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Linear mixed models and geostatistics for designed experiments in soil science: Two entirely different methods or two sides of the same coin?
Author(s) -
Slaets Johanna I. F.,
Boeddinghaus Runa S.,
Piepho HansPeter
Publication year - 2021
Publication title -
european journal of soil science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.244
H-Index - 111
eISSN - 1365-2389
pISSN - 1351-0754
DOI - 10.1111/ejss.12976
Subject(s) - geostatistics , covariance , analysis of covariance , variance (accounting) , statistics , mixed model , kriging , linear model , generalized linear mixed model , variogram , independence (probability theory) , mathematics , computer science , econometrics , spatial variability , accounting , business
Soil scientists are accustomed to geostatistical methods and tools such as semivariograms and kriging for analysis of observational data. Such methods assume and exploit that observations are spatially correlated. Conversely, analysis of variance (ANOVA) of designed experiments assumes that observations from different experimental units are independent, an assumption that is justified based on randomization. It may be beneficial, however, to perform an ANOVA assuming a geostatistical covariance model. Also, it is increasingly common to have multiple observations per experimental unit. Simple ANOVA assuming independence of observations is not appropriate for such data. Instead, a linear mixed model accounting for correlation among observations made on the same plot is required for proper analysis. The purpose of this paper is to demonstrate the benefits of integrating geostatistical covariance structures and ANOVA procedures into a linear mixed modelling framework. Two examples from designed experiments are considered in detail, making a link between terminologies and jargon used in geostatistical analysis on the one hand and linear mixed modelling on the other hand. We provide code in R and SAS for both examples in two supporting companion documents. Highlights Analysis of variance and geostatistical analysis can be joined in a mixed model. Randomization justifies the independence assumption in analysis of variance. Geostatistical models imply a correlation of errors and can improve efficiency. Lacking randomization, spatial correlation can be accounted for in a mixed model.