Dear community
Sorry if my question is a bit elementary, but I want to be sure that I'm using Procrustes ANOVA correctly. My goal is to evaluate the differences in shape between flowers of different species, but also the differences between flowers of the same species. In this case, I used a hierarchical ANOVA design, with "species" as the main effect and the effects of "individual" (plant) and "position" (position of the flower on the same plant) as random effects. To do this, I only considered the "individual" effect nested within "species", since the "position" effect has levels common to all individuals evaluated (basal, medial or apical flowers). Then, I performed the test as follows:
ANOVA_calyx_shape <- procD.lm(coords ~ species/individual + position, data = df_symm_calyx, iter = 999)
summary(ANOVA_calyx_shape)
And the results were as follows:
Df SS MS Rsq F Z Pr(>F)
species 4 1.3392 0.33480 0.33157 60.3784 9.2741 0.001 ***
position 2 0.0762 0.03809 0.01886 6.8699 3.1168 0.001 ***
species:individual 23 1.3926 0.06055 0.34479 10.9191 11.0215 0.001 ***
Residuals 222 1.2310 0.00555 0.30478
Total 251 4.0390
However, it occurred to me to consider the "position" effect nested in "individual" using the same function as follows:
ANOVA_calyx_shape <- procD.lm(coords ~ species + individual %in% species + position %in% individual, data = df_symm_calyx, iter = 999)
summary(ANOVA_calyx_shape)
The results in this case show that the position factor explains a greater proportion of variation in shape than in the previous case.
Df SS MS Rsq F Z Pr(>F)
species 4 1.3392 0.33480 0.33157 86.3039 10.0498 0.001 ***
species:individual 23 1.3926 0.06055 0.34479 15.6076 11.7664 0.001 ***
individual:position 56 0.6555 0.01170 0.16228 3.0172 7.2128 0.001 ***
Residuals 168 0.6517 0.00388 0.16136
Total 251 4.0390
I'm not sure which of the two models is correct, or whether the design applied in the first place is suitable for assessing differences in shape at the inter- and intraspecific level. I hope someone can clarify this matter for me.
Thanks in advance!
Gabriel