Moderator with control variable

[Thomas Polak]

How should I interpret the X, the moderator and control variable?

I know the effect of X is interpreted as an increase of 91.28 when the moderator is zero and vica versa with the moderator. But does the control variable change anything?

[Clyde Schechter]

But does the control variable change anything?

Not really. It just means that the effects you are estimating are regression adjusted for confounding by c1. But in all other respects, the interpretation is the same.

[Thomas Polak]

So may I write "A one-unit increase in the x variable corresponds to a 91.287 increase in the y variable, on average and ceteris paribus (and rounded to three digits), when the moderator variable is zero."
Or "A one-unit increase in the x variable corresponds to a 91.287 increase in the y variable, on average and ceteris paribus (and rounded to three digits), when the c1 and moderator variables are zero."

Or there's no need to even mention them?
e.g. "A one-unit increase in the x variable corresponds to a 91.287 increase in the y variable, on average and ceteris paribus (and rounded to three digits)."

[Clyde Schechter]

Assuming that this is a linear regression there is no need to mention c1 because the marginal effect of x, whether at means or average marginal effect, does not vary with c1. So I would go with "A one-unit increase in the x variable corresponds to a 91.287 increase in the y variable, on average and ceteris paribus (and rounded to three digits), when the moderator variable is zero."

If it is a non-linear regression model, then it's a different story.

All of that said, I don't think I would take this out to 3 decimal places. Your standard error is large enough that even the first decimal place is uncertain.

[Thomas Polak]

I agree. Thank you.

I guess the same logic goes when writing out the moderator:
"A one-unit increase in the moderator variable corresponds to a 0.175 decrease in the y variable, on average and ceteris paribus (and rounded to three digits), when the x variable is zero." -- so only the X is mentioned, and c1 is not.

But with regards to c1 should one omit the moderator and X, or add both?
"A one-unit increase in the c1 variable corresponds to a 0.007 increase in the y variable, on average and ceteris paribus (and rounded to three digits)."
"A one-unit increase in the c1 variable corresponds to a 0.007 increase in the y variable, on average and ceteris paribus (and rounded to three digits), when the x and moderator variables are zero."

[Clyde Schechter]

The mention of X when referring to a marginal effect of the moderator, or the mention of the moderator, when referring to a marginal effect of X is crucial, because these effects of either one depend on the other.

The mention of c1 is not necessary in either case because neither the marginal effect of X nor of the moderator depend on c1.

[Thomas Polak]

Thank you.