I am trying to calculate the variance explained by a fixed effect for my binary trait using the liability scale. I have run a null model (covarying for sex, age, age^2, 10 PCs) and alternative model (covarying for sex, age, age^2, 10 PCs and fixed effect of interest). To calculate the variance explained I want to use: (residual variance (null) - residual variance (alt)) / residual variance (null) However, it is not apparent how to get an estimate for residual variance on the liability scale.
My output (for the alternative model) is: Source Variance SE V(G) 0.000000 0.003491 V(e) 0.142612 0.004045 Vp 0.142612 0.002087 V(G)/Vp 0.000001 0.024482 The estimate of variance explained on the observed scale is transformed to that on the underlying scale: (Proportion of cases in the sample = 0.180701; User-specified disease prevalence = 0.130000) V(G)/Vp_L 0.000002 0.047268 logL 4395.453 logL0 4395.453 LRT 0.000 df 1 Pval 0.5 n 9358
Also (on a more basic note!), if I was wanting to perform a likelihood ratio test between this output and the output of my null model, I wasn't sure which logL to use, presumably logL rather than logL0?
I'm afraid gcta is unable to transform the Ve (residual variance) from observed scale to liability scale.
Did you fit the GRM in the model? If so, I think the GRM might be considered as the background control. Then, "--reml-pred-rand" can provide the residuals. And I think you may try fitting those effects in a logistic regression to estimate the R square of the fixed effect. If not, I think you may directly try a logistic regression. On the other hand, I'm not sure whether the fixed effect can be transformed to liability scale in the same way as additive effect. So a few tests might be needed to confirm that.
As a side note, the only reason I haven't gone for straight logistic regression is because my sample is a mix of individual and family data, so for other traits I have been using ASReml to allow me to include family structure as a random effect.