msr | R Documentation |

This function allows to generate spatially-constrained random variables preserving the global autocorrelation (Moran's I) and the spatial structures at multiple scales. Multiscale property is defined by the power spectrum (i.e. decomposition of the variance of the original variables) on a basis of orthonormal eigenvectors (Moran's Eigenvector Maps, MEM). The function provides methods for univariate randomization, joint randomization of a group of variables while keeping within-group correlations fixed and univariate randomization with a fixed correlation between original data and randomized replicates.

msr(x, ...) ## Default S3 method: msr( x, listwORorthobasis, nrepet = 99, method = c("pair", "triplet", "singleton"), cor.fixed, nmax = 100, simplify = TRUE, ... )

`x` |
For |

`...` |
further arguments passed to or from other methods |

`listwORorthobasis` |
an object of the class |

`nrepet` |
an |

`method` |
an character specifying which algorithm should be used to produce spatial replicates (see Details). |

`cor.fixed` |
if not missing, the level of correlation between the original variable and its randomized replicates |

`nmax` |
the number of trials used in the "triplet" procedure. |

`simplify` |
A logical value. If |

Three procedures are implemented in the function. The "pair" procedure is the more general as it can be applied in the three cases (univariate, univariate with fixed correlation and multivariate). This procedure preserves the power spectrum by pair of MEMs but not strictly the global autocorrelation level (Moran's I). The "singleton" procedure can be used for univariate and multivariate cases. It preserves strictly the global level of autocorrelation and the power spectrum. The "triplet" procedure can only be applied in the univariate case. It preserves the power spectrum by triplet of MEMs and strictly the global autocorrelation level.

Either a matrix (if `simplify`

is `TRUE`

) or a list with
randomized replicates.

Stephane Dray stephane.dray@univ-lyon1.fr and Helene H Wagner helene.wagner@utoronto.ca

Wagner, H.H. and Dray S. (2015) Generating spatially-constrained null models for irregularly spaced data using Moran spectral randomization methods. Methods in Ecology and Evolution, 6: 1169-1178. doi:10.1111/2041-210X.12407

`scores.listw`

, `nb2listw`

library(spdep) x1 <- matrix(rnorm(81*5), nrow = 81) lw1 <- nb2listw(cell2nb(9, 9)) moran.mc(x1[,1], lw1, 2)$statistic ## singleton x1.1 <- msr(x1[,1], lw1, nrepet = 9, method = "singleton") apply(x1.1, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) ## triplet x1.2 <- msr(x1[,1], lw1, nrepet = 9, method = "triplet") apply(x1.2, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) ## pair x1.3 <- msr(x1[,1], lw1, nrepet = 9, method = "pair") apply(x1.3, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) ## pair with cor.fixed x1.4 <- msr(x1[,1], lw1, nrepet = 9, cor.fixed = 0.5) apply(x1.4, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) cor(x1[,1], x1.4) ## pair preserving correlations for multivariate data x1.5 <- msr(x1, lw1, nrepet = 9, cor.fixed = 0.5) cor(x1) lapply(x1.5, cor) apply(x1, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) apply(x1.5[[1]], 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) ## singleton preserving correlations for multivariate data x1.6 <- msr(x1, lw1, nrepet = 9, method = "singleton") cor(x1) lapply(x1.6, cor) apply(x1, 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic) apply(x1.6[[1]], 2, function(x) moran.mc(x, listw = lw1, nsim = 2)$statistic)

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