|
Post by phage on Nov 15, 2013 17:37:13 GMT
Hello,
I've searched extensively but have been unable to find an explanation of how GCTA computes standard error for its heritability results, and I don't feel comfortable using the reported value unless I understand the methodology behind their calculation. How is this done?
Thank you!
|
|
|
Post by Terry on Nov 16, 2013 19:55:38 GMT
Hi, I agree, it would be nice to know it!
|
|
|
Post by Jian Yang on Nov 17, 2013 12:59:01 GMT
SE of a variance component = the square root of the corresponding diagonal element of inverse(AI matrix). See GCTA AJHG paper (page 2) for AI matrix.
|
|
|
Post by Terry on Nov 18, 2013 5:49:37 GMT
Thanks Jiang! Is there a way of computing the SE of the environmental influences standardised to the total variance, as V(e)/V(P), from the GCTA output?
|
|
|
Post by Jian Yang on Nov 18, 2013 9:26:45 GMT
This can be calculated in the the same way as that for V(G) / Vp.
Say x = V(G) and y = Vp
var(x/y) is approximately = (u_x/u_y)^2[var(x)/u_x^2 + var(y)/u_y^2 - 2*cov(x,y)/(u_x*u_y)], where u_x = E(x) and u_y = E(y). In practice, u_x (or u_y) is usually replaced by x (or y).
SE = the square root of var(x/y)
var(x), var(y) and cov(x,y) can be calculated from the variance-covariance matrix in the log file (the stuff printed out on the screen).
|
|
|
Post by Terry on Nov 19, 2013 8:44:17 GMT
Thanks again, Jian! That was very clear. It is easy to obtain var(x) and var(y) from the variance-covariance.
I am, however, somewhat confused on how you get the cov(x,y) from this variance-covariance matrix. Please, could you give me a hand to finally understand this issue? It would be MUCH appreciated.
Regards!
|
|
|
Post by Jian Yang on Nov 19, 2013 10:32:58 GMT
cov(Vg_hat, Vp_hat) = cov(Vg_hat, Vg_hat + Ve_hat) = cov(Vg_hat, Vg_hat) + cov(Vg_hat, Ve_hat) = var(Vg_hat) + cov(Vg_hat, Ve_hat)
Covariance between the estimates of variance components = off-diagonal elements of inverse(AI matrix)
|
|
|
Post by Terry on Nov 20, 2013 4:47:24 GMT
Thank you, Jian! Excellent... very clear and informative.
|
|
|
Post by Nick on Oct 29, 2014 0:22:27 GMT
What about the SE for the covariance? Would that correspond to the square root of the displayed value as well? How would that work if the value is negative?
|
|
|
Post by Nick on Oct 29, 2014 18:34:31 GMT
For example, how would one compute the SE for cov(G1, G2) / Vp if two variance components were used?
|
|
|
Post by Nick on Oct 31, 2014 19:38:17 GMT
Nevermind. I ended up using the deltamethod as implemented in R to compute what I needed based on the covariance/variance matrix output to the screen in addition to the V(G1), V(G1), V(e) estimates and SE.
|
|
|
Post by Jian Yang on Nov 4, 2014 3:33:34 GMT
The sampling variance of all the variance and co-variance components have been reported in the GCTA log output "Variance/Covariance Matrix of the estimates", which are calculated from the AI matrix.
Yes, the sampling variance (SE squared) of further linear combination of the estimates can be approximated by the Delta method.
|
|
|
Post by Jian Yang on Nov 4, 2014 3:33:40 GMT
The sampling variance of all the variance and co-variance components have been reported in the GCTA log output "Variance/Covariance Matrix of the estimates", which are calculated from the AI matrix.
Yes, the sampling variance (SE squared) of further linear combination of the estimates can be approximated by the Delta method.
|
|