On Dec 11, 2016, at 10:56 AM, Tsung Fei Khang <[email protected]
<mailto:[email protected]>> wrote:
Dear Mike,
Many thanks for the reply!
When the procD.allometry function performs HOS test with multiple
group labels given, does it compute the regression vectors for each
group, and then tests whether the coefficients of these vectors were
equal, using some multivariate statistical test? If so, is there an
option that outputs the regression vectors? Given the high frequency
of the latter being discussed in the primary GM literature, it seems
important to be able to extract this result from the function.
Finally, on the interpretation side - If group variation is
significant, but not logCS, then under the model shape~size+group,
does this imply that shape variation is mainly explained by variation
in species, and allometry is absent?
Regards,
T.F.
On Thursday, December 8, 2016 at 6:08:17 PM UTC+8, Mike Collyer wrote:
Dear Tsung,
The procD.allometry function performs two basic processes when
groups are provided. First, it does a homogeneity of slopes
(HOS) test. This test ascertains whether two or more groups have
parallel or unique slopes (the latter meaning at least one
groups’s slope is different than the others). The HOS test
constructs two linear models: shape ~ size + group and shape ~
size + group + size:group, and performs an analysis of variance
to determine if the size:group interaction significantly reduces
the residual error produced. (Note: log(size) is a possible and
default choice in this analysis.)
After this test, procD.allometry then provides an analysis of
variance on each term in the resulting model from the HOS test.
Regarding your question, if the HOS test reveals there is
significant heterogeneity in slopes, the coefficients returned
allow one to find the unique linear equations, by group, which
would be found from separate runs on procD.allometry, one group
at a time. If the HOS test reveals that there is not significant
heterogeneity in slopes, the coefficients constrain the slopes
for different groups to be the same (parallel).
Finally, and I think more to your point, the projected regression
scores are found by using for a (in the Xa calculation you note)
the coefficients that represent a common or individual slope from
the linear model produced. The matrix of coefficients, B, is
arranged as first row = intercept, second row = common slope,
next rows (if applicable) are coefficients for the group factor
(essentially change the intercept, by group), and finally, the
last rows are the coefficients for the size:group interaction (if
applicable), which change the common slope to match each group’s
unique slope. Irrespective of the complexity of this B matrix, a
is found as the second row. If you run procD.allometry group by
group, it is the same as (1) asserting that group slopes are
unique and (2) changing a to match not the common slope, but the
summation of the common slope and the group-specific slope
adjustment. One could do that, but would lose the ability to
compare the groups in the same plot, as each group would be
projected on a different axis.
Hope that helps.
Mike
On Dec 8, 2016, at 3:37 AM, Tsung Fei Khang <[email protected]>
wrote:
Hi all,
I would like to use procD.allometry to study allometry in two
species.
I understand that the function returns the regression score for
each specimen as Reg.proj, and that the calculation is obtained as:
s = Xa, where X is the nxp matrix of Procrustes shape variables,
and a is the px1 vector of regression coefficients normalized to
1. I am able to verify this computation from first principles
when all samples are presumed to come from the same species.
However, what happens when we are interested in more than 1
species (say 2)? I could run procD.allometry by including the
species labels via f2=~gps, where gps gives the species labels.
Is there just 1 regression vector (which feels weird, since this
should be species-specific), or 2? If so, how can I recover both
vectors? What is the difference of including f2=~gps using all
data, compared to if we make two separate runs of
procD.allometry, one for samples from species 1, and another for
samples from species 2?
Thanks for any help.
Rgds,
TF
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