## Comparing maximum likelihood ordination with principal components analysis and correspondence analysis for equicorrelated data |

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### Contents

Linear Gaussian Model | 6 |

Quadratic Gaussian Model | 28 |

Quadratic Bernoulli Model | 47 |

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### Common terms and phrases

1st order absolute values analysis and correspondence approximation asymptotic Average relative biases average relative standard bias 1 std bias mse biases and relative biases and standard binary logit Braak c=sumc(y Computes consistently estimates contingency table converges correlation correspondence analysis covariance matrix covariance structure defined dominant eigenvector ecological ecologists eigenvalue endif endo equicorrelated format rd identifiability constraint implies inconsistent independence iter iter]=stat(uhat iter=iter+l iter=l Kronecker's delta Let model likelihood equations linear Gaussian model linear model location and scale log-likelihood maximum likelihood ordination mean square errors measurement error model ML estimates ML ordination modified CA estimator Newton's method nonzero constant normalized output PCA estimator principal components analysis quadratic Bernoulli model quadratic Gaussian model rbias relative standard deviations rmse rngu scale change scale invariant statistic Simulation program comparing singular value decomposition species abundances species parameters std 1 bias true covariance u_ca=abs(u_ca u_pca=zeros(niter,m uhat'/sqrt(uhat'uhat uhat=uhat-meanc(uhat vector w=y-meanc(y x=x-meanc(x zero