eigvaldisp-package: eigvaldisp: Statistics of Eigenvalue Dispersion Indices

In watanabe-j/eigvaldisp: Statistics of Eigenvalue Dispersion Indices

eigvaldisp: Statistics of Eigenvalue Dispersion Indices

Description

This package involves functions for analyzing eigenvalue dispersion indices of covariance and correlation matrices, providing practical implementations for theoretical results of Watanabe (2022).

Details

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Run vignettes("eigvaldisp") for detailed descriptions and examples.

Author/Maintainer

Junya Watanabe [e-mail]

References

Watanabe, J. (2022) Statistics of eigenvalue dispersion indices: quantifying the magnitude of phenotypic integration. Evolution, 76, 4–28. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/evo.14382")}.

See Also

VE: Calculate eigenvalue dispersion indices

Exv.VXX: Moments of eigenvalue dispersion indices

AVar.VRR_xx: Approximate variance of relative eigenvalue variance of correlation matrix (internal functions)

VXXa: “Bias-corrected” eigenvalue dispersion indices

Exv.VXXa: Moments of “bias-corrected” eigenvalue dispersion indices

simulateVE: Simulate eigenvalue dispersion indices

GenCov: Generate covariance/correlation matrix with known structure

Exv.rx: Moments of correlation coefficients (internal functions)

hgf, sqrt_methods, centering, digit: Other internal utility functions

Examples

## Generate a population covariance matrix with known eigenvalues
Lambda <- c(4, 2, 1, 1)
(Sigma <- GenCov(evalues = Lambda, evectors = "random"))
all.equal(Lambda, eigen(Sigma)$values)  # TRUE

## Calculate eigenvalue dispersion indices of this matrix
EDI_pop <- VE(S = Sigma)

## Population eigenvalue variance ("V(Sigma)") and
## relative eigenvalue variance ("Vrel(Sigma)"):
EDI_pop$VE
EDI_pop$VR

## Simulate a multivariate normal sample
N <- 20
X <- rmvn(N = N, Sigma = Sigma)

## Calculating eigenvalue dispersion indices from the sample
EDI_sam <- VE(X = X)

## Sample eigenvalue variance ("V(S)") and
## relative eigenvalue variance ("Vrel(S)")
EDI_sam$VE
EDI_sam$VR
## These are typically biased upward

## Expectation and sampling variance of eigenvalue variance
## ("E[V(S)]" and "Var[V(S)]")
## The argument n is for the degree of freedom, hence N - 1 in this case
(E_V_Sigma <- Exv.VES(Sigma = Sigma, n = N - 1))
(Var_V_Sigma <- Var.VES(Sigma = Sigma, n = N - 1))

## Same for relative eigenvalue variance ("E[Vrel(S)]", "Var[Vrel(S)]")
(E_Vrel_Sigma <- Exv.VRS(Sigma, N - 1))
(Var_Vrel_Sigma <- Var.VRS(Sigma, N - 1))

## Usually sample estimates are within a few S.D. away from the expectation:
(EDI_sam$VE - E_V_Sigma) / sqrt(Var_V_Sigma)
(EDI_sam$VR - E_Vrel_Sigma) / sqrt(Var_Vrel_Sigma)

watanabe-j/eigvaldisp documentation built on Dec. 8, 2023, 4:38 a.m.