I'm new to the mixed effects approach and I'm struggling to understand how to apply it to my relatively complicated experimental design given that all tutorials and articles I read are not directly comparable.
We are studying how perceptual accuracy differs depending on a number of factors. Specifically, people are asked to explore some objects with touch and estimate their sizes. One group of participants explores the objects actively (moving their hand) and we record their trajectories (doesn't matter how for this question). Then, we have another group of participants who explore the objects passively by having the active participant's trajectories applied to their hand. Each "passive" participants receives the trajectories of a specific matched "active" participant in exactly the same order.
Each person is asked to explore 6 different objects in 2 possible orientations and receives 2 possible questions before the exploration. Each combination of factors is repeated 3 times resulting in 72 trials per person. We don't have any theoretical predictions regarding the different objects and orientations but we want to know how perceptual accuracy differs depending on the group (active-passive) and question manipulation and whether there is a possible interaction effect.
So, the variables we have are as follows:
- continuous response variable: perceptual accuracy (
- between-subject variable: active vs passive condition (
- within-subject variable: 2 types of questions (
- within-subject variable: 2 object orientations (
- within-subject variable: 6 different objects (
- possible learning effect: trial number (
I was trying to translate this into the LMM vocabulary and got as far as follows:
- fixed effects: 2 conditions and 2 question types
- random effects: subject, object orientation, object to account for random variability
Does that sound reasonable so far?
Typing this into R would be:
model1 <- lmer(accuracy ~ condition * question + (1+question|subjectID) +
(1|object) + (1|orientation), data = df)
What I struggle with specifically is
- How do I enter the possible effect of trial number?
- How can I take into account the fact that the subjects are paired through the trajectories that they perform to explore the object? That is, while the accuracy might differ depending on each person, it might also be affected by the specific ways of exploring the object introducing a possible source of variability between paired subjects. Is this some kind of nesting?
- Am I missing something about possible crossed effects? That is, the fact that each trial involves a specific combination of within-subject variables (question, object and orientation)?