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Missing data in linkage trees
Note that LINKTREE is able to tolerate some missing data in the abiotic matrix – the piecemeal form of LINKTREE’s conclusions lends itself to analysing whatever complete matrix is available locally, i.e. within each created subdivision. But distortions in inte...
RELATE on resemblance matrices
The BEST routine in the previous section introduced the concept of measuring how closely related two sets of multivariate data are, for a matching set of samples, by calculating a rank correlation coefficient (Spearman’s $\rho$, Kendall etc.) between all the e...
Model matrix construction
Model matrices corresponding to more complicated structures than simple seriation or cyclicity need first to be constructed by the user and then entered to RELATE in the same way as any other resemblance matrix being matched to the active sheet. There are at l...
RELATE hypothesis test
A permutation test can be applied to the matching coefficient $\rho$ between any two resemblance matrices which are independently derived, with all sample labels in the active matrix matched with (some) labels in the supplied resemblances. As remarked in the p...
Seriation (Phuket coral transects)
The Phuket coral-reef assemblages at equi-spaced positions down an onshore-offshore gradient (transect A) from Phuket Island, were seen previously in Sections 8, 9 and 11. Open the workspace Phuket ws, or if not available open just Phuket coral cover 83-87 fr...
RELATE test on two biotic arrays
Given the breakdown of the serial gradient structure for 1987, is it now the case that the pattern of change down the transect has nothing at all in common with that for 1983? To answer that question requires a further run of RELATE, but of the two similarity ...
2-way RELATE for seriation
A new feature in PRIMER 7 parallels that discussed for the BEST analysis of the previous section, namely a secondary factor is supplied, e.g. (✓Within levels of factor ), which turns this into a 2-way RELATE test. The matching statistic $\rho$ – wheth...
Seriation with replication
Return to the macrofaunal data set from the Ekofisk oilfield, with workspace Ekofisk ws last saved in C:\ Examples v7\Ekofisk macrofauna in Section 9, following an ordered 1-way ANOSIM test (with replication) on the similarity matrix B-C on sq rt from data Eko...
Other Model Matrix options
The conclusion is, of course, consistent with the different, but closely-related, ordered ANOSIM statistic R$^{\text Oc}$ = 0.67 (p<0.01%), calculated in Section 9. It is relatively easy to show algebraically that the unordered ANOSIM statistic – here R = 0.55...
Expanding an (abiotic) data matrix
A RELATE test could equally well have been carried out between the Ekofisk community pattern and a matching (abiotic) resemblance matrix computed not from the surrogate for increased impact – the nearness of the sites to the oil-field centre – but from a set ...
Expanded RELATE test (Exe nematodes)
As an example of Tools>Expand Samples on a data matrix (or Tools>Expand on a resemblance matrix, since the expansion can be equally well achieved either before or after the computation of Euclidean distance in this situation) we shall use the Exe nematode stud...
Expand Samples or Expand resemblances
The Exe environment matrix does not seem (from Plots>Draftsman Plot or Histogram Plot) to contain notable outliers and can safely be used without transformation of individual variables. It does however need Pre-treatment>Normalise Variables – rename it Abiotic...
Model matrix for 2D Euclidean; Cyclicity (Sea-loch macrofauna)
The other two Model Matrix options are (Type•Cyclicity (factor as cycles)) and (Type•Euclidean 2D). The latter simply calculates, for example, distance between samples in a geographic layout when the x, y co-ordinates of the sample points are not held in a sep...
2-way RELATE for cyclicity
A 2-way RELATE version of the above test where there are no replicates, and the cyclic factor under test is actually nested within a ‘nuisance’ factor whose effect we want to remove, is given by reverting to the full data sheet for the Loch Etive macrofauna sa...
(Leschenault estuarine fish, W Australia)
Veale L et al 2014 J Fish Biol 85: 1320-1354 describe trawl sampling for nearshore estuarine fish in the Leschenault estuary of Western Australia, over 4 regions (B - Basal, L - Lower, U - Upper, A - Apex of the estuary) and 4 seasons (Sp - Spring, S - Summer,...
Rationale for 2nd stage MDS
As seen above, the $\rho$ statistic, which rank correlates the elements of two similarity matrices, can provide a very useful and succinct summary of the extent of agreement between two ordinations (or, to be more precise, of agreement in the high-dimensional ...
Aggregation & transforms (Morlaix macrofauna)
Chapter 10 of CiMC gives several examples of aggregating species matrices to higher taxa – using the Tools>Aggregate routine – and the effect this has on the resulting multivariate (and univariate) analyses. We shall illustrate this with the benthic macrofauna...
Second-stage nMDS (Morlaix macrofauna)
The illustration below has calculated all combinations of species (sp), genus (gn) and family (fm) level data, under no transform (no), square-root (sqr), fourth-root (4th), log(x+1) (log) transforms and reduction to presence/absence (pa), with similarity shee...
2STAGE for resemblance coefficients (Clyde study)
The technique of 2nd stage plots has also been used (Clarke KR, Somerfield PJ, Chapman MG 2006, J Exp Mar Biol Ecol 330: 55-80) to examine the effects of different resemblance coefficient choices on a samples analysis, scaling this in relation to the effects o...
Conclusions on comparing resemblance coefficients
Clarke KR, Somerfield PJ, Chapman MG 2006, J Exp Mar Biol Ecol 330: 55-80 discuss this analysis (and that for several other data sets) in more detail, but to pick out just four general points: a) These 2nd stage plots have common features, irrespective of the ...