I'm working on a longitudinal dataset to which I've been fitting non-linear mixed effects model in R. Regarding normality, I have a few questions:

  1. Can I assume that a longitudinal data is normally distributed?
  2. Do tests such as the Shapiro test apply to longitudinal data?
  3. Is normality a strict requirement for mixed effects models?
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    $\begingroup$ WOW! The questions and their given answers are very important for my study! A lot thanks!❤ $\endgroup$
    – Alex2024
    Commented Jun 10, 2023 at 0:09

1 Answer 1

  1. There is nothing in the longitudinal nature of longitudinal data that necessitates it is normal. For example, there are longitudinal Bernoulli data (e.g., whether a child is out sick for every day of the school year). Even if data were continuous, there is nothing about that which necessitates the data be normal.

  2. The Shapiro-Wilk test assumes the data tested are iid (i.e., independent). That assumption would be violated for longitudinal data.

  3. I'm not sure what it means for normality to be a "strict requirement" of a model. However, linear mixed effects models typically assume normality in two senses:

    • First, they assume the residuals are normally distributed (really the errors, but that's more nuanced than you probably need to worry about). This isn't really different from non-mixed linear models. As with simpler models, if the deviations from normality are smaller, and/or you have more data, the violation of this assumption is less of a big deal.
    • Second, they tend to assume the random effects are normally distributed (although I believe it is possible to relax this and use the $t$ distribution for a more robust option). Again, the idea isn't that your sample is normally distributed, but that the population from which the random effects were drawn was normal. And again, violations of this assumption are less bad if you have more units and/or the deviations were minor.
  • $\begingroup$ I guess my other question is how do you test for normality in a longitudinal dataset? $\endgroup$
    – John_dydx
    Commented Feb 21, 2015 at 12:00
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    $\begingroup$ @John, you're welcome. "Normality" in what sense, the normality of the random effects distribution or of the residuals? You should be able to get a vector of either from your model, and then you could do a qq-plot or whatever you like. $\endgroup$ Commented Feb 21, 2015 at 14:23
  • $\begingroup$ For anyone interested, see jstatsoft.org/article/view/v056i05 for the R package ('HLMDiag') and a guide on testing the residuals from multilevel data for normality and the like. It gives you the vectors @gung noted above. $\endgroup$ Commented Feb 16, 2018 at 13:16

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