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I have tried looking here and elsewhere for information about sample sizes for nonlinear regression, but I'm finding it difficult to get concrete answers on this topic. Specifically, what is the established number of subjects or observations that are generally required? I will be potentially modeling a crossed random effects GAMM and I would imagine this would require a fairly large sample given the complexity of the model. For crossed random effects in GLMM, Brysbaert & Stevens give some recommendations, one being 1600 observations per condition.

Some sources that give too many numbers and vague answers to know for sure:

Shawn Hemelstrand
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    You might look at this answer for hints about how to proceed with GAMM sample size estimation. Carefully define the hypothesis that you want to test: just what do you want to learn from the GAM smooths and the random-effect structure? Then explore hypothesis tests on multiple samples of different sizes from simulated data sets that you generate based on your understanding of the subject matter. That gives you the best chance of avoiding an underpowered study. Tim is correct that a generic rule of thumb is unlikely to be helpful. – EdM Oct 21 '22 at 14:52
  • Nice. Thanks for the helpful comment. – Shawn Hemelstrand Oct 21 '22 at 22:12

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You probably won't find a single answer because non-linear regression is a catch-all phrase that can mean arbitrarily complicated models. In such a case, it's hard to give any recommendations. Also, keep in mind that most such recommendations are just rules of thumb that do not give any guarantees of correctness. There is even no single (or simple) answer for linear regression or logistic regression not to say about more complicated models.

Tim
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