Linear Models for Multivariate, Time Series, and Spatial Data

Christensen, Ronald

doi:10.1007/978-1-4757-4103-2

Cited by 137 publications

(97 citation statements)

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“…C 0 , C 1 and R are variogram parameters and AhA is the Euclidean distance between the point pairs. Thus, RK in matrix notation is (Christensen, 1990):…”

Section: The Spatial Prediction Technique: Regression-krigingmentioning

confidence: 99%

A generic framework for spatial prediction of soil variables based on regression-kriging

Hengl¹,

Heuvelink

Stein³

2004

Geoderma

899

558

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A methodological framework for spatial prediction based on regression-kriging is described and compared with ordinary kriging and plain regression. The data are first transformed using logit transformation for target variables and factor analysis for continuous predictors (auxiliary maps). The target variables are then fitted using step-wise regression and residuals interpolated using kriging. A generic visualisation method is used to simultaneously display predictions and associated uncertainty. The framework was tested using 135 profile observations from the national survey in Croatia, divided into interpolation (100) and validation sets (35). Three target variables: organic matter, pH in topsoil and topsoil thickness were predicted from six relief parameters and nine soil mapping units. Prediction efficiency was evaluated using the mean error and root mean square error (RMSE) of prediction at validation points. The results show that the proposed framework improves efficiency of predictions. Moreover, it ensured normality of residuals and enforced prediction values to be within the physical range of a variable. For organic matter, it achieved lower relative RMSE than ordinary kriging (53.3% versus 66.5%). For topsoil thickness, it achieved a lower relative RMSE (66.5% versus 83.3%) and a lower bias than ordinary kriging (0.15 versus 0.69 cm). The prediction of pH in topsoil was difficult with all three methods. This framework can adopt both continuous and categorical soil variables in a semi-automated or automated manner. It opens a possibility to develop a bundle algorithm that can be implemented in a GIS to interpolate soil profile data from existing datasets. D

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“…C 0 , C 1 and R are variogram parameters and AhA is the Euclidean distance between the point pairs. Thus, RK in matrix notation is (Christensen, 1990):…”

Section: The Spatial Prediction Technique: Regression-krigingmentioning

confidence: 99%

A generic framework for spatial prediction of soil variables based on regression-kriging

Hengl¹,

Heuvelink

Stein³

2004

Geoderma

899

558

View full text Add to dashboard Cite

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“…We follow but also see Christensen (1991). Suppose that X(p × 1) and Y (q × 1) are random vectors with some joint distri-bution, and with expectations E(X) and EY .…”

Section: Linear Least Squares Predictionmentioning

confidence: 99%

The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two‐sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one‐sided tests, however, one‐sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two‐sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well‐chosen one‐sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

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“…Universal kriging (UK) model that was said to have been introduced by [26] and by many statisticians considered to be the (only) best linear unbiased prediction model of spatial data [27], Section 6. Originally, UK was intended as a generalized case of kriging where the trend is modelled as a function of coordinates, within the kriging system.…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Assessment of Vegetation Productivity in the Northern Part of Nigeria

Yelwa¹,

Usman²

2017

AJCC

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Climate change is one of the greatest threats facing the global community and has been mainly induced by increasing atmospheric concentrations of greenhouse gases resulting from fossil fuel energy use and change in vegetation cover. This study used modelling techniques to determine how changes in climate could affect vegetation productivity in the northern part of Nigeria. Climatic parameters (Rainfall, Minimum and Maximum Temperatures) as well as coarse Normalised Difference Vegetation Index (NDVI) data for the growing seasons of 1981-2009 were utilised. Because of the relationship between climatic parameters and vegetation, Spatial method of data interpolation was tested. Results from the prediction elevation values ranged from −3e−9 to 2e−9. It was observed from prediction variance map that the values were higher in the upper portion of the study area which comprised Gusau (GS), Jos (JS), Katsina (KT), Minna (MN) and Zaria (ZR) and lower in the middle and lower parts of the study area which comprised mainly Funtua, Kano, Maiduguri and Sokoto. Further studies are encouraged with high resolution imageries and more meteorological data to cover the montane and forest zone of the country to determine the level of climatic impacts particularly on vegetation productivity in general.

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Linear Models for Multivariate, Time Series, and Spatial Data

Cited by 137 publications

References 0 publications

A generic framework for spatial prediction of soil variables based on regression-kriging

A generic framework for spatial prediction of soil variables based on regression-kriging

The Use of Score Tests for Inference on Variance Components

Assessment of Vegetation Productivity in the Northern Part of Nigeria

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