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How can I evaluate if the variance components of a nonlinear mixed model make sense (assuming or not assuming treatments factor)? For instance, if I am assuming an unstructured variance-covariance specification for the random effects, how can I be sure that this is correct for my study case. Note: I am contrasting the nonlinear response (parameters) of different treatments (fixed effects) against a control treatment.

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  • $\begingroup$ What is the relation between assuming treatment effect and variance components? $\endgroup$ – user158565 Jul 22 '19 at 18:18
  • $\begingroup$ I am not really sure. I would say that none since the treatment effects is represented by the fixed effects, while the random effects are modeling the variability of my subjects (or grouping structure). $\endgroup$ – User1234 Jul 22 '19 at 18:41
  • $\begingroup$ Then keep the fixed effect no change, fit two models with and without random effect. Compare their (log) likelihood values. $\endgroup$ – user158565 Jul 22 '19 at 18:43
  • $\begingroup$ Typically people use variance components to refer to a model with no predictors and a random intercept. If that is what you are doing, then user158565's approach is spot on. But you mention an unstructured variance-covariance matrix, which implies that you also have random slopes in the model. Is that what you have? And if so, do you also have the fixed effect predictor(s) for the random slope(s) in your model? $\endgroup$ – Erik Ruzek Jul 23 '19 at 21:49
  • $\begingroup$ @user158565 Thanks! I have implemented the approach and it does make sense. In my study case, any variance-covariance structure (for instance unstructured) improved the fit (the AIC and BIC were lower, while the (log) likelihood comparison was significant). $\endgroup$ – User1234 Jul 24 '19 at 1:26

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