I am trying to fit a mixed model in lme4 using the lmer.
the model form is:
model<- lmer(entropy ~ X1 * X2 + (1| video) + (1| subject), REML = FALSE
entropy is a continuous variable but normalised now between 0 and 1. X1 is a centred and scaled continuous predictor, and X2 is a categorical predictor with 4 levels. I should note that entropy was computed from a variable that had a too many zeros, and so, during the normalisation of the variable I had to add a very small number number to avoid undefined logarithms. As a result, the distribution of entropy is somewhat bimodal:
I am aware that the distribution of the outcome does not matter for the assumptions of linear models (whereas the residuals distribution do). However, the residual plot for this model shows a decreasing trend which I am worried about.
I am not quite sure what to make of this pattern, or how to improve this model. I initially fitted this using lmer, tried log-transforming and it didn't help. when I extract and compute the actual correlation between the fitted and residuals it is actually close to zero, which is puzzling considering this trend.
Histograms of the residuals look pretty normal, but I am aware histograms are not appropriate to check for the random distribution of residuals assumption of linear models.
I tried including other predictors that are of interest as well as running a few glmer (e.g. binonimal) models but I can't seem to resolve this.
Any suggestions on how to remedy this? How worried should I be about the first residual plot above?
Thanks, any suggestions are very much appreciated!