Proposed Manuscript Chronology

[Jorge_Stolfi]

This "Guttman effect" is a fancy name for the banal observation that, if you try to fit a simple arc of curve to a bunch of random points in 2 or more dimensions, the result will usually be a curved arc rather than a straight line.

Respectfully, this statement is not accurate. The Guttman effect by definition can only occur when a strong, single underlying linear gradient or sequential ordering is forced into a lower-dimensional space using linear dimension reduction techniques.

Sorry, I was referring to the "Guttman horseshoe".

Its very appearance does in fact mean there is some single underlying linear gradient in the data. You can argue that gradient does not represent time, but you can't claim that such a gradient does not exist. It very clearly does, and is a prequisite for the horseshoe shape to appear.

I still take issue to that.

I can't tell whether you are referring to statistics in general or to the VMS in particular.  I will assume the later for concreteness.

Those scatterplots do not look like a single snake-like cloud -- which would justify interpreting the data as the result of some stochastic process that depends non-linearly on one parameter that varies continuously over some interval. 

What I see in them is about 5 distinct clouds that look like they are mostly pairwise separable in n-dimensional space.  Some clouds are a bit elongated in those projections, but not in directions that point towards other clouds. 

If they are projected along some particular directions, the clouds may seem to be in a certain linear order.  But that is likely to happen if you take any n+1 clouds of points in d-space, for d >= n, with completely independent d-dimensional random distributions.  Like, if you take four random points in 3-space to be the centroids of four point clouds, for any order of the numbers 1..4 there will be directions in 3-space along which those centroids will seem to occur in that order.  And if you pick the main PCA direction, the deviation of the centroids from a straight line in that direction will be smaller than their extent in that direction.

So the "gradient" in that VMS data, and the ordering of the clouds, is an imposed assumption.  Not a property of that data.

All the best, --stolfi