I've trained many mixed effects models and plotted the residuals vs the fitted and found this skew is appearing in many of my models. I'm unsure if this shows that normality is being violated, to me it appears slightly skewed but I can't really describe in what way. I know normality is one of the least important assumptions for regression to hold but could this justify using bootstrap to construct confidence intervals or perhaps using something other than regression to make predictions?

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  • $\begingroup$ I don't see anything I would call "skewness" here. There's indication of underfitting. $\endgroup$
    – Glen_b
    Sep 11 at 0:47
  • $\begingroup$ @Glen_b Is that just because it doesn't look normal? $\endgroup$ Sep 11 at 6:06
  • $\begingroup$ 1. I don't know what you mean by "doesn't look normal"; they all look close to bivariate normal, but there's no reason to expect that these plots should do that. 2. There's a very strong slope left in the residual plots, indicating a substantial amount of linearity that could be captured with a coefficient that was larger in magnitude. This suggests that the regularization may be stronger than would be useful -- possibly. $\endgroup$
    – Glen_b
    Sep 11 at 6:56
  • $\begingroup$ @Glen_b can you recomend any academic sources I where I could read about this? $\endgroup$ Sep 11 at 16:56
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    $\begingroup$ First step: take a y and x that have some correlation and see what happens when the fitted coefficient is too small. Wait, here we go: x=rnorm(400);eps=rnorm(400,0,.5);y=3+0.8*x+eps;pp=par();par(mfrow=c(2,2)); plot(x,y);plot(x,y-3-.25*x);plot(x,y-3-.5*x);plot(x,y-3-.8*x);par(pp) $\endgroup$
    – Glen_b
    Sep 12 at 4:46

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