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A DOUBLY MULTIVARIATE MODEL FOR STATISTICAL ANALYSIS OF SPATIO‐TEMPORAL ENVIRONMENTAL DATA
Author(s) -
DUTILLEUL PIERRE,
PINELALLOUL BERNADETTE
Publication year - 1996
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/(sici)1099-095x(199611)7:6<551::aid-env233>3.0.co;2-9
Subject(s) - autocovariance , mathematics , heteroscedasticity , statistics , autocorrelation , mixed model , multivariate statistics , covariance matrix , random effects model , likelihood ratio test , econometrics , medicine , mathematical analysis , meta analysis , fourier transform
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.