Comparing Maximum Likelihood Ordination with Principal Components Analysis and Correspondence Analysis for Equicorrelated DataCornell University, 1995 - 176 pages |
Common terms and phrases
1st order approximation asymptotic Average relative biases average relative standard bias std bias biases and relative Braak Computes Consistency of PCA consistently estimates contingency table converges correlation correspondence analysis covariance matrix covariance structure cx,b dominant eigenvector ecologists eigenvalue endif endo equicorrelated finite sample format rd Greenacre 1984 identifiability constraint implies inconsistent k₁ k₂ Kronecker's delta least squares least squares approximation Let model likelihood equations linear Gaussian model linear model location and scale log-likelihood Maximum likelihood estimation maximum likelihood ordination mean square errors measurement error model ML estimates modified CA estimator nonzero constant normalized output PCA estimator principal components analysis Program for Tables quadratic Bernoulli model quadratic Gaussian model regression relative standard deviations sample sizes scale change scale invariant statistic singular value decomposition species abundances species parameters std bias std u_ca=abs(u_ca u_mca[iter,.]=rngu*uhat'/sqrt(uhat'uhat uhat=uhat-meanc(uhat vector x₁ y₁ Yijyik zero µ₁ Σχ