my apologies ahead of time if it's not as clear as I would like it to be. I'm using a linear mixed effect (nlme package) to determine the association between a modularity score (on a range of -1 to 1) and balance performance. The population is a unique sample, with only 14 participants that took almost a decade to collect. The "total" sample in the world only numbers likely hundreds, I only mention this because of the random effects (if it helps).
When I initially run the model as:
mod4 <- lme(Balance ~ modularity, random=~1|Subj,data=df,na.action=na.omit)
I get a non-significant p-value of 0.9216. However, we include age and sex (centered) as covariates in the model, and this has a massive effect on the results. Now, modularity has a p of 0.029, age 0.0194, and sex 0.0024. Great, this suggests there is a relationship.
My adviser, who is not a statistician wants me to plot the "adjusted values", which they say are the same as the residuals. Or, they want me to plot the modularity, with the effect of age and sex removed and visualize its relationship with balance. They also misinterpreted the correlation output as that between the independent and dependent variable (-0.85), when in reality I'm confident its the correlation between the independent variable and the intercept. Because of this they are looking for a strong negative relationship.
I initially plotted the marginal effects (wit SJPlot) and showed a positive relationship, or that as modularity increases so does balance. This did not coincide with their interpretation of the correlation, and told me to get these "adjusted values". However, if I plot the random and fixed effects (separately) with balance I find an entirely flat line, suggesting no relationship.
The differences between fixed and random effects I tentatively understand, or at least have found a definition that makes sense to me (it seems like there is an active conversation in the fields about it), but how exactly they play into marginal effects is less clear. I found this previous post: What is a difference between random effects-, fixed effects- and marginal model?, which roughly helped but my interpretation was of marginal models being a slightly different thing than marginal effects.
The primary point of my question being then, which of these would be the most similar to what someone would describe as the "adjusted values", or the effect of modularity with age and sex covaried for? And/Or, which of these do you think would be what is actually desired? As a person, I obviously want to go with the marginal effects, displaying the relationship that matches with how I interpret the statistics, but I'm not certain that's correct.
Thank you for any help!
