Q: Can I use the GRM to check for cryptic relatedness in my sample?
A: Yes, you can. The expected value of Ajk = 1) 1 for MZ twins / duplicated samples 2) 0.5 for 1st degree relatives (e.g. full-sibs or parent-offspring) 3) 0.25 for 2nd degree relatives (e.g. grandparent-grandchild) 4) 0.125 for 3rd degree relatives (e.g. cousins)
Note that these are the expected values. The realised GRM values come with sampling errors which is proportional to the number of markers used to compute the GRM. For distant relatives (e.g. cousins 2 times removed), we might not have enough power (or precision) distinguish them from unrelated pairs. See Supplementary Note #2 of Yang et al. (2010 Nature Genetics) for more details.