Hey there, fellow stats enthusiasts! I’m about to dive into a head-scratching conundrum that’s got me stumped. Imagine running a generalized linear mixed model (GLMM) with multiple emotional wellbeing metrics as outcomes and various health metrics as predictors. Sounds straightforward, right? Well, here’s the kicker: one predictor (age) is positively correlated with one emotional wellbeing measure, but negatively correlated with another. And get this – those two emotional wellbeing measures are highly correlated themselves!
I know, I know, it sounds like statistical voodoo. But bear with me, and let’s try to unravel this mystery together.
First, let’s break down the correlations. When we look at the relationship between age and each emotional wellbeing measure separately, we see a positive correlation with one and a negative correlation with the other. No surprises there. But when we examine the correlation between the two emotional wellbeing measures, we find a strong positive correlation. This is where things get weird.
How can two highly correlated outcomes have opposite relationships with the same predictor? It’s like trying to reconcile two conflicting stories.
To make sense of this, we need to dig deeper into the underlying relationships between these variables. One possible explanation is that the predictor (age) is influencing the two emotional wellbeing measures through different pathways. Perhaps age has a direct positive effect on one measure, while indirectly affecting the other through some intermediate variable.
Another possibility is that the correlation between the two emotional wellbeing measures is driven by some underlying factor that’s not accounted for in our model. This could be a confounding variable that’s causing the observed correlation, making it seem like the predictor has opposite effects on the two outcomes.
So, what’s the takeaway from this statistical puzzle? It’s a reminder that correlation doesn’t always imply causation, and that multiple correlations can sometimes lead to counterintuitive results. By carefully examining the relationships between our variables and considering alternative explanations, we can uncover the underlying mechanisms driving these correlations.
I’d love to hear your thoughts on this conundrum! Have you encountered similar situations in your own statistical adventures?