# Violating assumptions of linear mixed model

I am currently analyzing a dataset using a linear mixed model.

In the study - using a within-subjects design - participants had to rate the intensity of a stimulus (this is my dependent variable, DV) several times on a scale from 0-10. They were presented with several high intensity stimuli and several low intensity stimuli (this is my first predictor 'magnitude' with the levels "high"/"low") in one of three conditions (this is my second predictor 'condition' with the levels "A"/"B"/"C").

I am interested in how these ratings change depending on the condition and the magnitude.

Since the nature of the low intensity stimuli is that they have a low magnitude the ratings of my participants regarding these low intensity stimuli was most of the time around 0 and 1. The high intensity stimuli were rated higher and show a somewhat "better" distribution. This is what the distribution of my dependent variable looks like: To answer my question I specified a linear mixed model with the following formula:

mymodel <- lmer(DV ~ condition*magnitude + (1|participant), data = mydata)

Running the model and checking the assumptions gives me the impression that I violate quite a few of them. Using plot_model(mymodel, type='diag') from the sjPlot package I would say that my residuals are not normally distributed, that I have quite some outliers and that homoscedasticity is also somewhat not met.

The model output makes a lot of sense and fits very well with my research question. Additionally, running models based on mean statistics (e.g. RMANOVA or Friedman tests, dependent t-Tests or Wilcoxon Signed Rank Test) essentially lead to the same interpretation and conclusion.

I am still curious to analyze the data using LMM and was wondering what the best approach here would be. I stumbled across several suggestions but am not experienced enough to decide which approach would be the "best" one. Here are possible solutions:

1: Transformation of my dependent data (e.g. by log transform). It does not lead to a normal distribution of my DV so I guess it's not very useful.

2: Exclude outliers from the analysis. I did that, but still checking my model assumptions leads to very similar plots, so I guess also not very useful.

3: Specify a model that accounts for the weird distribution in my data e.g. a zero-inflated model. Would that make sense?

4: Run robust linear mixed models e.g. using the robustlmm package.

I would be very grateful about your tips and suggestions!

Thanks a lot in advance.

• In addition to the serious problems you identified, and depending on the timing of within-subject repeats, you may also be mismodeling the correlation structure as detailed here. Think about using a transformation-free semiparametric ordinal model for continuous Y as covered in chapters 15 and 22 of RMS. Sep 23 at 12:17