Multivariate Statistics, Part 2

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Multivariate Statistics, Part 2

• ESM 206, 5/19/05

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Cluster analysis

• Ordination organizes the samples along a set of
  latent variables that are continuous
• Cluster analysis organizes the samples along a
  set of latent variables that are categorical
• Find a set of discrete clusters such that the
  observations within a cluster are much more
  similar to each other than they are with
  observations in other clusters

• Requires some notion of distance in the
  P-dimensional space
• Euclidean distance
• Mahalanobis distance Like Euclidean but takes
  statistical correlations into account
• Dissimilarity coefficient often used for count
  data of species
• Non-hierarchical clustering
• Get just the clusters
• Hierarchical clustering
• Also get similarities between clusters

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Community composition at 6 sites
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Cluster Analysis

• Makes very few assumptions about data ?
• Lots of options and they matter ?
• Distance measure
• Agglomerate or divide
• Rules for growing or dividing clusters
• Other challenges
• Only finds spherical clusters
• Finds clusters even when data are following
  continuous variables
• If this is true then different approaches will
  build very different clusters

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Discriminant Analysis

• Have predefined groups each observation has
  unique value
• Presence or absence of a species
• Political party affiliation
• Vegetation type
• Also have set of continuous variables measured at
  each observation
• Want to find linear combinations of continuous
  variables that best discriminate among the groups
• Sort of like logistic regression

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Example presence/absence of a marine invertebrate

• Data from EPA EMAP surveys in estuaries on US
  east coast
• Presence/absence of Mediomastus ambiseta
• Data on 16 water quality variables
• Salinity, temperature, etc. at surface and bottom

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Stepwise procedure suggests most discrimination
from surface salinity and pH PAR at bottom
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Classification accuracy

• Confusion matrix

• Kappa statistic