Procrustes analysis (vegan procrustes and protest conventions)

ProcrustesFit: centred (optionally unit-scaled) configurations, rotation \(A = VU'\) from \(X'Y = USV'\), dilation \(\sum S/tr(Y'Y)\), residuals and Procrustes correlation (Gower 1971; Peres-Neto and Jackson 2001). GeneralizedProcrustes: orthogonal generalised Procrustes analysis (Gower 1975).

Usage

ProcrustesFit(X, Y, scale = TRUE, symmetric = FALSE)

GeneralizedProcrustes(configs, tol = 1e-12, maxit = 1000L)

Arguments

X

Target configuration.

Y

Configuration to rotate.

scale

Fit a dilation.

symmetric

Scale both to unit sum of squares.

configs

List of configurations.

tol

Convergence tolerance.

maxit

Maximum iterations.

Value

List.

References

Gower, J. C. (1975). Generalized Procrustes analysis. Psychometrika 40, 33-51.

Peres-Neto, P. R. and Jackson, D. A. (2001). How well do multivariate data sets match? Oecologia 129, 169-178.

Examples

ProcrustesFit(rbind(c(0, 0), c(1, 0), c(0, 1)), rbind(c(0, 0), c(0, 2), c(-2, 0)))$scale
#> [1] 0.5