Reduced Rank Regression

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.