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
• Cross-validation

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 Data with Nondetects
• 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

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