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I want to predict a categorical outcome variable (A or B) by 3 independent variables. Two of these are within (FactorWithin = 2 levels; FactorWithin2 = 5 levels) and one of them between (FactorBetween = 3 levels). I tested 15 subjects for each level of the between factor; N = 45. Each subjected completed 6 trials in each condition (i.e., 60 trials per subject; 2700 data points from 45 subjects).

The model that I have identified as most suitable is the following (using the glmer function from lme4):

glmer(outcome ~ FactorWithin1 * FactorWithin2 * FactorBetween + (1 | subject) , family=binomial, data = mydata)

First, is this the right approach?

I then get the warning:

Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.00146887 (tol = 0.001, component 1)

Is the right approach to then simplify the model (e.g., remove an interaction term)? I am hesitant to do that, because I am looking for the interaction effects. Is it possible that my model is underpowered?

Thanks!

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