# Which random effects to include in a mixed effects model?

I am analyzing data from a perceptual decision making experiment (10 participants, 1800 trials each). Participants made perceptual decisions (3 possible responses) and then rated their confidence on a continuous scale between 0 and 1.

My question is what predicts decision confidence, and whether the contribution of different variables interacts with response.

I am trying to fit a mixed effects model to my data (using Matlab's fitlme), with columns being:

• s (subject index, categorical)
• response (categorical, 3 options)
• logRT (continuous)
• correct (accuracy, binary)
• evidence_sum (stimulus feature, continuous)
• evidence_diff (stimulus feature, continuous)
• confidence (continuous)

My effects of interest on confidence are the effects of logRT, correct, evidence_sum and evidence_diff on confidence, their interaction with response, and the main effect of response.

So I know the fixed effects part of my formula should be:

confidence ~ logRT + correct + response + evidence_sum + evidence_diff + logRT:response + correct:response + evidence_sum:response + evidence_diff:response

However, I am not sure about the random effects part. I assume I should have a random intercept term (1|s). Should I also include a random version (e.g., (response|sum)) for each of my fixed effects? If I don't, fixed effects become super-significant, but I guess that's just because I'm treating my data as if I have 18,000 trials with one participant, after mean-centering the confidence ratings of all participants? However, if I just include a random version for every effect of interest I worry that my effects of interest will be attributed the subject-specific regressors.

So my question is, given my research question of interest and given that I want to generalize my conclusions beyond my 10 participants, which random effects should I include in my model?

Thanks!

• This looks like a multivariate problem to me. Correct and confidence (and maybe logRT) are also dependent on response and other variables, and are measured with error. You'll see that the problem is simplified if you treat it this way. Jan 19, 2019 at 8:14