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How to use nlmer on a dataset with multiple fixed and random effects

Thanks for responding - a few others have also suggested including
quadratic terms.  However, I'm not sure that quadratic is the best fit
for the data either....the residual plots are still not great.  My
uncertainty as to what would be the best method for my data led me to
want to pursue non-linear methods.  Perhaps I should have phrased my
question as: How do you know which model is the best? Ie: a glmer with
or without quadratic terms? A non-linear model?
Is the best method to look at the fitted values vs the residuals?

Thanks,
Lauren