RELATE directive

Relates the observed values on a set of variates to the results of a principal coordinates analysis.


Options

COORDINATES = matrix
Points in reduced space; no default i.e. this option must be specified

NROOTS = scalar
Number of latent roots for printed output; default * requests them all to be printed


Parameters

DATA = variates
The data values

TEST = strings
Test type, defining how each variate is treated in the calculation of the similarity between each unit (Jaccard, simplematching, cityblock, Manhattan, ecological, Pythagorean, Euclidean); default * ignores that variate

RANGE = scalars
Range of possible values of each variate; if omitted, the observed range is taken


Description

One way of interpreting the principal coordinates obtained from a similarity matrix by PCO is by relating them to the original variates of the data matrix. For each coordinate and each data variate, an F-statistic can be computed as if the variate and the coordinate vector were independent. This is not the case but, although the exact distribution of these pseudo F-values is not known, they do serve to rank the variates in order of importance of their contribution to the coordinate vector.

   Qualitative variates are treated as grouping factors, and the mean coordinate for each group is calculated. Only 10 groups are catered for; group levels above 10 are combined. The pseudo F-statistic gives the between-group to within-group variance ratio. Missing values are excluded.

   Quantitative variates are grouped on a scale of 0-10 (where zero signifies a value up to 0.05 of the range), and mean coordinates for each group are calculated. The printed pseudo F statistic is for a linear regression of the principal coordinate on the ungrouped data variate, after standardizing the data variate to have unit range; the regression coefficient is also printed.

   The DATA parameter lists the variates that are to be related to the PCO results and the TEST parameter indicates their "type" as in the FSIMILARITY directive. The RANGE parameter contains a list of scalars, one for each variate in the DATA list, allowing you to standardize quantitative variates.

   The COORDINATES option must be present and must be a matrix. It represents the units in reduced space. Usually the coordinates will be from a principal coordinates analysis. The number of rows of the matrix must match the number of units present in the variates, taking account of any restriction.

   The output from RELATE can be extensive. You may not be interested in relating the variates to the higher dimensions of the principal coordinates analysis even though you may have saved these in the coordinate matrix. The NROOTS option can request that results for only some of the dimensions are printed. If NROOTS is not specified, RELATE prints information for all the saved dimensions: that is, for the number of columns of the coordinates matrix.

 

Options: COORDINATES, NROOTS.

Parameters: DATA, TEST, RANGE.