modelling genetically correlated traits

[mahlet-teka]

I have setup the SP and used the SP$addTraitA to generate the traits;

SP$addTraitA(nQtlPerChr=nQTL, mean = c(85, 200, 40, 850, 85, 200, 40, 850), var = Vg, corA=rho)

add error variance as function of heritability

SP$setVarE(h2 = founderh2)

# add genotype platform (i.e add/sample markers)
SP$addSnpChip(nM)

founders <- newPop(founderPop)

rho is an 8X8 correlation matrix where the correlation between some of the traits (such as trait 1 and 5) is really high (0.9). But the when I try to see if indeed the genetic correlation between trait 1 and trait 5 is really 0.9, I used;
cor(founders@gv[,1], founders@gv[,5]), and the correlation is way lower than 0.9.

why is that?

I appreciate your help!
Mahlet.

[gregorgorjanc]

@mahlet-teka this can indeed happen, but it will be highly dependent on sample size - number of individuals, number of chromosomes and QTL. If you simulate few individuals, chromosomes, and QTL you can get quite a bit of deviation from the targeted correlation. Maybe you expand your code with just two traits and show your numbers of chromosomes, QTL, and individuals. I think this is an important example that can benefit others in the community too.

[gregorgorjanc]

@mahlet-teka is the corresponding covariance matrix positive-definite? Simple test is to see if you can invert it - use solve().

[mahlet-teka]

Yes, I can invert it. but when I check is.positive.definate(rho), its seems its not.

[gregorgorjanc]

Ok, this is the problem. You need a valid covariance matrix. AlphaSimR internally “fixes” the matrix, but as you see this can impact the output of simulation.

@gaynorr we need to throw a warning in such cases so users are aware - will open an issue to track this.

[mahlet-teka]

Alright. I will fix it and try with the correct matrix.

[gregorgorjanc]

@mahlet-teka can you tag/mark one of the above posts as an answer so other people are aware of what to look for?