Partial Correlation vs. Interaction Analysis type: linear mixed-effects model
DV: cortisol (4 time points per participant - morning, noon, 5pm, 9pm)
IV 1: time-since-waking (continuous, repeated measure, variably 
spaced/unstructured time variable)
IV 2: prior-day bedtime (9pm) cortisol levels
IV 3: interaction between IV 1 and IV 2
Results: significant interaction term
Question: is the relationship of prior-day bedtime PM cortisol with next day diurnal slope stronger than or independent of the relationship between PM cortisol the day before and PM cortisol the next day? In other words, is it just driven by the consistency of high PM cortisol, or is it more than that?
A) Is there a way to address the above question and is it relevant? Do I need to adjust for that? 
B) I (1) extracted subjects’ predicted slope coefficients from the mixed model (ie., time-since-waking, on a model that only had time-since-waking as a predictor) and (2) ran a partial correlation looking at the relationship between prior-day bedtime cortisol levels and slope coefficients, controlling for the current day’s PM cortisol level (9pm sample, used in calculating the slope coefficients). The partial correlation was not significant and also in the opposite direction of the interaction. 
I am not sure what to make of this or how to address the above question. 
 A: A) I would interpret the lack of significant coefficients for both variables independently as a suggestion that the observed effect(s) is driven by some unknown synergist mechanism between the two variables rather than either alone. Is your significance result from an ANOVA or the individual t-tests returned by summary? If you haven't already, run a Type III ANOVA, which will give you a measure of the significance of each IV after accounting for all other IVs. This will likely give similar results. In other words, I'd say your results already suggest that next-day cortisol is not driven simply by the consistency of high PM cortisol the day before. 
B) I wouldn't trust the correlation between data and parameter estimates since they are functions of the data. Assuming that previous-day and current-day PM cortisol are highly correlated across individuals, it's not surprising that the partial correlation you calculated is negligible. It's also not particularly illuminating. The sign is just an artifact of the sample data.
