和正态性。给出了矩阵正态模型下时空自协方差矩阵的极大似然估计算法，包括收敛准则和解的存在性准则。所得的最大似然估计用于时空重复测量的修正方差分析和相关分析。特别是，矩阵正态模型允许(i)在调整空间、时间和时空效应的修正方差分析f检验的显著性概率时计算不同的Box's epsilo n估计，以及（ii）在相关分析中开发Dutilleul's修正t检验的时空版本。以浮游植物生物量为随机变量的湖沼学案例研究的Sp -temporal重复测量数据说明了该模型及其推导框架。
A doubly multivariate statistical model, called the matrix normal model, is presented for its ability to take spatial and temporal autocorrelation, heteroscedasticity and non-stationarity in the mean into account. Its only underlying assumptions are sp ace-time separability of the theoretical autocovariance function and normality. An algorithm for maximum likelihood estimation of the spatial and temporal autocovariance matrices under the matrix normal model, including criteria of convergence and existen ce of solutions, is given. The resulting maximum likelihood estimates are used in modified ANOVA and correlation analysis of spatio-temporal repeated measures. In particular, the matrix normal model allows (i) the computation of distinct Box's epsilo n estimates in adjusting the significance probability of the modified ANOVA F-tests for space, time and space-time effects, and (ii) the development of a spatio-temporal version of Dutilleul's modified t-test in correlation analysis. Sp atio-temporal repeated measures data from a case study in limnology, with phytoplankton biomass as random variable of interest, illustrate the model and derived framework.