Can I infer moderation of a relationship without a control group with multiple linear regression?

Question

I'm writing a paper in which I want to research to research the extent to which hedonic capacity affects affective and physical inflammatory sickness response to lipopolysaccharide (LPS). The following is hypothesized: individuals with higher hedonic capacity experience less reduction in positive affect during inflammatory induced sickness response as well as smaller increases of the physical inflammatory sickness response . This will be assessed by measuring baseline hedonic capacity of individuals, as well as their physical and affective response to LPS over a set amount of time in one 8-hour session.

The data already shows that positive affect is reduced during sickness and that the physical response increases.

Now I was told to calculate the difference scores ( 2hours - o hours relative to lps administration) for each dependent variable so that you end up with the following variables:

• IV TEPS scores (measured before experiment)
• DV 1 difference score of Positive Affect
• DV 2 difference score of physical sickness symptoms (higher scores on the VAS mean stronger physical sickness response)
• DV 3 difference score of cytokine concentrates (higher cytokine concentrates means stronger the physical sickness response).

And then do 3 multiple linear regression analyses, with the scores on the TEPS as predictor and then each DV in a separate analysis. Can I use that method to make conclusions about the intensity of that relationship? Does a coefficient like that then tell me if hedonic capacity moderates the negative relationship with positive affect and physical sickness response? and what kind of coefficients would I expect if they were in line with my hypothesis? Or should I look for a different statistical method?

Answer 1

There are a variety of models you can use, including mixed effect models, fixed effects models, and a simple regression on the difference scores that will give you approximately the same results. As I understand it, you are proposing to fit the following regression model: $$ \text{DV}_i = \beta_0 + \beta_1 \text{TEPS}_i + \varepsilon_i $$

The coefficient $\beta_1$ corresponds to the association between TEPS score and your DV, which, for example, would be the difference in cytokine concentrates between post and pre. A positive value of $\beta_2$ means that higher values of TEPS are associated with more positive changes (i.e., larger changes of all changes were positive, less negative changes if some were negative). So a negative value of $\beta_1$ would indicate that those with a higher value of TEPS (I assume this is hedonic threshold because you didn't explain that your question) would have smaller increases (or larger decreases) in the physical inflammatory sickness response than those with a lower value of TEPS. You could run this same model for your three DVs. In the regression of change in positive affect on TEPS score, a positive value of $\beta_1$ would support your hypothesis that those with higher values of TEPS scores have smaller decreases in positive affect from pre to post.

This is a single regression, not a multiple regression. I wouldn't exactly call it "moderation"; you are interested in the association between a baseline variable and an outcome, which happens to be a change score. This strategy tests each of your hypotheses separately.