Stress values in PC-ORD

[Elizabeth Bent]

Hi, so I've been told that an acceptable "rule of thumb" value for stress in an ordination is 0.2 or so, and that PC-ORD output multiplies the reported stress values by 100 so that an acceptable cutoff in PC-ORD output is 20. Is this actually the case, or not? I am wondering because while I found this information in an online user group (not this one), I can't find it again and I am wondering if it is true. 

Thank you,

Liz

(PS- if it is not- what would be an acceptable "rule of thumb" threshold for stress in an ordination done in PC-ORD?)

[Bruce McCune]

Liz, PC-ORD's stress is expressed as a percentage rather than proportion, so yes it is 100x that of some other software. That 0.2 cutoff is a weak rule of thumb that should not be adhered to religiously. You can have a poor ordination with much lower stress and a good ordination with somewhat higher stress. Use the randomization test in PC-ORD to help with this too.

Bruce McCune

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[gpmal...@gmail.com]

Bruce, I think you may be the source, and in any case I would like a good source to cite: I have been looking at the correlation between the similarity matrix used in NMS and a matrix of distances in NMS-space (Sorensen for the former, Euclidean for the latter), using the Mantel test in pc-ord. This correlation complements stress closely, and is more intuitive for me (at least). Does this make sense? Thanks. - George Malanson

[Bruce McCune]

George, if you have PC-ORD 7, see the help topic, "Measures of Fit with NMS". What you are referring to is essentially the same as what Jari Oksanen calls "metric fit". See the table contrasting the properties of that with stress-based measures.My summary statement in that table about metric fit is, "Widely used but foreign criterion to NMS because NMS does not attempt to maximize this measure of fit. Allows partitioning of fit by axis. Is usually lower than nonmetric fit, although they tend to covary unless the Shepard plot is strongly nonlinear."  Keeping in mind that it is not a measure of fit that is inherent to NMS, its main utility is partitioning fit by axis. In PC-ORD you don't need to calculate the Mantel statistic for this, just click the R2 button in the graph window.

Bruce 

On Tue, Jul 17, 2018 at 6:54 PM, <gpmal...@gmail.com> wrote:

Bruce,  I think you may be the source, and in any case I would like a good source to cite:  I have been looking at the correlation between the similarity matrix used in NMS and a matrix of distances in NMS-space (Sorensen for the former, Euclidean for the latter), using the Mantel test in pc-ord.  This correlation complements stress closely, and is more intuitive for me (at least).  Does this make sense?  Thanks.  - George Malanson

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[David Houghton]

Bruce,

Do you have a tutorial on how to do the randomization test in PC-ORD to evaluate stress after an NMS analysis?

Thanks,

     -Dave

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[Bruce McCune]

Dave, the process is briefly described on p. 131 of McCune & Grace, Analysis of Ecological Communities, with points on interpretation on subsequent pages. I view it as a very useful heuristic tool, but like all criteria for choosing a solution, there is no single foolproof method. For example, I have definitely seen cases where perfectly good solutions do not beat the randomization test.

Bruce McCune

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[Bruce McCune]

p.s. The built-in Help system for PC-ORD also has lots of info on this. See the help topics Randomization Test and Ways to Run NMS.

On Wed, May 6, 2020 at 4:48 AM David Houghton <dhou...@hillsdale.edu> wrote:

[David Houghton]

Thanks, Bruce. I already report those values. I thought there was a fancier test than that available in PC-ORD, something similar to what Dexter et al. (doi: 10.1002/lom3.10257) did. I’ll contact them directly.

 

     -Dave

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[Bruce McCune]

Dave, as I understand it the approach they are advocating is what PC-ORD has been doing for a long time. They tried a different randomization method than that used by PC-ORD, but I didn't see any evaluation of the two methods. I'm not sure one is fancier than the other, they just preserve/randomize different aspects of the data. In both cases the correlation structure among species is destroyed.

-Bruce

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[David Houghton]

Bruce,

 

I am sorry if this is a stupid question, but it has stumped me for 2 days.

 

See attached. How do I access the data that compose the side scatterplots? Ideally, I would like to download them into Excel and reproduce the graphs. I’ve tried saving scores and envelope curve data, but nothing seems to be correct. What am I missing?

 

Thank you in advance,

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[Bruce McCune]

Dave, the basic data for the side scatterplots come from two sources. The overlay variable is already in one or your spreadsheets, either the main or second matrix. The ordination axis scores you can write to a spreadsheet from the Graph module. Select File | Save Scores As | Rows | Spreadsheet | *.xlsx. The rows will be in the same order as in your main and second matrices. Then you can put those together with Excel if you like. 

Alternatively you can select Save Scores As | Rows | Add to second... This augments your second matrix with the coordinates of the points from the ordination.

The curves themselves are not written to those files. The side scatterplots show straight line fits (easily reproduced in Excel or elsewhere) and they also show nonparametric regression curves. The latter are fitted with a kernel smoother (local mean, Gaussian kernel, with the flexibility of the curve under your control). It will be tricky to reproduce these exactly in other software without some experimentation with kernel smoothers (there are many kinds). The PC-ORD help system describes how PC-ORD does it. One difference from a usual kernel smoother is that instead of estimating the local mean, it estimates a value 2 standard deviations above the mean, such that the fitted line envelopes most of the data points.

If you save all of the envelope curves (as you have tried), you will see that it gives you regression estimates for each response variable at equal intervals along the ordination axis, not the ordination scores for your particular data points. This assures that you get a continuous curve along the axis.

At any rate, those sets of numbers are the complete information that PC-ORD uses to create the side scatterplots, and all of that information is available to you as spreadsheets, except for the linear fits.

Bruce McCune

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[David Houghton]

Yes, that worked. Thank you!

 

I don’t really need the curves. Linear or polynomial fits in Excel will work just fine.

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