mixed effect models

• As I understand it, these are effects that occur at the group level. So you can imagine that in a given hospital, you want to plot the outcome of each patient. The outcomes are effected by the drugs they take. But each doctor results in a different y-intercept for the group of patients that they are treating.
• random effects:
  • the effects might change depending on how you did the experiment
  • for example, the doctor effect should not be a fixed effect, since it was up to chance which doctors would be included in the experiment
  • we assume that the doctors included in our study are drawn from a pool of doctors, which has its own distribution that can be estimated
  • in this way, we can think of random effects a little like nuisance variables
• basically, random effects are there to avoid the problem of treating samples like they are all drawn from the same pool
  • when in reality, they are drawn from many pools, where each pool is fairly homogeneous
• my favorite stack overflow answer

• random effect is something that we don't build into the model, but we still want to model it
• there are group effects that we want to model
• important where differences between individuals (groups) are important
  • so you can fit a random slope and/or a random intercept to make assumptions about where individuals start with respect to the target, and where they will end up based on treatment

• How do I get the p-values?
• lmertest gives you p-values https://github.com/runehaubo/lmerTestR via Satterthwaite's degrees of freedom method
• but this is not always advisable see https://stats.stackexchange.com/questions/22988/how-to-obtain-the-p-value-check-significance-of-an-effect-in-a-lme4-mixed-mode

and https://stat.ethz.ch/pipermail/r-sig-mixed-models/2008q2/000904.html

• what's the difference between adding a covariate and adding a random effect? See here: https://stats.stackexchange.com/questions/530035/mixed-effects-model-adding-covariate-vs-adding-random-effect seems to suggest that random effects are a smaller assumption
• see also here: https://stats.stackexchange.com/questions/4700/what-is-the-difference-between-fixed-effect-random-effect-in-mixed-effect-model/4702#4702

• what's the difference between a fixed and random effect?
• introduction to linear mixed models
• mixed effects models explained with r
• An Introduction to Linear Mixed Effects Models for the Social Sciences