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.