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I'm using a model to simulate how tree growth rates vary with different traits, but I'm not sure how to correctly account for the non-independence in the data in my statistical tests.

I generated 100 'plants' that vary continuously in Trait A (the between-subjects variable). I then assumed each plant varied in a categorical variable Trait B. Trait B has 3 levels, so I turned it into two dummy variables, Cat 1 and Cat 2.

I want to test whether the effects of Cat 1 and Cat 2 on growth depend on the value for Trait A, but I'm not sure if my model is correctly expressing the data structure. I've found examples that I interpret as recommending either:

lmer(growth ~ traitAcat1 + traitAcat2 + (1|traitA)) or

lmer(growth ~ traitAcat1 + traitAcat2 + (1|traitA/cat1) + (1|traitA/cat2)

The second model doesn't converge, but the first model doesn't seem like enough information. Any help on how to correctly specify the random variable term would be much appreciated.

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