[adegenet-forum] MANOVA significant testing with DAPC

[Jonathan Richardson]

Hi Thibaut and Adegenet users,

I have a follow-up question to one I asked back in March 2012. I have more
data to appreciate what you were suggesting then (original correspondence
pasted below).

In short, we would like to test whether "groups" of genotypes are
significantly separated in discriminant function space. We proposed using a
MANOVA of the individual coordinates coming from DAPC to do this. Now that
I've tested another 2 datasets, Thibaut was correct that these usually come
out significant regardless of actual clustering patterns in DF space. The
original code looked like this:

model <- manova(dapcobject$ind.coord~genindobject$pop)
summary(model, test=”Wilks”)

But you mentioned that a MANOVA could be done on the retained PCs after the
PCA step - the more traditional test with discriminant analysis. After
trying to apply this with our new datasets, we are hoping to clarify 2
things:

1. To execute this, do you mean to use the $tab item in the dapc output
(i.e. "retained PCs of PCA"), in place of the $ind.coord item? Or did you
mean a step earlier in the find.clusters PC retention step?

2. If you meant the dapc step, the structure of the $tab data appears to
make it much more difficult to pull into an MANOVA analysis (i.e., it is a
data frame with 1 observation per genotype, and # of variables equal to PCs
retained). The $ind.coord data is numeric with (not surprisingly) 2 values
per genotype relating to the location in DF space.

I'm hoping you can confirm question 1 before I spend too much more time
figuring out the data formatting issue in #2.

I should also say thank you for your time and efforts developing and
supporting Adegenet; I am finding it more useful through the years.

Thank you very much!

- Jon



_______________________
Archived emails:

3March2012:

Hello again Dr. Jombart and Adegenet users,

I have a follow-up question related to the grouping of individuals not
using k-means.

We would like to test whether the group assignment (assigned by us) is
significantly related to the location of individuals in the discriminant
function (DF) space. To do this we have taken the following approach:

1. Perform a MANOVA on the individual DF coordinates with group class as
the predictor variable. The idea here is that (A) the Wilks lamba test
provides a metric of separation among the groups and (B) accounts for
correlation among variables (DFs). The test code is:

model <- manova(dapcobject$ind.coord~genindobject$pop)
summary(model, test=”Wilks”)

2. However, we are worried that the significance value obtained by MANOVA
(which was remarkably small) might be anti-conservative (i.e. high Type-I
error) because DAPC has already maximized among group variation and
uncovered structure that might be evident even in random datasets.

Therefore, we came up with a randomization test.  We first create a null DF
distribution by randomizing the rows/individuals in the “genind” data
object so that the number of individuals per group remains the same, but
the individuals contained in each group are now randomized. We do this 1000
times and perform the DAPC and MANOVA operations on all 1000 sets to obtain
the randomized distribution. Lastly, we compare our empirical Wilks lambda
value with the randomized distribution to determine if our Wilks is larger
than expected based on random chance.

Does this seem reasonable? Our hesitation is related to some initial
results from our dataset. When we run the empirical dataset with 3 defined
groups, the DAPC produces 3 clear clusters with some small overlap (i.e.
the 3 a priori groups segregate very nicely in DF space). However, when we
randomized the alleles and genotypes, the resulting DAPC with the same
group sizes also results in 3 clear clusters, but that have noticeably more
ellipse overlap than the empirical data. So we are wondering whether the a
priori group designation (related to a substantial habitat and phenotypic
difference in our case) will mandate some level of clustering – but with
DAPC also looking to optimize grouping segregation in DF space the patterns
become clearer and maybe somewhat spurious (at least in our case)?

Any insight you can provide would be greatly appreciated. Thank you in
advance.

Jon

_________

6 March 2012:

Hello,
Yes, as you suggest the approach described in 1 is circular, and the test
should nearly always be significant. The second approach is not ideal
because the amount of discrimination - and therefore your test statistics -
depends on the retained variation in the dimension-reduction/PCA step,
which is likely to vary from one permutation to another.

I would perform the MANOVA on the retained PCs after the PCA step. This
should be less computer intensive, and is the traditional test associated
to discriminant analysis.

Cheers

Thibaut
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