Abstract
While a variety of statistical models now exist for the spatio-temporal analysis of two-dimensional (surface) data collected over time, there are few published examples of analogous models for the spatial analysis of data taken over four dimensions: latitude, longitude, height or depth, and time. When taking account of the autocorrelation of data within and between dimensions, the notion of closeness often differs for each of the dimensions. Here, we consider a number of approaches to the analysis of such a dataset, which arises from an agricultural experiment exploring the impact of different cropping systems on soil moisture. The proposed models vary in their representation of the spatial correlation in the data, the assumed temporal pattern and choice of conditional autoregressive (CAR) and other priors. In terms of the substantive question, we find that response cropping is generally more effective than long fallow cropping in reducing soil moisture at the depths considered (100 cm to 220 cm). Thus, if we wish to reduce the possibility of deep drainage and increased groundwater salinity, the recommended cropping system is response cropping.
Highlights
Where data are collected from a set of sites, at a series of time points, observations taken close to each other in either time or space may be autocorrelated
Autocorrelated observations reduce the number of effective observations, and statistical analyses and inferences which fail to take this autocorrelation into account are more prone to identification of erroneous significant relationships
Dynamical spatio-temporal models described in [1,2,3] utilise differential equations
Summary
Where data are collected from a set of sites, at a series of time points, observations taken close to each other in either time or space may be autocorrelated. Autocorrelated observations reduce the number of effective observations, and statistical analyses and inferences which fail to take this autocorrelation into account are more prone to identification of erroneous significant relationships. The spatial autocorrelations are the focus of interest, but in other applications, the aim is to account for them in order to obtain accurate and precise parameter estimates. Spatio-temporal data are often analysed using models where spatial and temporal autocorrelation effects are separable, that is, with the assumption of no interaction between time and space. Cressie and Wikle [1] comment that separable covariance models “have very particular properties that are rarely seen in empirical studies of spatio-temporal dependence”. Dynamical spatio-temporal models described in [1,2,3] utilise differential equations
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