Multivariate Statistics for Wildlife and Ecology Research

Agglomerative Nonhierarchical Clustering.- 3.6.2 Polythetic Divisive Nonhierarchical Clustering.- 3.7 Hierarchical Clustering.- 3.7.1 Polythetic Agglomerative Hierarchical Clustering.- 3.7.2 Polythetic Divisive Hierarchical Clustering.- 3.8 Evaluating the Stability of the Cluster Solution.- 3.9 Complementary Use of Ordination and Cluster Analysis.- 3.10 Limitations of Cluster Analysis.- Appendix 3.1.- 4 Discriminant Analysis.- 4.1 Objectives.- 4.2 Conceptual Overview.- 4.2.1 Overview of Canonical Analysis of Discriminance.- 4.2.2 Overview of Classification.- 4.2.3 Analogy with Multiple Regression Analysis and Multivariate Analysis of Variance.- 4.3 Geometric Overview.- 4.4 The Data Set.- 4.5 Assumptions.- 4.5.1 Equality of Variance-Covariance Matrices.- 4.5.2 Multivariate Normality.- 4.5.3 Singularities and Multicollinearity.- 4.5.4 Independent Random Sample and the Effects of Outliers.- 4.5.5 Prior Probabilities Are Identifiable.- 4.5.6 Linearity 153.- 4.6 Sample Size Requirements.- 4.6.1 General Rules.- 4.6.2 Specific Rules.- 4.7 Deriving the Canonical Functions.- 4.7.1 Stepwise Selection of Variables.- 4.7.2 Eigenvalues and Associated Statistics.- 4.7.3 Eigenvectors and Canonical Coefficients.- 4.8 Assessing the Importance of the Canonical Functions.- 4.8.1 Relative Percent Variance Criterion.- 4.8.2 Canonical Correlation Criterion.- 4.8.3 Classification Accuracy.- 4.8.4 Significance Tests.- 4.8.5 Canonical Scores and Associated Plots.- 4.9 Interpreting the Canonical Functions.- 4.9.1 Standardized Canonical Coefficients.- 4.9.2 Total Structure Coefficients.- 4.9.3 Covariance-Controlled Partial F-Ratios.- 4.9.4 Significance Tests Based on Resampling Procedures.- 4.9.5 Potency Index.- 4.10 Validating the Canonical Functions.- 4.10.1 Split-Sample Validation.- 4.10.2 Validation Using Resampling Procedures.- 4.11 Limitations of Discriminant Analysis.- Appendix 4.1.- 5 Canonical Correlation Analysis.- 5.1 Objectives.- 5.2 Conceptual Overview.- 5.3 Geometric Overview.- 5.4 The Data Set.- 5.5 Assumptions.- 5.5.1 Multivariate Normality.- 5.5.2 Singularities and Multicollinearity.- 5.5.3 Independent Random Sample and the Effects of Outliers.- 5.5.4 Linearity.- 5.6 Sample Size Requirements.- 5.6.1 General Rules.- 5.6.2 Specific Rules.- 5.7 Deriving the Canonical Variates.- 5.7.1 The Use of Covariance and Correlation Matrices.- 5.7.2 Eigenvalues and Associated Statistics.- 5.7.3 Eigenvectors and Canonical Coefficients.- 5.8 Assessing the Importance of the Canonical Variates.- 5.8.1 Canonical Correlation Criterion.- 5.8.2 Canonical Redundancy Criterion.- 5.8.3 Significance Tests.- 5.8.4 Canonical Scores and Associated Plots.- 5.9 Interpreting the Canonical Variates.- 5.9.1 Standardized Canonical Coefficients.- 5.9.2 Structure Coefficients.- 5.9.3 Canonical Cross-Loadings.- 5.9.4 Significance Tests Based on Resampling Procedures.- 5.10 Validating the Canonical Variates.- 5.10.1 Split-Sample Validation.- 5.10.2 Validation Using Resampling Procedures.- 5.11 Limitations of Canonical Correlation Analysis.- Appendix 5.1.- 6 Summary and Comparison.- 6.1 Objectives.- 6.2 Relationship Among Techniques.- 6.2.1 Purpose and Source of Variation Emphasized.- 6.2.2 Statistical Procedure.- 6.2.3 Type of Statistical Technique and Variable Set Characteristics.- 6.2.4 Data Structure.- 6.2.5 Sampling Design.- 6.3 Complementary Use of Techniques.- Appendix: Acronyms Used in This Book.