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I have a hard time trying to understand what is the meaning of the correlation among random effects and how it affect the estimation of the variances of random effect and predictions.

I work with genetic effects and there is a negative correlation among them and I can see that the estimated variances are being affected since these effect are not orthogonal.

Does anyone provide an explanation of this?

marb_021
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  • Do you have specific interest in the variances and covariance of the random effects, or only their impact on predictions ? And what do you mean by "I can see that the estimated variances are being affected since these effect are not orthogonal." ? – Robert Long Nov 11 '20 at 15:00
  • Hi Robert, thanks for your comment. Yes, I have specific interest in the variances (and also in the predictions, but actually not in the covariances). I can see that the effect are not orthogonal due to when I run a model only with one of my effects (let´s call it the "additive effect") the variance is different from when I run a model with the both effects ("additive effect" + the other random effect that we can call it the "epistatic effect"). – marb_021 Nov 11 '20 at 15:34
  • Could you perhaps include the output of these models in your question so we can get a better understanding of these issues ? – Robert Long Nov 11 '20 at 15:44
  • Hi Robert, I am using an specific software for variance component estimation of genetic effects. This software works with AI-REML, and have several outputs. For example, the optimization process, the estimated variance and covariances, and more. If you told me what information you want to see I can try to find it and share. Otherwise, if I can have a more general explanation from an statistical point of view, it also would be very good. – marb_021 Nov 12 '20 at 08:25
  • If I could understand your question then I could try to give a general statistical explanation. The model output would help me understand, if you can frame the question in terms of some specific output. Perhaps you can create a simple simulation in R or some other software that demonstrates the issue ? – Robert Long Nov 12 '20 at 08:30

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