I hope to get a confirmation about how the genetic relationship matrix (GRM) is estimated.
Based on Yang et al. AJHG (2011), the jk'th element of GRM (the genetic relationship between individuals j and k) can be calculated by:
Ajk = sum(over all SNPs i)[wij * wik]/N
where wij is the standardized genotype dosage defined by: (xij-2pi)/sqrt(2pi(1-pi)), and N is the total number of SNPs.
1) Does GCTA use the above formula to estimate Ajk?
2) My understanding is that Ajk is asymptotically the correlation coefficient between the two standardized genotype dosage vectors for individuals j and k. Am I right?
3) If the answer to Q2 is yes, then majority of Ajk values should be between (-1, 1), and most likely between (0,1). However, in our real data analysis, we see a following summary for diagonal values: Min. 1st Qu. Median Mean 3rd Qu. Max. 0.8651 0.9198 0.9463 1.0050 1.0070 18.5600 We observe quite some values > 1, with maximum at 18. Why is that? Are there anything I should be concerned about?