Okey,
I understood that, and I agree with you, but that is what I got wuth 4
dimensions...
The graph is great, but what about the Stress?

Call:
metaMDS(comm = sqrtABCD, distance = "bray", k = 4, trymax = 100,
autotransform = F)

Nonmetric Multidimensional Scaling using isoMDS (MASS package)

Data:     sqrtABCD
Distance: bray shortest

Dimensions: 4
Stress:     11.68632
Two convergent solutions found after 2 tries
Scaling: centring, PC rotation, halfchange scaling
Species: expanded scores based on ‘sqrtABCD’

I am going to try with decorana now, I would see how it work...
Cheers,

Gian


Gian,
>
> This looks very much like badly degenerate solution. You shouldn't use 23
> axes in NMDS, in particular with 40 x 20 source data. In Euclidean space
> that data would give you rank of 20 or you could find at maximum 20 axes in
> metric scaling. In the Bray-Curtis space the situation is more complicated,
> but one random data set (Poisson random variates with lambda = 3.14) gave
> 25
> positive and 14 negative eigenvalues. Probably the 23 dimensions you
> specify
> exhaust the real part of your space even in metric scaling, and probably
> (and obviously) fail miserably in nonmetric scaling. You shouldn't get
> stress of that magnitude with a decent model with data like that.
>
> It has never occurred to me that anybody would like to have NMDS with that
> high number of dimensions. Usually we want to use two, sometimes one or two
> more, but that's about the limit. Do the same and set k=2 to k=4 at
> maximum.
> If you want to have mapping of all of your real space (i.e., ignore the
> complex space), you can use metric scaling. The standard R choice is
> cmdscale(). The vegan alternatives are capscale() which also can do
> unconstrained metric scaling, returns information both on the real and
> imaginary components of your space, and has plot and other support
> functions. The low level alternative in vegan is wcmdscale() which also is
> used by capscale(), but does not have any support functions (lacks even
> print.wcmdscale!)
>
> NMDS is really intended for nonlinear mapping onto *low* number of
> dimensions.
>
> Cheers, Jari Oksanen
>
> >> NMS.trial
> >
> > Call:
> > metaMDS(comm = sqrtABCD, distance = "bray", k = 23, trymax = 100,
> > autotransform = F)
> >
> > Nonmetric Multidimensional Scaling using isoMDS (MASS package)
> >
> > Data:     sqrtABCD
> > Distance: bray shortest
> >
> > Dimensions: 23
> > Stress:     0.2548688
> > Two convergent solutions found after 8 tries
> > Scaling: centring, PC rotation, halfchange scaling
> > Species: expanded scores based on ŒsqrtABCD‚
> >
> > With more than 23 dimensions R gave me that result:
> >
> >> metaMDS(sqrtABCD, distance = "bray", k = 30, trymax = 50,
> > Using step-across dissimilarities:
> > Too long or NA distances: 230 out of 780 (29.5%)
> > Stepping across 780 dissimilarities...
> > Errore in isoMDS(dist, k = k, trace = isotrace) :
> >   initial configuration must be complete
> > Inoltre: Warning messages:
> > 1: In cmdscale(d, k) : some of the first 30 eigenvalues are < 0
> > 2: In sqrt(ev) : Si è prodotto un NaN
> >>
> >
> > ...Is normal I got better ordination (sepatation of different samples,
> that
> > I know they're different) with few dimension also if the Stress is high?
> >
> > ... I supposed, that If we use as many dimensions as there are variables,
> > then we can perfectly reproduce the observed distance matrix. Isn't it?
> But,
> > of course, our goal is to reduce the observed complexity of nature, that
> is,
> > to explain the distance matrix in terms of fewer underlying dimensions...
> > So what is best at the end??
> > And also wich is the function for plotting the stress values versus the
> > number of dimnsions and how to read the plot?
> > I hope I was clear, thank you so much!
> > Yours,
> >
> > G.
> >
>
>

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