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  2. 2. CAP
  3. 3. Description This program does canonical analysis of principal coordinates (canonical correlation analysis or canonical discriminant analysis) based on any distance measure as described by Anderson and Robinson (2003) and Anderson and Willis (2003). The test is done by permutation (using the trace and first canonical root statistics) and canonical axes for ordination are also given in the output.
  4. 4. Characteristics 1. Eigenvalues and eigenvectors from the principal coordinate analysis. The latter are the PCO axes that can be used to plot an unconstrained (metric MDS) of the data. 2. Canonical correlations and squared canonical correlations 3. Canonical axes scores (position of multivariate points on the canonical axes to be used for plotting). 4. Correlations of each of the original variables with each of the canonical axes.
  5. 5. 5. Correlations of each X variable with each of the canonical axes (if a canonical correlation is done). 6. Diagnostics used to determine the appropriate value for the choice of m. The criterion used is either the value of m resulting in the minimum misclassification error (in the case of groups) or the minimum residual sum of squares (in the case of X containing one or more quantitative variables). Also, m must not exceed p or N and is chosen so that the proportion of the variability explained by the first m PCO axes is more than 60%and less than 100% of the total variability in the original dissimilarity matrix.
  6. 6. 7. In the case of groups, a table of results for the “leave-one-out” classification of individual observations to groups is given, along with the misclassification error for the choice of m used. 8. If requested, the results of a permutation test using the two different test statistics, (trace and largest root).
  7. 7. Description: The program offers essentially two options: one can either ask for a forward selection of individual variables, or for a forward selection of sets of variables. The first is useful in the general case, e.g. for fitting individual environmental variables sequentially in the linear model. The second is useful for the situation where one wishes to fit a sequential model of whole sets of variables. For example, in the paper by Anderson et al. (2004), there were seven sets of environmental variables of interest.
  8. 8. Characteristics 1. Ambient sediment grain size variables (GS1 – GS4), 2. Depositional environment classification (contrasts between High, Medium and Low depositional environments, labeled HvML and MvL). 3. Trapped sediment characteristics (Sdep, gt125, Perfin) 4. Erosion variables (bed height movement, labeled BH and sdBH) 5. Distance from the mouth of the estuary (D and D2). 6. Chlorophyll a (Chla) and 7. Organics (Ora)