Linear Mixed Models

#1
For a course, you need to understand superficially an applied statistical approach in a research paper. I chose the following research paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6005466/.

The researchers used linear mixed models to see if there were differences between subjects in the study. From what I've been able to glean from quick searches, linear mixed models take into effect variation explained by independent variables, in this case the melatonin versus placebo; and variation not explained by independent variables, in this case differences between study participants. Even though we are not specifically measuring the differences between individuals, the model acknowledges that differences exist. This type of model allows us to have missing data cells and unbalanced designs.

Is this thinking correct, or are there important aspects of the model that I am missing? Thank you!
@hlsmith
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
There is a quote out there, "once you know multilevel model, all models look like they could be multilevel models." Yes, their benefit is that they control for this additional component of variability in data (within and between group variability). If there were groupings in the dataset (e.g. clusters [patient from same hospitals] or repeated measures within a subjects) and you didn't control for this - you could risk having a type I error. Which is, rejecting the null when it is true. This is caused by not controlling for the variability. When you do control for it, your confidence intervals become wider, since their is more modelable error to account for. Meaning, if your confidence intervals are narrower you could erroneously conclude there is a difference - since they exclude the null value. Though when controlling for random-effect based variability you would not exclude the null in some scenarios and have more generalizable results that addressed the group-level variability.