What is the difference between Procrustes ANOVA and MANOVA and how to do both in geomorph

[YW]

Dear all,

In Prof. Kingenberg's paper "Shape analysis of symmetric structures: quantifying variation among individuals and symmetry", the difference between Procrustes ANOVA and MANOVA lies in the former assumes isotropic variation at all landmarks while the latter relived such stringent assumption. In "Quick Guide to geomorph 3.0.5", Procrustes ANOVA was performed with procD.lm, as shown below:

However, in the same page of this guide, various applications of procD.lm were illustrated with the name MANOVA/MANCOVA rather than Procrustes ANOVA, as shown below:

My question is: (1) what are on earth the differences between Procrustes ANOVA and MANOVA; (2) how to do both in geomorph; and (3) how to determine which to choose. Thank you.

YW

[Mike Collyer]

YW,

The simple, imprecise answer is that Procrustes ANOVA and MANOVA are the same.  The M in MANOVA just indicates that the data are multivariate.  In the Quick Guide you are reading (not version 3.0.5, but older), they were treated as the same.

However, in more recent versions of geomorph, we have tried to not use these words interchangeably and more precisely use the word, ANOVA, to indicate the use of statistics calculated from the (Procrustes) distances of shapes from the overall mean or estimated values; i.e., these are univariate statistics (SS, MS, F values, etc.) based on distances, even if the data are multivariate.  This approach is nice because the number of variables has no influence on the statistics.

We now use a more precise definition of MANOVA to use multivariate test statistics (Wilks Lambda, Pillai trace, Hotelling-Lawley trace, Roy’s maximum root) rather than ANOVA statistics (SS, MS, Rsq, F).  Note that traditionally, parametric MANOVA would convert these statistics into approximate F values to infer “significance”.  The manova.update function (with more discussion of this on the help page) uses RRPP to generate distributions of multivariate test statistics.  Because multivariate test statistics are sensitive to the number of variables, there are also options for reducing data dimensionality.

The manova.update (RRPP function) help page and the vignette in the same package ("ANOVA vs MANOVA in RRPP") go into much more detail.

Note, the vignettes in RRPP and geomorph are always current with respect to the functions in those packages; the "quick guide" still exists but is no longer maintained with the geomorph package.

Hope that helps!

Mike

On Aug 15, 2019, at 12:27 AM, YW <wyf...@connect.hku.hk> wrote:

Dear all,

In Prof. Kingenberg's paper "Shape analysis of symmetric structures: quantifying variation among individuals and symmetry", the difference between Procrustes ANOVA and MANOVA lies in the former assumes isotropic variation at all landmarks while the latter relived such stringent assumption. In "Quick Guide to geomorph 3.0.5", Procrustes ANOVA was performed with procD.lm, as shown below:

<1.png>

However, in the same page of this guide, various applications of procD.lm were illustrated with the name MANOVA/MANCOVA rather than Procrustes ANOVA, as shown below:

<2.png>

My question is: (1) what are on earth the differences between Procrustes ANOVA and MANOVA; (2) how to do both in geomorph; and (3) how to determine which to choose. Thank you.

YW

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<1.png><2.png>

[Adams, Dean [EEOB]]

YW,

 

I will add one thing to Mike’s comprehensive answer from a historical perspective. In the earlier literature (from Goodall 1991 through Klingenberg), significance levels from Procrustes ANOVA were evaluated using parametric F-distributions. That is where the isotropic error assumption came into play.

 

However, this should be avoided.  Instead, permutation, or more precisely, residual randomization, should be used to evaluate significance, and to obtain effect sizes. This is what is implemented in geomorph.  The rest is exactly as Mike so clearly described.

 

Dean

 

Dr. Dean C. Adams

Director of Graduate Education, EEB Program

Professor

Department of Ecology, Evolution, and Organismal Biology

Iowa State University

https://www.eeob.iastate.edu/faculty/adams/

phone: 515-294-3834

To view this discussion on the web, visit https://groups.google.com/d/msgid/geomorph-r-package/46EDC4D3-659B-4520-B5AA-DD05B6AE0959%40gmail.com.