In a series of posts I have been writing about the technical details of interactions. I have realized that it might be important to write a post emphasizing why we should care so much about these technical details.
First of all, imagine a statistical association.
It might be:
\[\text{intervention} \rightarrow \text{outcome} \tag{1}\]
Or it might be:
\[\text{parenting behavior} \rightarrow \text{child development} \tag{2}\]
We might think it is important to ask whether the relationships in Equation 1 or Equation 2 are consistent, or very different, across groups, across identities, or across various social contexts, such as countries or cultures.
Interactions are one of our major statistical tools for examining similarity or difference in statistical relationships across groups, identities, or contexts.
I tend to think a lot in my own work about whether statistical relationships are generalizable across contexts, but we could also think about whether there are risk factors or protective factors that might strengthen or weaken the relationships in Equation 1 or Equation 2. Interactions are a key tool to study this kind of effect modification.
In social research, so many of the outcomes we study are crucially important to people’s well being. If we get the technical details of estimating interactions wrong, it is possible that we may mis-state our substantive findings.
Thus, understanding the technical details of interactions is important.