This is a more conceptual question and I think it highlights my lack of knowledge of what can be assumed using mixed-effects modelling on a non-experimental repeated-measures data.
Let's pretend we have a repeated-measures data set where data is :
- clustered by
participant(i = 1, 2, ... 50)
- collected over several
days(t = 1, 2, ... 10)
- where outcome variable is
pain rating(0 to 100)
- where key predictor variable is
happiness rating(0 to 100 as well)
- and where I expect the relationship between
happiness ratingto be mediated by hours of
sleepthat day (0 to 10 hrs)
Let's imagine I have sufficient prior theoretical knowledge to reasonably expect increase in
happiness rating to decrease
pain rating but that effect to be mediated by hours of
sleep. I want to test that so I have participants complete my survey for 10 days straight to gather enough data per participant. I create a mixed-effects model and I find exactly what theory suggests.
m1 <- lmer(pain rating ~ happiness rating + (1 | sleep) + (1 | participant))
- Draw a causal inference such as (very simplified) "Happiness reduced pain"?
My intuitive answer is no. But I could say "Happiness is associated with pain".
- Go further and conclude causality about
sleep, e.g. "Hours of sleep affected pain"?
My intuitive answer again is no and instead I would say "The hours of sleep explained some of the variance in the pain".