Dear All, beside the excellent review by Carmelo, I suggest a few other papers on ME in geometric morphometrics: Arnqvist, G., Martensson, T. Measurement error in geometric morphometrics: empirical strategies to assess and reduce its impact on measures of shape. Acta Zoologica Academiae Scientiarum Hungaricae, 1998, 44: 73–96. (A bit outdated but still wonderfully accurate in how they explain different sources of ME). Klingenberg, C.P., Barluenga, M., Meyer, A. Shape Analysis of Symmetric Structures: Quantifying Variation Among Individuals and Asymmetry. Evolution, 2002, 56: 1909–1920. (From where most of us have borrowed the protocol for assessing ME). Viscosi, V., Cardini, A. Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners. PLoS ONE, 2011, 6: e25630. Galimberti, F., Sanvito, S., Vinesi, M.C., Cardini, A. “Nose-metrics” of wild southern elephant seal (Mirounga leonina) males using image analysis and geometric morphometrics. Journal of Zoological Systematics and Evolutionary Research, 2019, 57: 710–720.
There's also another one I like, by the Viennese morphometricians (in a paper on human mandibles, or teeth, symmetric and asymmetric variation, if I remember well), but I can't find it now. In general, the idea is that differences among individuals (averaged replicates) in a representative sample should be larger than differences between replicates of the same individual (the estimate of ME). This is what is tested by 'individual' in the Procrustes ANOVA in MorphoJ. It might be important to control for main effects in the analysis. For instance, by including species and sex before individual in the hierarchical analysis, I 'statistically remove' (with some assumptions) the average effect of these factors before comparing individual variation to ME, which makes the test more conservative (NB whether this is OK or not it depends on the question one is asking in her/his study). For shape data, even if the P value of individual vs residual is significant, I would not conclude that ME is negligible for sure. I'd check that the individual Rsq is much larger than the ME (residual) Rsq and also that shape distances between replicates of the same individual are smaller than distances among different individuals (if this is true, replicates should cluster 'within individual' in a UPGMA phenogram). Then, I feel a bit more confident that ME might be negligible. If ME is large, it may happen that its Rsq is larger than the individual Rsq (or, which is the same ME SSQ > individual SSQ). For the F ratio, however, one should look at the mean SSQ, which take df into account. From the MSSQ, one computes F. The F ratio in MorphoJ employs an isotropic model but, with large samples (relative to the number of variables), the software also provides P values using Pillai, that does not depend (if I recall well!) on an isotropic model. That N is large and the sample representative is crucial if one is using a subsample in the assessment of ME to avoid replicate measurements of all individuals, which would be better but might take too long if one has hundreds or thousands individuals. In R, I generally use adonis that employs an F test (same as in MorphoJ, for a simple design) but uses permutations instead of parametric tests. The use of permutations was also suggested as desirable in Klingenberg et al., 2002. Other packages I suspect might do something similar, although maybe using different permutational approaches. I am sure it is explained in their help files. Cheers Andrea On 03/11/2022, ying yi <[email protected]> wrote: > Dear all, > I used the “procD.lm” function in the geomorph package to test the > measurement error. I was surprised to find that the within-groups ANOVA sum > > of squares I got was greater than the among-groups ANOVA sum of squares. I > > wonder if something went wrong. What does it mean for “procD.lm” function > to get an F value <1? > I would be very happy if someone could help me. > Yours, > Sam > > References are as follows: > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/06065841-c42e-4a58-a5d3-a96eb3c5787dn%40googlegroups.com. > -- E-mail address: [email protected], [email protected] WEBPAGE: https://sites.google.com/view/alcardini2/ or https://tinyurl.com/andreacardini -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/CAJ__j7Ouo%3D5tXHBp1-nm%2BzrQm-S_pGejF_Yd2j%2BxdqhK-174pA%40mail.gmail.com.
