I have a response variable that is bimodal (basically, 2 normal distributions that are sticked together) and want to model it using a linear mixed effect model.
Here is a quick example (in R):
library(mixtools) n1 =500 n2 =500 x = rnorm(n1,mean = 10) y = rnorm(n2,mean = 15) hist(c(x,y),breaks =25)
I can run an Expectation-Maximization algorithm for gaussian mixture to get the two distributions (this is a very simple example so the 2 distributions cluster very well)
ores = mixtools::normalmixEM(c(x,y), sigma = NULL, mean.constr = NULL, sd.constr = NULL, epsilon = 1e-15, maxit = 1000, maxrestarts=50, # verb = TRUE, fast=FALSE, ECM = FALSE, arbmean = TRUE, arbvar = TRUE) ores plot(ores,whichplots = 2)
My question is:
- Is it possible to model this bimodal variable as a response variable in a linear mixed effect model (or a GLMM if there exists a link function for that)?
- Should I need to separate the bimodal distribution in 2 distinct unimodal Gaussian distributions and construct 2 identical models but using each distribution in the separate models?
- What would be the effect of modelling a bimodal distribution with a linear mixed effect model (with a unimodal residual error)?
Finally, I heard that quantile normalization would be a way to compare the 2 distributions. How can quantile normalization be used to compare the 2 distributions in a linear mixed effect model?