Multivariate Analysis in the Human Services

1 Introduction.- 2 Mathematical Preliminaries.- Functions of Variables.- Matrices.- Matrix Algebra.- Some Matrices We Will Encounter.- Singularity of Matrices and Determinants.- Inverse of Matrices.- Problems.- 3 Multiple Regression I.- The Model in Matrix Terms.- Review of Analysis of Variance.- Two-Way Analysis of Variance.- The Analysis of Variance of Regression.- Interpretation of Regression Coefficients.- Residuals.- 4 Multiple Regression II.- Building a Regression Equation.- Coding of Categorical Variables for Regression Analysis.- and Partial Correlation-Statistical Control.- 5 More on Matrices.- Vectors.- Transformation of a Vector by a Matrix.- Projections.- Problems.- 6 Principal Components Analysis.- Two Variables, Three Cases.- Two Variables, n Cases.- Three Variables.- p Variables.- Scaling of Principal Components.- Reducing the Number of Principal Components.- Naming the Principal Components.- Example.- 7 Factor Analysis.- Points as Variables Instead of Individuals.- Subspaces.- The Decomposition of Variables.- The Correlation Matrix and Its Factors.- Extraction Methods.- Rotation.- Factor Scores.- Example.- 8 Multivariate Tests of Means.- Single-Sample Mean Test.- Two-Sample Mean Test.- Three or More Samples.- Example.- 9 Discriminant Analysis.- Geometric Representation.- Algebra of Discriminant Analysis.- The Discriminant Coefficients.- Significance Testing.- Classification.- 10 Other Multivariate Techniques.- Multivariate Multiple Regression.- Canonical Correlation.- Multivariate Analysis of Covariance.- 11 Repeated Measures Analysis.- Single-Group Designs.- N-Sample Case.- Appendixes.- A. The Greek Alphabet.- B. Random Variables, Expected Values, and Variance.- C. A Little Calculus.- D. A Little Trigonometry.- E. Still More on Matrices.- F. Logarithms.- G. Matrix Routines in SAS.