[adegenet-forum] DAPC group choice and MANOVA significance testing

[Jombart, Thibaut]

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


________________________________________
From: adegenet-forum-bounces at r-forge.wu-wien.ac.at [adegenet-forum-bounces at r-forge.wu-wien.ac.at] on behalf of J. Richardson [jrichardson4 at gmail.com]
Sent: 03 March 2012 03:00
To: adegenet-forum at r-forge.wu-wien.ac.at
Subject: [adegenet-forum] DAPC group choice and MANOVA significance testing

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



On Thu, Feb 23, 2012 at 9:08 AM, Jombart, Thibaut <t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk>> wrote:

Hello,

so I think the in the DAPC vignette, the example based on H3N2 data (section 3.4) uses the year of sampling as group factor in DAPC. Also, in the same document, the microbov example (p25-34) uses the cattle breeds as group factor in DAPC. The H3N2 example was also presented in the original paper.

So yes, it does make sense. DAPC provides the best achievable reduced space representation of between-group diversity (in the sense of a F statistic, var between / var within). It is comparable to STRUCTURE or any other similar method when the same groups are used, to the extent that the methods give comparable outputs - in this case, the only common thing is group membership probabilities.

Cheers

Thibaut


________________________________________
From: adegenet-forum-bounces at r-forge.wu-wien.ac.at<mailto:adegenet-forum-bounces at r-forge.wu-wien.ac.at> [adegenet-forum-bounces at r-forge.wu-wien.ac.at<mailto:adegenet-forum-bounces at r-forge.wu-wien.ac.at>] on behalf of J. Richardson [jrichardson4 at gmail.com<mailto:jrichardson4 at gmail.com>]
Sent: 22 February 2012 22:30
To: adegenet-forum at r-forge.wu-wien.ac.at<mailto:adegenet-forum at r-forge.wu-wien.ac.at>
Subject: [adegenet-forum] DAPC group choice

Hi Dr. Jombart and Adegenet users,

I have a question related to DAPC that I have not found in the manual, tutorials or forum archive.

I am wondering what the DAPC operation is doing (i.e. how it is configuring clusters relative to each other) when you
do not use the groups created in "find.clusters" (i.e. grp$grp output), but rather use the population of origin as the
group designation (i.e. dataset$pop)?

I ran "find.clusters" and performed the DAPC with these created groups. I also performed a DAPC with the groups set
as the sampling sites (populations of origin) using the number of clusters derived from k-means. Interestingly, the DAPC using the k-means
groupings don't make a lot of intuitive sense. However, the DAPC results using the sampling sites/populations of origin for the group
designation make sense and correspond closely to the output from STRUCTURE using their location prior.

So I am wondering if using the sampling site/population designation as the group designation is (A) analogous to the
STRUCTURE operation using the location prior or "population flags", and (B) if this is valid if you have good a priori information on
your population delineations (e.g. a species breeding in discrete, contained habitats)?

Thank you so much in advance for any insight you can provide.

Jon