"Wow, this COVID-19 quarantine time has been really great for my productivity! I bet the longer this goes on, academics will see increases in their publication rates. I can't wait to hit the job market with all these new papers." - random dude on the internet

Questions: Is this guy seeing the whole picture clearly? Is quarantine time universally helpful for graduate students' academic productivity, or might this relation depend on other cicumstances?

• This is an example of an effect that, I argue, is likely to be moderated.
• I would hypothesize that the effect of quarantine time on academic productivity depends on or is moderated by socioeconomic status.

• The term "moderation" may be new to you, but the way to test for a moderating effect is not novel.
• To hypothesize a moderating effect is identical to hypothesizing the presence of an interaction effect in regression.
• If I want to test whether SES moderates the effect of quarantine time on academic productivity, I simply model:

Manuscripts = TimeQuarantine + SES + SES*TimeQuarantine

• A significant interaction is evidence for moderation
• However, If the moderating variable itself is predicted by an excluded variable (such as race, for example), then SES isn't the true moderator- perhaps it is just a proxy moderator, and the true moderator here is race.
• Further, a moderating variable should be one that either doesn't change much over time (e.g. race) or that has set values before the predictor variable values are determined. This is to be sure that the predictor variable isn't a cause of the moderating variable.

Moderation effects are often depicted in the literature using diagrams. Let's see what that might look like:

Moderation Path Model

• Effect sizes in moderation have been a point of discussion in the literature

• Cautionary Tales: Effect sizes for moderating effects would often be considered very small by conventional standards (e.g. effect sizes of less than .01). This is especially a concern when the moderator is a categorical variable. The implication is that many studies are underpowered for detecting a moderating effect, and may therefore fail to detect a moderation effect even if it exists.

• When determining sample size for any study it is best not to use Cohen's conventions of effect size to calculate power.
• Instead, consider what a meaningful effect size would be for your study and to calculate power based on that.

• Yes, it is possible, but the model requires many constraints and assumptions that may not be realistic.
• A recent article poses a Bayesian approach to testing moderating effects in SEM as a possible alternative (Asparouhov & Muthen, 2019).
• For this course we focus on moderation analysis in a regression framework.