mca: Multiple-descriptors, Multiscale Codependence Analysis
In codep: Multiscale Codependence Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

Functions to perform Multiscale Codependence Analysis (MCA)

MCA(Y, X, emobj)
test.cdp(object, alpha = 0.05, max.step, response.tests = TRUE)
permute.cdp(object, permute, alpha = 0.05, max.step,
            response.tests = TRUE)
parPermute.cdp(object, permute, alpha = 0.05, max.step,
               response.tests = TRUE, nnode, seeds, verbose = TRUE,
               ...)

`Y`	a numeric matrix or vector containing the response variable(s).
`X`	a numeric matrix or vector containing the explanatory variable(s).
`emobj`	a `eigenmap-class` object.
`object`	a `cdp-class` object.
`alpha`	type I (alpha) error threshold used by the testing procedure.
`max.step`	maximum number of steps to perform when testing for statistical significance.
`response.tests`	a boolean specifying whether to test individual response variables.
`permute`	The number of random permutations used for testing. When omitted, the number of permutations is calculated using function `minpermute`.
`nnode`	The number of parallel computation nodes.
`seeds`	Random number generator seeds for parallel the computation nodes.
`verbose`	Whether to return user notifications.
`...`	Parameters to be passed to `parallel::makeCluster()`

Multiscale Codependence Analysis (MCA) allows to calculate correlation-like (i.e.codependence) coefficients between two variables with respect to structuring variables (Moran's eigenvector maps). The purpose of this function is limited to parameter fitting. Test procedures are handled through test.cdp (parametric testing) or permute.cdp (permutation testing). Additionaly, methods are provided for printing, displaying the testing summary, plotting results, calculating fitted and residuals values, and making predictions. It is noteworthy that the test procedure used by MCA deviates from the standard R workflow since intermediate testing functions (test.cdp and permute.cdp) need first to be called before any testing be performed. For MCA, testing functionalities had been moved away from summary.cdp because testing is computationally intensive. Function parPermute.cdp allows the user to spread the number of permutation on many computation nodes. It relies on package parallel. Omitting parameter nnode lets function parallel::detectCores() specify the number of node. Similarly, omitting parameter seeds lets the draw seeds uniformly between ±.Machine$integer.max. If needed, one may pass initialization parameters to parallel::makeCluster().

A cdp-class object.

Guillaume Guénard, Département des sciences biologiques, Université de Montréal, Montréal, Québec, Canada.

Guénard, G., Legendre, P., Boisclair, D., and Bilodeau, M. 2010. Multiscale codependence analysis: an integrated approach to analyse relationships across scales. Ecology 91: 2952-2964

Guénard, G. Legendre, P. 2018. Bringing multivariate support to multiscale codependence analysis: Assessing the drivers of community structure across spatial scales. Meth. Ecol. Evol. 9: 292-304

eigenmap

#
###### Begin {Salmon exemple}
#
data(Salmon)
#
## Converting the data from data frames to to matrices:
Abundance <- log1p(as.matrix(Salmon[,"Abundance",drop=FALSE]))
Environ <- as.matrix(Salmon[,3L:5])
#
## Creating a spatial eigenvector map:
map1 <- eigenmap(x=Salmon[,"Position"],weighting=Wf.binary,boundaries=c(0,20))
#
## Case of a single descriptor:
mca1 <- MCA(Y=Abundance,X=Environ[,"Substrate",drop=FALSE],emobj=map1)
mca1
mca1_partest <- test.cdp(mca1)
mca1_partest
summary(mca1_partest)
par(mar = c(6,4,2,4))
plot(mca1_partest, las = 3)
mca1_pertest <- permute.cdp(mca1)
## Not run: 
## or:
mca1_pertest <- parPermute.cdp(mca1,permute=999999)

## End(Not run)
mca1_pertest
summary(mca1_pertest)
plot(mca1_pertest, las = 3)
mca1_pertest$UpYXcb$C # Array containing the codependence coefficients
#
## With all descriptors at once:
mca2 <- MCA(Y=log1p(as.matrix(Salmon[,"Abundance",drop=FALSE])),
            X=as.matrix(Salmon[,3L:5]),emobj=map1)
mca2
mca2_partest <- test.cdp(mca2)
mca2_partest
summary(mca2_partest)
par(mar = c(6,4,2,4))
plot(mca2_partest, las = 3)
mca2_pertest <- permute.cdp(mca2)
## Not run: 
or:
mca2_pertest <- parPermute.cdp(mca2,permute=999999)

## End(Not run)
mca2_pertest
summary(mca2_pertest)
plot(mca2_pertest, las = 3)
mca2_pertest$UpYXcb$C # Array containing the codependence coefficients
mca2_pertest$UpYXcb$C[,1L,] # now turned into a matrix.
#
###### End {Salmon exemple}
#
###### Begin {Doubs exemple}
#
data(Doubs)
#
## Creating a spatial eigenvector map:
map2 <- eigenmap(x=Doubs.geo[,"DFS"])
#
mca3 <- MCA(Y=log1p(Doubs.fish),X=Doubs.env,emobj=map2)
mca3
mca3_pertest <- permute.cdp(mca3)
## Not run: 
## or:
mca3_pertest <- parPermute.cdp(mca3,permute=999999)

## End(Not run)
mca3_pertest
summary(mca3_pertest)
par(mar = c(6,4,2,4))
plot(mca3_pertest, las = 2)
mca3_pertest$UpYXcb$C # Array containing the codependence coefficients
#
## Display the results along the transect
spmeans <- colMeans(log1p(Doubs.fish))
pca1 <- svd(log1p(Doubs.fish) - rep(spmeans,each=nrow(Doubs.fish)))
par(mar = c(5,5,2,5)+0.1)
plot(y = pca1$u[,1L], x = Doubs.geo[,"DFS"], pch = 21L, bg = "red",
     ylab = "PCA1 loadings", xlab = "Distance from river source (km)")
#
x <- seq(0,450,1)
newdists <- matrix(NA, length(x), nrow(Doubs.geo))
for(i in 1L:nrow(newdists))
  newdists[i,] <- abs(Doubs.geo[,"DFS"] - x[i])
#
## Calculating predictions for arbitrary sites under the same set of
## environmental conditions that the codependence model was built with.
prd1 <- predict(mca3_pertest,
                newdata=list(target = eigenmap.score(map2, newdists)))
#
## Projection of the predicted species abundance on pca1:
Uprd1 <- (prd1 - rep(spmeans, each = nrow(prd1))) %*% pca1$v %*% diag(pca1$d^-1)
lines(y = Uprd1[,1L], x = x, col=2, lty = 1)
#
## Projection of the predicted species abundance on pca2:
plot(y = pca1$u[,2L], x = Doubs.geo[,"DFS"], pch = 21L, bg = "red",
     ylab = "PCA2 loadings", xlab = "Distance from river source (km)")
lines(y = Uprd1[,2L], x = x, col=2, lty = 1)

#
## Displaying only the observed and predicted abundance for Brown Trout.
par(new=TRUE)
plot(y = log1p(Doubs.fish[,"TRU"]),Doubs.geo[,"DFS"],pch=21L,bg="green",
     ylab="",xlab="",new=FALSE,axes=FALSE)
axis(4)
lines(y = prd1[,"TRU"], x = x, col=3)
mtext(side=4, "log(Abundance+1)", line = 2.5)
#
###### End {Doubs exemple}
#
###### Begin {Oribatid exemple}
#
data(Mite)
#
map3 <- eigenmap(x = mite.geo)
# Organize the environmental variables
mca4 <- MCA(Y = log1p(mite.species), X = mite.env, emobj = map3)
mca4_partest <- test.cdp(mca4, response.tests = FALSE)
summary(mca4_partest)
plot(mca4_partest, las = 2, lwd = 2)
plot(mca4_partest, col = rainbow(1200)[1L:1000], las = 3, lwd = 4,
     main = "Codependence diagram", col.signif = "white")
#
rng <- list(x = seq(min(mite.geo[,"x"]) - 0.1, max(mite.geo[,"x"]) + 0.1, 0.05),
            y = seq(min(mite.geo[,"y"]) - 0.1, max(mite.geo[,"y"]) + 0.1, 0.05))
grid <- cbind(x = rep(rng[["x"]], length(rng[["y"]])),
              y = rep(rng[["y"]], each = length(rng[["x"]])))
newdists <- matrix(NA, nrow(grid), nrow(mite.geo))
for(i in 1L:nrow(grid)) {
  newdists[i,] <- ((mite.geo[,"x"] - grid[i,"x"])^2 +
                    (mite.geo[,"y"] - grid[i,"y"])^2)^0.5
}
#
spmeans <- colMeans(mite.species)
pca2 <- svd(log1p(mite.species) - rep(spmeans, each = nrow(mite.species)))
#
prd2 <- predict(mca4_partest,
          newdata = list(target = eigenmap.score(map3, newdists)))
Uprd2 <- (prd2 - rep(spmeans, each = nrow(prd2))) %*% pca2$v %*% diag(pca2$d^-1)
#
### Printing the response variable
prmat <- Uprd2[,1L]
dim(prmat) <- c(length(rng$x),length(rng$y))
zlim <- c(min(min(prmat),min(pca2$u[,1L])),max(max(prmat),max(pca2$u[,1L])))
image(z = prmat, x = rng$x, y = rng$y, asp = 1, zlim = zlim,
      col = rainbow(1200L)[1L:1000], ylab = "y", xlab = "x")
points(x = mite.geo[,"x"], y = mite.geo[,"y"], pch = 21,
  bg = rainbow(1200L)[round(1+(999*(pca2$u[,1L]-zlim[1L])/(zlim[2L]-zlim[1L])),0)])
#
###### End {Oribatid exemple}
#