BEE 553 Multivariate Analysis

Instructor:

When offered:

Description

An introduction to multivariate statistical analysis for biologists. Topics include general least-squares analysis, MANOVA, cluster analysis, and factor analysis. It is an advanced biometry course that should be useful for the analysis of data from ecology, evolution, and other fields. 3 credits

Prerequisites:

Tentative course outline

1. Introduction and review of matrix algebra. Chapter 2.
2. Univariate least-squares analysis using general linear models. FJR notes.
   • Anova and ancova models including unbalanced designs.
   • Experimental design models
   • Regression and multiple regression
3. Multivariate normal distribution. Estimation of parameters, linear transformations. Chapter 4.
   • Introduction to principal components analysis.
   • Multivariate least-squares Chapters 5, 6, and 7.
   • Manova, mancova, and multivariate linear regression methods. Chapters 5, 6, and 7.
4. Other linear models
   • Generalized least-squares (allowing for lack of independence)
   • Biassed regression methods (ridge regression, PCA regression)
   • Partial least-squares regression
   • Mixed effect models
   • Autoregressive models
   • Catagorical dependent variable (e.g., logistic regression)
5. Analyses of relationships among variables
   • Canonical correlation and 2-block partial least-squares analyses.Chapter 10.
   • Path analysis , structural equation models with latent variables.
   • Factor analysis (models, methods, simple structure, scores, and interpretation). Chapter 9.
6. Analyses to detect patterns among observations
   • Discriminant analysis & canonical vectors analysis. Chapter 11.
   • Ordination methods (PCA, CPCA, PCOORD, MDSCALE, SVD, biplots, CA). Chapter 12.
   • Clustering methods (SAHN methods, etc.). Chapter 12.
   • Graph theoretic methods
7. Misc. multivariate methods (as time permits)

The topics listed above are expected to be covered but the sequence may be different. Details will be given on the BlackBoard website.

Grades are based on a mid-term and a final exam. There also are homework assignments that require the use of a computer.

Textbook

This year we will use the text "Applied multivariate statistical methods" 6th edition, 2007. By R. A. Johnson and D. W. Wichern. Prentice-Hall. ISBN: 0130925535.

Software

Most of the methods covered are not practical without the use of appropriate software.

The university has licenses for the PC version of the comprehensive SAS statistical software.

You will find the Matlab software very convenient for matrix operations. It is available in the SINC sites. A link to some Matlab resources. There is also a free clone for both Windows and Linux called Octave (not too stable the last time I tried it)..

The NTSYSpc software will also be available for use in the course.

While matrix operations are slightly less convenient using the R software (a free clone of Splus), it provides more types of built-in statistical analyses. You can download a copy from their website here. There are versions for Windows, Linux, and various version of Mac OS. There are also many user manuals and guides.