عنوان

Canonical analysis.

3642698786

9783642698781

b572864

Canonical analysis.

[Book]

R Gittins

[Place of publication not identified]

Springer-Verlag Berlin An

2012

1. Introduction.- 1.1 The study of relationships.- 1.2 Objectives.- 1.3 Canonical analysis: overview.- I. Theory.- 2. Canonical correlations and canonical variates.- 2.1 Introduction.- 2.2 Formulation.- 2.3 Derivation of canonical correlation coefficients and canonical variates.- 2.3.1 Eigenanalysis.- 2.3.2 Singular value decompositon.- 2.3.3 Other derivations.- 2.3.4 Concluding remarks.- 2.4 Properties of canonical correlation coefficients, weights and variates.- 2.4.1 Properties of canonical correlation coefficients.- 2.4.2 Properties of canonical weights.- 2.4.3 Properties of canonical variates.- 2.5 Computation.- 2.5.1 Numerical methods.- 2.5.2 Further remarks.- 3. Extensions and generalizations.- 3.1 Introduction.- 3.2 Further interpretive devices.- 3.2.1 Correlations between canonical variates and the original variables.- 3.2.2 Variance extracted by a canonical variate.- 3.2.3 Redundancy.- 3.2.4 Total redundancy.- 3.2.5 Variable communalities.- 3.2.6 Concluding remarks.- 3.3 Extensions and generalizations.- 3.3.1 Redundancy analysis: an alternative to canonical analysis.- 3.3.2 Improving the interpretability of canonical weights.- 3.3.3 Rotation of canonical variates.- 3.3.4 Validation.- 3.3.5 Predicting a criterion of maximum utility.- 3.3.6 Generalizations of canonical analysis.- 3.3.7 Concluding remarks.- 3.4 Hypothesis testing.- 3.4.1 Independence.- 3.4.2 Dimensionality.- 3.4.3 The contribution of particular variables.- 3.4.4 Hypothesis tests for nonnormal data.- 3.4.5 Residuals from a fitted model.- 4. Canonical variate analysis.- 4.1 Introduction.- 4.2 Binary-valued dummy variables.- 4.3 Formulation and derivation.- 4.3.1 Point conceptualizations of NXp and NZq.- 4.3.2 Derivation.- 4.4 Further aspects of canonical variate analysis.- 4.5 Hypothesis testing.- 4.5.1 Equality of g vector-means.- 4.5.2 Dimensionality.- 4.6 Affinities with other methods.- 4.6.1 Canonical variate analysis, multivariate analysis of variance and multiple discriminant analysis.- 4.6.2 Canonical variate analysis and principal component analysis.- 4.7 Imposition of structure.- 4.7.1 Designed comparisons.- 4.7.2 Separating the sources of variation.- 4.7.3 Further comments.- 4.8 Concluding remarks.- 5. Dual scaling.- 5.1 Introduction.- 5.2 Formulation and derivation.- 5.2.1 Maximizing the correlation between rows and columns.- 5.2.2 Maximizing the separation between rows and columns.- 5.3 Further aspects of dual scaling.- 5.4 Hypothesis testing.- 5.4.1 Independence.- 5.4.2 Dimensionality.- 5.5 Affinities with other methods.- 5.5.1 Dual scaling and the analysis of contingency tables.- 5.5.2 Dual scaling, correspondence analysis and principal component analysis.- 5.6 Relationships among statistical methods.- 5.7 Concluding remarks.- II. Applications.- General introduction.- 6. Experiment 1: an investigation of spatial variation.- 6.1 Introduction.- 6.2 Results.- 6.2.1 The canonical correlation coefficients.- 6.2.2 Independence.- 6.2.3 Dimensionality.- 6.2.4 The canonical variates.- 6.2.5 Variable communalities.- 6.3 Conclusions.- 7. Experiment 2: soil-species relationships in a limestone grassland community.- 7.1 Introduction.- 7.2 Results.- 7.2.1 The canonical correlation coefficients.- 7.2.2 Independence.- 7.2.3 Dimensionality.- 7.2.4 The canonical variates.- 7.2.5 Variable communalities.- 7.3 Conclusions.- 8. Soil-vegetation relationships in a lowland tropical rain forest.- 8.1 Introduction.- 8.2 Results.- 8.2.1 The canonical correlation coefficients.- 8.2.2 Independence.- 8.2.3 Dimensionality.- 8.2.4 The canonical variates.- 8.2.5 Variable communalities.- 8.3 Ecological assessment of the results.- 8.4 Conclusions.- 9. Dynamic status of a lowland tropical rain forest.- 9.1 Introduction.- 9.2 Results.- 9.2.1 The canonical correlation coefficients.- 9.2.2 Independence.- 9.2.3 Dimensionality.- 9.2.4 The canonical variates.- 9.2.5 Variable communalities.- 9.3 Ecological assessment of the results.- 9.4 Conclusions.- 10. The structure of grassland vegetation in Anglesey, North Wales.- 10.1 Introduction.- 10.2 Results.- 10.2.1 The canonical correlation coefficients.- 10.2.2 Equality of community centroids.- 10.2.3 Collinearity.- 10.2.4 The canonical variates.- 10.2.5 Variable communalities.- 10.3 Ecological assessment of the results.- 10.4 Conclusions.- 11. The nitrogen nutrition of eight grass species.- 11.1 Introduction.- 11.2 Multivariate analysis of variance.- 11.2.1 Results.- 11.2.2 Designed comparisons.- 11.3 Canonical variate analysis.- 11.3.1 Results.- 11.4 Relationships between multivariate analysis of variance, discriminant analysis and canonical variate analysis.- 11.5 Ecological assessment of the results.- 11.6 Conclusions.- 12. Herbivore-environment relationships in the Rwenzori National Park, Uganda.- 12.1 Introduction.- 12.2 Contingency table analysis.- 12.2.1 Results.- 12.3 Dual scaling.- 12.3.1 Results.- 12.4 Relationships between contingency table analysis and dual scaling.- 12.5 Ecological assessment of the results.- 12.6 Conclusions.- III. Appraisal and Prospect.- 13. Applications: assessment and conclusions.- 13.1 Introduction.- 13.2 Assessment.- 13.3 Conclusions.- 14. Research issues and future developments.- 14.1 Introduction.- 14.2 Data collection.- 14.2.1 Choice of variables.- 14.2.2 Experimental design.- 14.3 Initial data exploration.- 14.3.1 Homogeneity.- 14.3.2 Assessing joint distribution.- 14.3.3 Re-expressing variables.- 14.4 Potential data problems.- 14.4.1 Outlying or influential observations.- 14.4.2 Long-tailed distributions.- 14.4.3 Collinearity.- 14.5 Statistical assessment.- 14.5.1 Residuals in canonical analysis.- 14.5.2 Does the model fit?.- 14.5.3 Stability of results.- 14.5.4 Miscellanea.- 14.6 Concluding remarks.- Appendices.- A.1 Multivariate regression.- A.2 Data sets used in worked applications.- A.3 Species composition of a limestone grassland community.- References.- Species' index.- Author index.

R Gittins

R Gittins

[Book]

Y