[adegenet-forum] rda/dbMEM vs sPCA

[Jombart, Thibaut]

Hi Xavier, 

the approaches are close but not identical. 

You description of sPCA is accurate, and shows that it is very different from a RDA on MEMs. The first decomposes a product of variance and autocorrelation, the second maximises the variance explained by the MEMs. 

The similarity is in the global/local tests, which indeed rely on the (full) decomposition of the data onto the MEMs basis. By definition, the R2 of this decomposition is 1. The test statistic we use there is the highest R2 with a single MEM. This is what explains that the test itself lacks power: we only capture spatial structures which resemble at least one of the MEMs. 

Best
Thibaut
________________________________________
From: adegenet-forum-bounces at lists.r-forge.r-project.org [adegenet-forum-bounces at lists.r-forge.r-project.org] on behalf of Xavier Giroux-Bougard [x.giroux.bougard at gmail.com]
Sent: 19 February 2014 01:28
To: adegenet-forum at lists.r-forge.r-project.org
Subject: [adegenet-forum] rda/dbMEM vs sPCA

Hello,


over the past year I have been experimenting with various types of spatial analysis in R to interpret genetic data. While I haven't gone into the repositories of PCNM and adegenet to check the code (and frankly I suspect this could take a long long time for me to figure out on my own), I am wondering if rda/dbMEM and sPCA are similar in the way they use Moran's I to detect spatial structures. From my understanding, sPCA combines matrices of variance and Moran's I, then decomposes them into eigenvalues to look for structures. While we can test for significance of these eigenvalues using global/local.randtest(), is the observation value in the output (which I am assuming is R2) analogous to the R2 you would obtain if you plugged a dbMEM into a canonical redundancy analysis (rda) on a table of allele frequencies?

Can anyone point out the similarities and differences between these two techniques?

Thank you,

Xavier