S3. Variance partitioning as a tool for controlling the type I error in ANOVA/MANOVA routines:
a suggested R code.
### If you identify any problem or have any suggestion to improve this code, please contact
the author of the manuscript (pedrov.eisenlohr@gmail.com).
### This code was prepared and edited by Danilo R.M. Neves (University of Leeds) and Pedro
V. Eisenlohr (Universidade Federal de Minas Gerais), with the help of Mário José Marques
Azevedo (Universidade Estadual de Campinas), considering the following references:
# 1. Legendre, P., D. Borcard and D. W. Roberts. 2012. Variation partitioning involving
orthogonal spatial eigenfunction submodels. Ecology 93: 1234-1240.
# 2. Borcard, D., F. Gillet & P. Legendre. 2011. Numerical Ecology with R. Springer, New York,
302p.
# 3. Peres-Neto, P. R. and P. Legendre. 2010. Estimating and controlling for spatial structure in
the study of ecological communities. Global Ecology and Biogeography 19: 174-184.
# 4. Blanchet F. G., P. Legendre, and D. Borcard. 2008. Forward selection of explanatory
variables. Ecology 89: 2623-2632.
# 5. Dray, S., P. Legendre and P. Peres-Neto. 2006. Spatial modelling: a comprehensive
framework for principal coordinate analysis of neighbor matrices (PCNM). Ecological Modelling
196: 483-493.
# 6. Legendre, P. and E. Gallagher. 2001. Ecologically meaningful transformations for
ordination of species data. Oecologia 129: 271-280.
# 7. Anderson, M. J. & P. Legendre. 1999. An empirical comparison of permutation methods for
tests of partial regression coefficients in a linear model. Journal of Statistical Computation and
Simulation 62: 271-303.
### Preparing data matrices:
# X matrix: full model (without latitude and longitude). VarDep is the response variable
# W matrix: latitude and longitude
# Y matrix: only response variable (s) (VarDep or, in case of MANOVA, VarDep1, VarDep 2 etc.)
### Choose the directory (File->Change Dir...)
### If packages are not installed, run the following commands:
install.packages("vegan")
install.packages("packfor", repos="http://R-Forge.R-project.org")
install.packages("spacemakeR", repos="http://R-Forge.R-project.org")
install.packages("spdep")
install.packages("venneuler")
install.packages("tripack")
### Uploading the packages:
library(vegan)
library(packfor)
library(spacemakeR)
library(spdep)
library(venneuler)
library(tripack)
### Importing and verifying data matrices:
X<-read.table(file.choose(),row.names=1,header=T,sep=",")
edit(X)
W<-read.table(file.choose(),row.names=1,header=T,sep=",")
edit(W)
Y<-read.table(file.choose(),row.names=1,header=T,sep=",")
edit(Y)
### Generating and testing the significance of spatial variables (Moran's Eigenvector Maps MEMs):
ll.temp<-tri2nb(W) ### Can be changed. See Borcard et al. (2011) and Legendre and Legendre
(2012) for details.
ll.transf = nb2listw(ll.temp, style = "minmax") ### Can be changed. See Borcard et al. (2011)
and Legendre and Legendre (2012) for details.
mem<-scores.listw(ll.transf)
colnames(mem$vectors)<-paste("MEM",1:ncol(mem$vectors))
colnames(mem$vectors)
mem.teste<-test.scores(mem,ll.transf,999)
sel.mem<-mem
sel.mem$vectors<-sel.mem$vectors[,mem.teste[,2]<0.05]
dim(sel.mem$vectors)
write.table(sel.mem$vectors,"mem_all.csv")
### Selecting MEMs via forward selection:
lm1<-lm(VarDep~sel.mem$vectors, data=Y)
r2.lm1<-RsquareAdj(lm1)$adj.r.squared
r2.lm1
sel.lm1<-forward.sel(Y,sel.mem$vectors,adjR2thresh=r2.lm1)
sel.lm1
### Peres-Neto & Legendre (2010) suggested performing a MEMs selection for each response
variable individually and, then, using those which have been selected at least once.
### The following commands should be used only for checking the ANOVA/MANOVA results
when spatial structures are not considered.
lm2<-lm(VarDep~treat, data=X)
anova(lm2)
r2.lm2<-RsquareAdj(lm2)$adj.r.squared
r2.lm2
### Preparing selected variables for variance partitioning:
espaciais<-colnames(mem$vectors)%in%sel.lm1$variables
sel.valores<-sel.mem$values[sel.lm1$order]
sel.vetores<-sel.mem$vectors[,sel.lm1$order]
dim(sel.vetores)
write.table(sel.vetores,"mem_selected.csv")
treat <- model.matrix(VarDep~treat, data=X)[ ,-1]
### Variance partitioning:
all.varpart<-varpart(Y,treat,sel.vetores)
all.varpart
plot(all.varpart)
### Testing the significance of the treatment (fraction [a]), after considering the effect of
selected MEMs:
amb.rda<-rda(Y,treat,sel.vetores)
teste.amb<-anova(amb.rda)
teste.amb
### In case of significance, you should perform post hoc tests (Tukey etc.) using the selected
MEMs as covariables.