8. Multi-dimensional scaling (Non-metric nMDS, Metric mMDS, Combined MDS)
Rationale for nMDS & mMDS
Chapter 5 of the CiMC methods manual describes the operation and rationale of multi-dimensional s...
Combined MDS & ‘Fix Collapse’
A further new feature of nMDS in PRIMER 7 is the ability to minimise a combination of two stress ...
Diagnostic tools for MDS plots
In addition to the ability in a previous PRIMER version to Graph>Special>Overlays>(✓Overlay clust...
Overlaying factors or other data (bubble plot)
The ability to display, on any ordination plot, external structure such as factors (e.g. for site...
Running an nMDS (Exe nematodes)
From the directory C:\Examples v7\Exe nematodes, File>Open the workspace Exe ws, last seen in Sec...
MDS results window
As with all results windows, the MDS1 window first lists the resemblance sheet on which analysis ...
Shepard diagrams
That the stress is low here is also evident from the Shepard diagrams for the 2-d and 3-d solutio...
Dissimilarity preservation as a matrix correlation
One can also ask how well the (Euclidean) distances among points in the nMDS plot correlate with ...
Accuracy & fit scheme
For the MDS run above, two of the defaults taken for options in the MDS dialog were (Minimum stre...
Graph menu: rotating and flipping the 2-d ordination
nMDS ordinations (unlike mMDS) have no meaningful axis scales for the configuration, since they u...
Align graphs automatically
A new feature in PRIMER 7 is the ability to automatically reflect in the axes and rotate an MDS c...
Zoom & MDS subset plots
It is scarcely necessary here, with only 19 samples, to zoom in on part of the plot in order to s...
Special menu for ordination; Aspect ratio of boundary
We have seen before that, whilst the Graph>Sample Labels & Symbols and General menus are universa...
Diagnostics for MDS: join pairs
There are a number of new diagnostic tools available in PRIMER 7 for assessing how well a low-d o...
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...
Minimum spanning tree (MST)
The minimum spanning tree (MST, see CiMC for the Gower and Ross, 1969 reference) is used in the s...
Linking MDS plots to cluster analysis
The 2-d ordination plot shows a clear separation of the nematode assemblages at these 19 sites in...
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 ...
Dendrogram & 2-d MDS in a 3-d plot
Rather than creating a small number of (arbitrary) slices through a dendrogram, superimposed on a...
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, ...
Rotate axes or rotate/flip data
The 3-d Exe nematode nMDS plot should be in the current workspace as Graph5 under Multiplot1 (if ...
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 no...
(W Australia fish diets)
Re-open the workspace WA fish ws from C:\Examples v7\WA fish diets, which will provide an example...
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>...
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 pe...
(Morlaix macrofauna, Amoco-Cadiz oil spill)
Some data sets have a natural sequence to their samples, usually a time series (though this can b...
Overlay trajectories
A trajectory joining points on an ordination is simply added using Graph>Special>Overlays and tak...
Sequence animation, captured in 2- & 3-d
The time pattern above is evident from simple addition of the trajectory but there are occasions ...
Trajectories split & then sequence animated
In fact, if the animation is repeated with trajectories running across months, separately drawn f...
(Tees Bay macrofauna time series)
A clearer, static, example of the benefits of split trajectories on ordination plots is provided ...
Matching variable sets; (Ekofisk oil-field study)
The final two sections of the Graph>Special dialog concern overlaying vectors and ‘bubbles’ of nu...
Bubble plots of single variables
The above MDS draws on all 174 species (with more abundant species given greater weight) but only...
Bubble colours
A new feature in PRIMER 7 is that these bubbles will be plotted in different colours – or in mono...
Bubble key
The key to the left of the plot, which gives the root-transformed scale for Abra prismatica count...
Bubble images
A further new option on this Key dialog is to replace single-coloured circles with a (rectangular...
Duplicate graphs
Abra prismatica appears to be a species which can tolerate the contaminant or disturbance effects...
Vector plots for species
One tempting alternative, commonly found in the literature, is to plot (species) variables as vec...
Environment bubble & vector plots
An important use for a bubble plot is in displaying the behaviour of a further measured variable,...
Segmented bubble plots
Given the inadequacies of vector plots for displaying species contributions to ordinations, but t...
(Bristol Channel zooplankton)
The BC zooplankton density data sheet in C:\Examples v7\BC zooplankton was used in the last half ...
Bubble plots in 3-d MDS; (W Australia fish diets)
Another new feature in PRIMER 7 is the ability to construct bubble plots in 3-d ordinations, wher...
Bubble plots on averages
For these data, a segmented bubble plot on a 2-d ordination provides a succinct summary of the re...
Bubble data selection error & Refresh
It is worth repeating the point made at the start of these examples on bubble plots: if the routi...
Metric MDS; (Great-circle distances for world cities)
A significant new feature in PRIMER 7 is the construction of metric MDS ordinations (mMDS), toget...
Identifying points on the Shepard plot
Show this by running the matching nMDS to the above mMDS, this time setting (Minimum stress: 0.00...
Animating the mMDS/nMDS iterations
Another feature introduced in PRIMER 7 is more of a teaching tool than an analysis method per se,...
(Morlaix macrofauna, Amoco-Cadiz oil spill)
Close the World cities worksheet (it will not be needed again) and re-open workspace Morlaix ws, ...
Threshold metric MDS (tmMDS)
The mMDS Shepard diagram above strongly suggests a middle course between simple metric and non-me...
Metric MDS for ordinating few points
Though usually greatly inferior to nMDS for typical ordinations from community similarities (e.g....
‘Fix collapse’ in nMDS; (Ko Phuket transects of coral reefs)
The PRIMER 7 nMDS dialog box includes a new option to (✓Fix Collapse). This addresses the problem...
Combined nMDS; (Messolongi diatoms & abiotic data)
A variation of the above, and a final new PRIMER 7 feature to discuss in this section, is the opt...