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My QQ-plot indicates normality (a fairly straight line), but my density plot shows departures from normality. Why is this happening? Is this a big problem for my model?

Here's my model syntax:

response ~  block*f_transition* f_manner + (1 + block || id ), 
            data = aggrdata, control = lmerControl(optimizer = "Nelder_Mead", 
            optCtrl=list(maxfun=200000)))

enter image description here

enter image description here

Here is also the residuals vs fitted plot

enter image description here

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    $\begingroup$ What features of the QQ plot lead you to conclude it's "fairly straight"? It shows significant evidence to the contrary, especially in the tails. Whether this is a "big problem" depends on your model, so you'll need to provide more information about that. $\endgroup$
    – whuber ♦
    Commented Jun 5, 2020 at 14:04
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    $\begingroup$ I don't know that I would say the density plot departs from normal. There is that one blip around -1, but you can see that in the QQ-plot as well. Regardless, things seem to still be unimodal and roughly symmetric. I don't see why this would be any problem. Have you used a numeric test for normality (i.e. Shapiro-Wilk, etc.)? $\endgroup$
    – Todd Burus
    Commented Jun 5, 2020 at 14:04
  • $\begingroup$ I agree with @whuber. You could say the QQ-plot in not normal in the tails. Do you know anything about the values at the ends (particularly on the high end)? Maybe they could be removed and redo the plots. $\endgroup$
    – Todd Burus
    Commented Jun 5, 2020 at 14:07
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    $\begingroup$ The plot I first want to see is residuals versus fitted. $\endgroup$
    – Nick Cox
    Commented Jun 5, 2020 at 14:16
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    $\begingroup$ I'm confused by that, because p-values have nothing to do with prediction. $\endgroup$
    – whuber ♦
    Commented Jun 5, 2020 at 14:22

1 Answer 1

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As evident from the comments above, it seems that you have a bounded outcome for which a Beta mixed-effects model would be more appropriate. You can fit such a model, using, for example, the GLMMadaptive package I've written. A sample analysis with such a model can be found here.

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  • $\begingroup$ I fit a beta-binomial model specified here: cran.r-project.org/web/packages/TailRank/vignettes/…. However, the pp_check plots still look quite bad and don't capture all the peaks. $\endgroup$
    – user3635550
    Commented Jun 5, 2020 at 16:56
  • $\begingroup$ @user3635550 but did you fit a beta-binomial mixed model? $\endgroup$
    – Dimitris Rizopoulos
    Commented Jun 5, 2020 at 17:04
  • $\begingroup$ @ Dimitris Rizopoulos Yes I did. $\endgroup$
    – user3635550
    Commented Jun 5, 2020 at 17:05
  • $\begingroup$ @ Dimitris Rizopoulos unfortunately, looking at your sample analysis, I don't seem to have the skills right not to understand or fit your beta mixed model. I'm just starting out as a student. $\endgroup$
    – user3635550
    Commented Jun 5, 2020 at 17:07

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