TY - JOUR
T1 - Birnbaum–Saunders spatial modelling and diagnostics applied to agricultural engineering data
AU - Garcia-Papani, Fabiana
AU - Uribe-Opazo, Miguel Angel
AU - Leiva, Victor
AU - Aykroyd, Robert G.
N1 - Funding Information:
The authors thank the Editors and anonymous referees for their constructive comments on an earlier version of the manuscript, which resulted in this improved version. We are grateful to Carolina Brianezi-Melchior, who translated this work into English, from its original Portuguese. This research work was partially supported by CNPq Grants from the Brazilian Government, and by FONDECYT 1120879 Grant from the Chilean Government.
Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum–Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered—which is extremely important for agricultural management.
AB - Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum–Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered—which is extremely important for agricultural management.
KW - Asymmetric distributions
KW - Local influence
KW - Matérn model
KW - Maximum likelihood methods
KW - Monte Carlo simulation
KW - Non-normality
KW - R software
KW - Spatial data analysis
UR - http://www.scopus.com/inward/record.url?scp=85011663841&partnerID=8YFLogxK
U2 - 10.1007/s00477-015-1204-4
DO - 10.1007/s00477-015-1204-4
M3 - Article
AN - SCOPUS:85011663841
VL - 31
SP - 105
EP - 124
JO - Stochastic Environmental Research and Risk Assessment
JF - Stochastic Environmental Research and Risk Assessment
SN - 1436-3240
IS - 1
ER -