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Take this mixed effects model in R:

$y_i = \beta_0 + \beta_1X_{ij} + u_{j} + e_{ij}$

where $u$ is a random effect (level 2 residual) with groups $j$. It is possible to allow the variance of $e_{ij}$ (level 1 residuals) to be a function of $X$. This could potentially result in a 'fanning out' or 'fanning in' of level 1 residuals within each group $j$.

Is it possible to implement this 'complex level 1 variance' mixed effects model in R? Does lme4 allow it?

(Stack Overflow doesnt appear to allow LaTeX formatting of mode formula so I've asked this question here)

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lme4 does not offer possibility to model variance components, however it is possible with nlme package, where you can define different variance functions. Check also this answer and the references: Modeling error structure in lmer in R?

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  • $\begingroup$ Why is this feature implemented in an older version of lme but not a newer version? $\endgroup$
    – luciano
    Commented Dec 26, 2014 at 15:54
  • $\begingroup$ nlme is not older version of lme4, I don't know why it was not implemented in lme4 - you could ask the authors. $\endgroup$
    – Tim
    Commented Dec 26, 2014 at 16:22

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