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Hi I have two important questions to ask. (1) My research is a psychological research that focuses on variable A predicting variables B and C. I aim to do two separate linear regression analyses to see if variable A can predict variable B and C. In addition, I also want to see in a separate analysis if variable B which is predicted by A can be also be a moderator between the relationship of A and C. So my first question is, B was an outcome variable in regression analyses, can it also be a moderator variable?

(2) If i have not administered research instrument to measure a particular variable, but have only measured it by asking a descriptive question in demographic sheet, can it still be considered an important variable and can i use in my regression or moderation analysis?

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Regarding your first question, yes, it can.

Let's say that the real causal model of these events is:

$A \rightarrow B \rightarrow C$

which means that $A$ causes $B$ and $B$ causes $C$. As you can see, I did not draw any edge from $A$ to $C$, which means that $A$ and $C$ are independent given $B$ (all the effect from $A$ to $C$ goes through $B$). But we don't know that, right? And in reality, maybe this is not the case for the data that you have. You can do the three things you mentioned, as long as you are convinced it makes sense. If you think it's $A \rightarrow C \rightarrow B$, the contribution you may find for $B$ is actually spurious, because $B$ is not mediating anything in here.

The second question is less clear to me. If I understood it well, yes, you can. This is what is done all the time in many fields. The difference is that you have less control about what it really means, as compared to research instruments.

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