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I am currently reading this paper , according to which

Linear mixed-effects (LME) (Laird & H.Ware, 1982) and nonlinear mixed-effects (NLME) models (Pinheiro & Bates, 2000) are typically used to describe grouped data for which the random effects and the error term are assumed to follow a normal distribution. But normal Linear mixed-effects (N-LME) and normal nonlinear mixed-effects (N-NLME) models suffer from the same lack of robustness against departures from distributional assumptions as other statistical models based on the Gaussian distribution and may be too restrictive to provide an accurate representation of the structure that is present in the data.

I fitted a nonlinear mixed-effects model using nlmer() in lme4 to a repeated measures data, but both the distribution of the residuals of the fitted model and the distributions of each of the random effects seem to deviate from normality.

Question: Does the implementation of the function nlmer() assume normality of residuals and random effects and, if so, if these deviate from normality, how strongly would that effect the model?

Should I consider the model suggested in this paper?

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Indeed lme4:::nlmer() works under the assumption that both the error terms and the random effects are normally distributed.

In general, departure from normality is more serious for the error terms than for the random effects. Linear mixed models are known to be robust against misspecification of the random effects distribution; however, nonlinear mixed models may be more susceptible.

If you have serious indications that the normality assumption does not hold for your data, you could try the alternative approach you mentioned.

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