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I had an email exchange with Jeff Malins, who asked several questions about growth curve analysis. I often get questions of this sort and Jeff agreed to let me post excerpts from our (email) conversation. The following has been lightly edited for clarity and to be more concise.

I’ve fit some curves for accuracy data using both linear and logistic approaches and in both versions, one of the conditions acts strangely. As is especially evident in the linear plots, the green line is not a line! Is this an issue with the fitted() function you’ve come across before? Or is this is a signal something is amiss with the model?
In the logistic model, some curvature is reasonable because the model is linear on the logit scale, but that is curved when projected back to the proportions scale. Since all of the model fits look curved for the logistic model, that seems like a reasonable explanation.
I am not sure what is going wrong in your linear model, but one possibility is that it is some odd consequence of unequal numbers of observations (if that is even relevant here).
Unequal number of trials turned out to be part of the problem, which Jeff fixed, then followed up with a few more questions:
(1) If I create a first-order orthogonal time term and then use this in the model (ot1 in your code), my understanding is this is centered in the distribution as opposed to starting at the origin. So for linear models fit using ot1, an intercept term to me seems to be indexing global amplitude differences in the model fits (translation in the y-direction) rather than a y-intercept. Is this correct?
(2) My understanding is that one only needs to generate orthogonal time terms if fitting second order models or higher. However, I performed a logistic GCA which was first order and it failed to converge when I used my raw time variable and only converged when I transformed it to an orthogonal polynomial with the same number of steps.
(3)  I am unclear as to when to include a “1” in the random effects structure for conditions nested within subjects. For example, what is the difference between (1+ot1 | Subject:Condition) and (ot1 | Subject:Condition)? I have the former in the linear GCA and the latter in the logistic GCA.