Multiscale Codependence Analysis (MCA) consists in assessing the coherence of pairs of variables in space (or time) using the product of their correlation coefficients with series of spatial (or temporal) eigenfunctions. That product, which is positive or negative when variables show similar or opposing trends, respectively, are called codependence coefficients. These eigenfunctions are obtained in three steps: 1) a distance matrice calculated from the locations of samples in space (or the organisation of the sampling schedule). 2) from that distance matrix, a matrix of spatial weights is obtained; the same matrix as to calculate Moran's autocorrelation index, hence the name, and 3) the spatial weight matrix is eigenvalue-decomposed after centering each rows and columns of the spatial weight matrix.
The statistical significance of the codependence coefficients is
tested using parametric or permutational testing of a \(\tau\)
statistic. The \(\tau\) statistic is the product of the two
Student's \(t\) statistics obtained from each of the two
variables with a given eigenfunction. The \(\tau\) statistic
can take both positive and negative values, thereby allowing one to
perform one-directional or two-directional testing. For multiple
response variables, testing is performed using the \(phi\)
statistic instead. That statistics is the distribution of the product
of two Fisher-Snedocor F statistics (see
Product-distribution for details).
| Package: | codep |
| Type: | Package |
| Version: | 0.6-2 |
| Date: | 2015-11-10 |
| License: | Copyleft |
| LazyLoad: | yes |
Function MCA performs Multiscale Codependence Analysis
(MCA).
Functions test.cdp and permute.cdp handle
parametric permutational testing of the codependence coefficients,
respectively.
Methods are provided to print and plot cdp-class objects
(print.cdp and plot.cdp, respectively) as
well as summary (summary.cdp), fitted values
(fitted.cdp), residuals (residuals.cdp),
and to make predictions (predict.cdp).
Function eigenmap calculates spatial eigenvector maps
following the approach outlined in Dray et al. (2006), and which are
necessary to calculate MCA. It returns a
eigenmap-class object. The package also features methods
to print (print.eigenmap) and plot
(plot.eigenmap) these objects. Function
eigenmap.score can be used to make predictions for
spatial models built from the eigenfunctions of eigenmap
using distances between one or more target locations and the sampled
locations for which the spatial eigenvector map was built.
The package also features an examplary dataset Salmon
containing 76 sampling site positions along a 1520 m river segment as
well as functions cthreshold and
minpermute, which calculates the testwise type I error
rate threshold corresponding to a given familywise threshold and the
minimal number of permutations needed for testing Multiscale
Codependence Analysis given the alpha threshold, respectively.
Dray, S.; Legendre, P. and Peres-Neto, P. 2006. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbor matrices (PCNM). Ecol. Modelling 196: 483-493
Gu<U+00E9>nard, G., Legendre, P., Boisclair, D., and Bilodeau, M. 2010. Multiscale codependence analysis: an integrated approach to analyse relationships across scales. Ecology 91: 2952-2964
Legendre, P. and Legendre, L. 2012. Numerical Ecology, 3rd English edition. Elsevier Science B.V., Amsterdam, The Neatherlands.