I have simulated a data using gama distribution that resulted in normal phenotypic distribution, however non-normal true breeding values (simulated) with a little skewed QQ plot and significant Shapiro Wilks.
Now the question is I want to use GBLUP and not Bayesian approach. However, I am not getting a reference for the same. BLUP is sturdy, however can it be used ignoring bayesian methods? Can I use BLUP for such data/ and if yes, is there a reason to do so?
The best linear unbiased methods typically assume everything is multivariate normal and all relationships are fully described with a Gaussian copula. Your data does not have that. The functional form to fit your data will not be linear, so you need a different method. The qq plot shows non-normality so you need to use a non normal fit. Try a few distributions to see which fits your data better and respects the Shapiro-Wilks and qq results. This can be frequentist or Bayesian, classical or machine learning, parametric or non parametric. What it cannot be is BLUP.
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