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.
MCA performs Multiscale Codependence Analysis
(MCA). Functions test.mca and permute.mca handle
parametric permutational testing of the codependence coefficients,
respectively.
Methods are provided to print and plot mca-class objects
(print.mca and plot.mca, respectively) as
well as summary (summary.mca), fitted values
(fitted.mca), residuals (residuals.mca),
and to make predictions (predict.mca).
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.
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 give familywise threshold and the number of
permutations suitable for testing Multiscale Codependence Analysis,
respectively.