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.

• You mean "IV 3: interaction between IV 1 and IV 2", right? – deasmhumnha Apr 6 '18 at 5:33
• Fixed. Thank you for your answer below @DezmondGoff – Santi Allende Apr 6 '18 at 15:18

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.