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Shepard diagrams
That the stress is low here is also evident from the Shepard diagrams for the 2-d and 3-d solutions (possibly Graph4 & Graph6). They are scatter plots of distances between samples in the ordination against original (dis)similarities, in which the deviations of...
Dissimilarity preservation as a matrix correlation
One can also ask how well the (Euclidean) distances among points in the nMDS plot correlate with the dissimilarities in the resemblance matrix. The former are calculated by running the ordination co-ordinates (output to Data4 and Data5 by the ✓Ordinations to w...
Accuracy & fit scheme
For the MDS run above, two of the defaults taken for options in the MDS dialog were (Minimum stress: 0.01) and (Kruskal fit scheme•1). Changing the former from 0.01 to 0.001 would decrease the lower threshold of stress at which the iteration decides that it h...
Graph menu: rotating and flipping the 2-d ordination
nMDS ordinations (unlike mMDS) have no meaningful axis scales for the configuration, since they use only ranks rather than original dissimilarities. There are also no defined directions for plot axes (unlike PCA, Section 12, or PCO, PERMANOVA+ add-on), so MDS ...
Align graphs automatically
A new feature in PRIMER 7 is the ability to automatically reflect in the axes and rotate an MDS configuration (and rescale it, if necessary) such that it best matches the pattern of another supplied configuration. This can make it quicker and simpler to compar...
Zoom & MDS subset plots
It is scarcely necessary here, with only 19 samples, to zoom in on part of the plot in order to see the detailed structure, though this is possible using the Zoom In, Zoom Out and Cancel Zoom options on the Graph menu (also accessible from the , and ...
Special menu for ordination; Aspect ratio of boundary
We have seen before that, whilst the Graph>Sample Labels & Symbols and General menus are universal, having dialog boxes of the same form for all the graphics routines, the Graph>Special dialogs are specific to each routine, and this option is at its most exten...
Diagnostics for MDS: join pairs
There are a number of new diagnostic tools available in PRIMER 7 for assessing how well a low-d ordination represents the structure in the resemblance matrix. One of the simplest is to join pairs of points on the ordination which have similarity greater than s...
Features that carry over to 3-d ordination
It is worth saying, as we start to explore the wide range of tools which can be applied to an MDS or other ordination that, although demonstrated for 2-d plots, most of the techniques are also available for 3-d configurations. This includes all joining operati...
Minimum spanning tree (MST)
The minimum spanning tree (MST, see CiMC for the Gower and Ross, 1969 reference) is used in the same way, to identify parts of the configuration which do not fully represent the underlying (dis)similarity matrix. All samples are connected on the ordination by ...
Linking MDS plots to cluster analysis
The 2-d ordination plot shows a clear separation of the nematode assemblages at these 19 sites into 5 groups (which CiMC, Chapter 11, shows can be related to sediment properties such as the median particle size, anoxic layer depth and interstitial salinity). A...
Cluster overlays on MDS plots
The second way in which a cluster analysis can be displayed on a 2-d MDS plot, to aid assessment of the level of agreement, is to draw smoothed envelopes around each of the cluster groups, either for one or more slices at arbitrarily chosen similarity levels (...
Dendrogram & 2-d MDS in a 3-d plot
Rather than creating a small number of (arbitrary) slices through a dendrogram, superimposed on a 2-d MDS, a further new feature in PRIMER 7 is the ability to draw the dendrogram as the third dimension in a 3-d plot of the 2-d MDS (or any ordination). As with ...
3-d ordination plots & axes selection
As we have seen for the nMDS run on the Exe nematode data, in the first graphic of this Section, a default MDS run produces both 2-d and 3-d configuration plots, and their associated Shepard diagrams, placed into a multi-plot (Multiplot1). A different plot win...
Rotate axes or rotate/flip data
The 3-d Exe nematode nMDS plot should be in the current workspace as Graph5 under Multiplot1 (if necessary create it again, with default options, by Analyse>MDS>Non-metric MDS (nMDS) on the Bray-Curtis resemblance matrix for a square-root transform of the data...
Drawing verticals for 3-d plots
Whilst it is relatively easy to visualise a 3-d plot by rotation of the axes – and PRIMER 7 is now able to output digital video of such rotations (as *.mp4, see below) – it is much harder to produce a convincing 3-d plot for static reproduction in 2-d, e.g. fo...
(W Australia fish diets)
Re-open the workspace WA fish ws from C:\Examples v7\WA fish diets, which will provide an example where a 3-d MDS is necessary to get a reliable feel for the multivariate structure. The workspace WA fish ws should contain a data sheet Data2 of the dietary asse...
Higher-d & scree plots (WA fish diet)
Run nMDS at a wider range of dimensionalities than the default and ask for a scree plot: Analyse> MDS>Non-metric MDS (mMDS)>(Min. dimension: 2) & (Max. dimension: 8) & (✓Scree plot), taking the other defaults (i.e. including Shepard plots). On the resulting mu...
Spinning a 3-d MDS & capture in a movie file
The 3-d MDS plot box can be made to rotate horizontally, automatically (from whatever vertical perspective view it is manually set to), by Graph>Spin. This adds a top line of controls for the animation: to the left is a slider control w...
(Morlaix macrofauna, Amoco-Cadiz oil spill)
Some data sets have a natural sequence to their samples, usually a time series (though this can be a single spatial gradient), and it is usually a good idea to join the points on an ordination plot in that order – then referred to as trajectory plots. This is ...