
Post by mbilow on Oct 19, 2015 2:49:03 GMT
I'm running some computations using GCTA and I'm finding some differences on the order of 12% in some of my Vp calculations and the ones returned by GCTA using a single fixed effect environmental factor for GxE analysis.
Setting:
Y = 1 x M quantitative phenotype (uncentered) x_e = 1 x M environmental variable (the only fixed effect) X_e = 2 x M matrix where the first column is all 1's and the second column is x_e
b_e = (X_e^T . X_e)^(1) *(X_e^T . Y)
The variance of (Y  X_e . b_e)estimated with M degrees of freedomis very close, but not quite the same as the V_p I get in the .hsq file by running:
gcta64 reml remlmaxit 10000 remlalg 2 remlnolrt grm {plink} pheno {pheno} gxe {gxe} remllrt 2 out {pheno}
Is there a step somewhere that the fixed effect (b_e) is getting reestimated? Looking on page 77 of the AJHG 2011 paper in the second column, it appears that V_p is assumed to be known before the REML iterations, since the initial estimates for the variance components are based on V_p.



Post by Jian Yang on Oct 21, 2015 6:24:56 GMT
For a GxE analysis, E is fitted as fixed effect, the phneotypic variance is calculated as V _{p} = V _{g} + V _{gE} + V _{e}. This could be different from the empirical variance of y, i.e. var(y), depending on how much proportion of variance is explained by the fixed effects. See this post gcta.freeforums.net/thread/211/estimatingfixedeffectsgctagreml for the estimation of fixed effects.

