Untangling Multivariate Relationships
Course Outline

Intro to Multivariate Methods
Goals and objectives of each method
Classification vs Dependence
Available Software
Graphing Multivariate Data
Visualizing patterns in 3 and more dimensions
Biplots, score plots
Multidimensional Scaling
Other plots
Principal Component Analysis
What PCA accomplishes
How PCA is computed
Interpreting scores and loadings
Factor Analysis
What FA can and cannot accomplish
Differences between FA and PCA
How many factors?
Correspondence Analysis
CA objectives
Relation to contingency table tests
Plot of associations
Detrended CA
Cluster Analysis
Methods of clustering. Linkages
How well can known clusters be identified?
Determining the number of clusters
Interpreting dendrograms

Discriminant Analysis & Logistic Regression
Classifying observations into groups
Parametric DFA vs. nonparametric LR
Canonical Correlation and Canonical Correspondence Analysis
Correlations between sets of variables
What can and cannot be accomplished
Tests of significance for correlation
Canonical correlation between species and sites
Nonparametric Methods
Nonmetric Multidimensional Scaling
Nonparametric MANOVA to differentiate groups
Multivariate trends
Determining which variables contribute most to group differences
Methods for Censored Data
Problems with substitution
Binary methods for 1 detection limit
Ordinal methods for 1 detection limit
Trends, PCA, cluster, NMDS on data with multiple reporting limits