I am attempting to build a model for the following dataset:
Level 1 Observations (Product-Level): 89000
Level 2 Observations ("BU_SBU" Department-Level): 135
Unfortunately I cannot share a sample of my data, since it is confidential.
The dependent variable in the model is a percentage (Delivery Reliability, 0-100%). Fixed effects include roughly 20 variables at level 1 and 5 variables at level 2. The only random effects are the intercepts at level 2. Having run the regression, I have a number of questions regarding the violation of model assumptions which I cannot answer myself:
Constant variance of residuals: The graphic shows that there appears to be an upper- and lower-bound of the residuals. My guess is that this is due to the limitation of the dependent variable. But do the upper- and lower-bounds shown in the graphic actually indicate a violation of model assumptions? I have also run a GLMER model with a
binomial(logit)-link but this did not resolve the issue. The diagnostic plots look almost identical in all three cases.
Distribution of residuals: Is there a way to compute confidence intervals for residual QQ-plots of LMER models? And is it possible to compute heteroskedasticity-robust standard errors via the lme4-package?
Normal distribution of level-2 intercepts: The level-2 intercepts do not appear to be Normally distributed. Is this an issue and if so, how can I resolve it?
I would greatly appreciate, if someone could help me at least with some of these questions. I am currently stuck and was not able to find any resources that provide answers. I am also grateful for recommendations to helpful literature.