Applied Factor Analysis in the Natural Sciences Book

	Preface
	Glossary of the most commonly used symbols
	Preface to first edition
1	Introduction
1.1	Structure in multivariate data	1
1.2	An example of principal component factor analysis	2
1.3	Overview of problems amenable to treatment by factor-analytical techniques	11
2	Basic Mathematical and Statistical Concepts
2.2	Geometrical interpretation of data matrices	18
2.3	Elementary vector operations	20
2.4	The geometry of vectors	23
2.5	Types of matrices	26
2.6	Elementary matrix arithmetic	27
2.7	Normal and orthonormal vectors and matrices	34
2.8	Descriptive statistics in matrix notation	35
2.9	Rotation of coordinate systems	44
2.10	The structure of a matrix	47
2.11	Eigenvalues and eigenvectors	54
2.12	Basic structure of a matrix and the Eckart-Young theorem	62
2.13	Least-squares properties of eigenvalues and eigenvectors	66
2.14	Canonical analysis of asymmetry	68
3	Aims, Ideas, and Models of Factor Analysis
3.2	Fixed and random cases	72
3.3	Discussion of models	73
3.4	Model of the variances and covariances	76
3.5	Principal component versus true factor analysis	78
3.6	Transformational indeterminacy of factors	79
3.7	Factor pattern and factor structure	81
3.8	Example of true factor analysis	81
3.9	Representation of results	86
3.10	True factor analysis summarized	86
4	R-Mode Methods
4.2	Principal component analysis	89
4.3	True factor analysis	102
4.4	Robust principal component analysis	111
4.5	Principal component analysis and cross-validation	115
4.6	Principal component analysis of compositional data	121
4.7	Path analysis and Wrightian factor analysis	128
5	Q-Mode Methods
5.2	Principal coordinates	137
5.3	Logcontrast principal coordinate analysis	144
5.4	Q-mode factor analysis	145
5.5	The analysis of asymmetry	161
6	Q-R-Mode methods
6.1	Correspondence analysis	172
6.2	Comparison of Q-modes methods and correspondence analysis	179
6.3	The Gabriel biplot method	182
6.4	Canonical correlation analysis	187
7	Steps in the Analysis
7.2	Objectives	194
7.3	Categories of data	195
7.4	The data matrix	197
7.5	Selection of the measure of association	203
7.6	Choice of the factor method	205
7.7	Selection of the number of factors	206
7.8	Rotation of factor axes	208
7.9	Factor scores	222
8	Examples and Case Histories
8.2	R-mode principal components in mineral chemistry	228
8.3	R-mode factor analysis in paleoecology	231
8.4	R-mode factor analysis in sedimentology	235
8.5	R- and Q-mode analyses in subsurface brine geochemistry	240
8.6	Imbrie Q-mode factor analysis in sedimentology	244
8.7	Imbrie Q-mode factor analysis in foraminiferal ecology	248
8.8	Principal coordinate analysis of soils	253
8.9	Q-R-mode analysis of maturation of crude oils	255
8.10	Correspondence analysis of metamorphic rocks	257
8.11	True factor analysis in marine ecology	259
8.12	A problem in soil science	262
8.13	The method of principal warps	264
8.14	Two simple case histories	280
	Appendix: Computer programs	289
	Bibliography	352
	Index	365