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# Needing help on Linear Mixed Models

Hi everyone,

I am a beginner in linear mixed models and would like some advice on what I would like to do with my data. I work in the field of cognitive neuroscience and my research focuses on understanding face processing in adults. We measure face processing using eye-tracking measures (here pupil dilation) and a paradigm using social (images and videos of real faces and avatars) and non-social (objects) stimuli.

I would explore if the physiological engagement, indexed by pupil diameter variations, is caused by the motion. To do that, we quantified the motion amount for each video by a coefficient. My data set consists of 7 variables (participant, movements, actors/actresses, categories, movement coefficient, and pupil dilation) with 1320 observations.

• categories are broken down into 3 components: object (non-social stimulus), avatars, and real faces (social stimulus)
• movements are broken down into 3 components: static, micro, and macro movement
• actors/actresses: there are 4 videos (2 actors+2actresses) per category per movement
• movement coefficient: one coefficient for each stimulus, as it depends on the actors and actresses. They are different people so the quantity of movement is not identical according to the movements (micro movement -> neutral expression; macro-movement -> neutral to happy and neutral to sad). When the movement category is static, the motion coefficient is 0 (only for avatars and real faces as it is static photography but for objects, they are videos with really small motion coefficients and smaller than micro and macro movement)

I thought a LMM would be an excellent analysis to answer my question, as I can consider the fixed effect and random effect but I am a bit lost about the model's writing... I tried random effect for a particular participant to allow the deviations of the intercept of that participant's pupil dilation from the population. In addition, I was thinking to add another random effect for a particular motion coefficient where the deviations in the ordinate of the pupil dilation of the motion coef in question from the total motion coefficient sample.

I have tried several LMMs but I don't know if the models I have tested are correct in writing about my research question: can motion predict pupil dilation? is the motion quantity influence pupil dilation?

```modela <- lmer(pupil_dilation ~ categories*movements*actors + (1 | participants) + (1 | motion_coef), data = data, REML = FALSE)
modelb <- lmer(pupil_dilation ~ categories+movements+actors + categories:movements:actors + (1 | participants) + (1 | motion_coef), data = data, REML = FALSE)
modelc <- lmer(pupil_dilation ~ categories+movements+actors + (1 | participants) + (1 | motion_coef), data = data, REML = FALSE)
modeld <- lmer(pupil_dilation ~ categories + movements + (1 | participants) + (1 | motion_coef), data = data, REML = FALSE)
modele <- lmer(pupil_dilation ~ categories + (1 | participants) + (1 | motion_coef), data = data, REML = FALSE)
```

For your information: categories, movements, actors, motion_coef, and participants were converted as factors.

So few questions come to my mind:

• Is LMM a good way to answer my question?
• Do I have to normalize my data before starting my LMM?
• Are the models above seem consistent according to my research question?

I hope I was clear about my description. Also, I am sorry if I didn't explain well about the LMM but as I am new I tried my best!

Thank you all in advance for your precious help!

Camille

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