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I'm new to mixed effect models, but I think I should use a crossed random effect model: V ~ A + (1|B) + (1|C) + (1|D) + (1|P). Could you please tell me if I'm right?

I ran an experiment with 10 participants. Each participant had to complete several trials. My analyses include:

  • 1 continuous dependent variable V.
  • 5 categorical independent variables : A (2 categories), B (8 categories), C (2 categories), D (2 categories), P (the participant, 10 categories). The combination of these 5 variables allow to uniquely describe each trial (e.g., trial X had: A category 1, B category 6, C category 1, D category 2, P participant 10).

To note, each participant had the same number of trials with each category of the variables B, C and D, BUT the number of trials with each of the two categories of the variable A differed between participants.

I'm interested in answering the question: does A affect V? But I want to control for the potential effects B, C, D and P might have on V.

Any help would be appreciated!

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  • $\begingroup$ How many total trials were there? $\endgroup$
    – David B
    Commented Mar 31, 2023 at 16:47
  • $\begingroup$ 16 trials per participant, 160 in total $\endgroup$
    – statuser
    Commented Mar 31, 2023 at 16:53

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You're describing a saturated random effects model. You'll need to remove at least one of the random effects. I agree that you should adjust for Participant. With so few trials per participant, you're probably better off controlling for your independent variables as fixed-effects.

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  • $\begingroup$ Thanks a lot for your answer! Am I understanding correctly that you recommend using V ~ A + B + C + D + (1|P), or do I still need to remove one independent variable? $\endgroup$
    – statuser
    Commented Apr 1, 2023 at 23:20
  • $\begingroup$ That should be fine $\endgroup$
    – David B
    Commented Apr 1, 2023 at 23:40

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