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.
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
3. Canonical axes scores (position of multivariate
points on the canonical axes to be used for
4. Correlations of each of the original variables
with each of the canonical axes.
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
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
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.
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
5. Distance from the mouth of the estuary (D and D2).
6. Chlorophyll a (Chla) and
7. Organics (Ora)