Nonlinear Multivariate Analysis

Conventions and controversies in multivariate analysis; Content analysis of MVA books; Correspondence analysis of tables of content; A shortsummary and some problems; Data analysis and statistics; Data analyticprinciples of this book; Specific problems of MVA; Definition of MVA; Some important ingredients; Epilogue; Coding of categorical data; The complete indicator matrix and its properties; Quantification; The incomplete indicator matrix; Missing data; The reversed indicator matrix; The indicator matrix for a contingency table; Grouping of categories; Grouping of variables; Epilogue; Homogeneity analysis; Homogeneity of variables; Historical preliminares of differential weighting; Maximizing homogeneity by linear a weighting: principal components analysis; Alternating least squares algorithms for linear weighting; Linear weighting for K sets of variables; More historical comments on pca; Maximizing homogeneity by nonlinear transformation: nonlinear PCA; Categorical PCA: homals; Relations between homals and linear PCA; The relationship between homals and total chi-square; An illustration: hartigan's hardware; Homals with incomplete indicator matrix; Reserved indicator matrix; Epilogue; Nonlinear principal components analysis; Metric principal components analysis; Nonmetric principal components analysis; Theory of join loss; Theory of meet loss; Geometric of meet loss; The princicals program; An example comparing multiple and single nominal treatment; An example with preference rank orders; An example with discretization of continuous variables; Epilogue; Nonlinear generalized canonical analysis; Previous work; Loss function and normalization of overals; Overals as a special case of homals: the use of interactive variables; Missing data; Algorithm construction; An example: effects of radioactivity on fish; Epilogue; Nonlinear canonical correlation analysis; Previous work; Theory; The canals program; Example 1: economic inequality and political stability; Example 2: prediction of a school achievement test; Epilogue; Asymmetric treatment of sets: some special cases, some future programs; Multiple regression and morales; Discriminant analysis and criminals; Multivariate analysis of variance and manovals; Path analysis and pathals; Partial canonical correlation analysis and partals; Some examples; Epilogue; Multidimensional scaling and correspondence analysis; Homogeneity and separation; Minimum distance analysis of homogeneous groups of objects; Correspondence analysis; Contigency and correlation; The program anacor; The program anaprof: analysis of profile frequencies; Some gauging results for binardy data; Epilogue; Models as gauges for the analysis of binardy data; Some general formulas; Monotone latent trait models; Nonmonotonic latent trait models; Order analysis of binardy matrices; Dichotomized multinormal distriibutions; Epilogue; Reflections on restrictions; The class of restrictions closed under linear transformations; Equality constraints; Other linear constraints; Zeros at specific places; Nonlinear restrictions; Epilogue; Nonlinear multivariate analysis: principles and possibilities; Join and meet; Choice of basis; Some infinite-dimensional gauges; Analysis of stochastic processes; Alternative criteria; Epilogue; The study of stability; Analytical stability; Algebraic stability; Replicationstability; Epilogue; The proof of the pudding; Multiple choice examination; Controversial issues; As years go by; Parliament survey; Crime and fear; Epilogue; Notation; Matrix algebra; Images; Hyperellipsoids; Invariant directions; Singular vectors and singular values; Eigenvectors and eigenvalues; Algebraic applications of eigenvectors and singular vectors; Optimization properties of the SVD; Generalized eigenvector problem; Applications in linear MVA; Joint plots; Cones and projection on cones.