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I'm trying to analyse a survey study in which I'm interested in the way that individual differences between my participants influence how they respond to my stimuli. The stimuli are pieces of writing randomly selected from a large pool of such, and I'm not currently interested in any fixed effects of these stimuli.

My participants each view 5 pieces of writing and make a binomial choice about each on a single-item DV. I have personality variables from each of the participants that I'm interested in as a predictor of their response. When setting up a mixed-effects model in lmer (with a long dataset) I know that I should include a term for the random effects of the stimuli. My question is whether I should also include a term for the random effects of participant, along with the fixed effects of the personality variable. Because differences between participants on my personality measure are my variable of interest, does it make sense to control for random participant effects?

Also, if I do control for the random effects of participant, what am I conceptually doing here? Partitioning out all the participant-level variance that can't be explained by my personality variable? Controlling for the random effects of participant seems to consistently reduce the predictive power of any personality variable I include in the model, which is why I ask.

Some illustrative lmer syntax for the two options: Without participant random effects:

glmer(Choice ~ Personality + (1| StimID), data=choice.long, family='binomial')

With participant random effects:

glmer(Choice ~ Personality + (1| StimID) + (1| PartID), data=choice.long, family='binomial')

Am I specifying the latter model right?

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