Reduced rank regression is widely used in statistics to model multivariate data. In this monograph, theoretical and data analytical approaches are developed for the application of reduced rank regression in multivariate prediction problems. For the first time, both classical and Bayesian inference is discussed, using recently proposed procedures such as the ECM-algorithm and the Gibbs sampler. All methods are motivated and illustrated by examples taken from the area of quantitative structure-activity relationships (QSAR).
Inhaltsverzeichnis
1. Quantitative Structure Activity Relationships (QSAR). - 1. 1. Introduction. - 1. 2. Modification of Substances. - 1. 3. Physico Chemical Descriptors. - 1. 4. Biological Descriptors. - 1. 5. Prediction Model. - 1. 6. The Development of an Insecticide: an Example. - 2. Linear Multivariate Prediction. - 2. 1. Introduction. - 2. 2. Multivariate Prediction. - 2. 3. Prediction Criteria. - 2. 4. Exploratory Graphical Methods. - 2. 5. Method and Variable Selection. - 2. 6. Assessment of the Goodness of Prediction of the Selected Model. - 3. Heuristic Multivariate Prediction Methods. - 3. 1. Introduction. - 3. 2. Principal Component Regression. - 3. 3. Partial Least Squares. - 3. 4. Dimension Selection. - 3. 5. Example. - 4. Classical Analysis of Reduced Rank Regression. - 4. 1. Introduction. - 4. 2. QSAR: Biological Responses. - 4. 3. Reduced Rank Regression Models. - 4. 4. Extensions of the Standard Reduced Rank Regression Model. - 4. 5. Prediction Criteria for the Rank Selection of Reduced Rank Regression Models. - 4. 6. Variable Selection for Reduced Rank Regression Models. - 5. Bayesian Analysis of Reduced Rank Regression. - 5. 1. Introduction. - 5. 2. The Reduced Rank Regression Model. - 5. 3. Markov Chain Monte Carlo Methods. - 5. 4. Example. - 6. Case Studies. - 6. 1. ®Voltaren: An Anti-Inflammatory Drug. - 6. 2. Development of a Herbicide. - 7. Discussion. - A. 1 Introduction. - A. 2 Multivariate Regression MR. - A. 3 Principal Component Analysis PCA. - A. 4 Partial Least Squares PLS. - A. 5 Canonical Correlation Analysis CCA. - A. 6 Reduced Rank Regression with Diagonal Error Covariance Matrix RRR. - A. 7 Redundancy Analysis RDA. - A. 8 Software. - A. 9 Matrix Algebra Definitions. - A. 10 Multivariate Distributions. - References. - Main Notations and Abbreviations.
