I tried to create an Index as the moderator has 4 measures but it's not consistent since one measure is based on a Likert scale, the other two a binary (yes/no) and the final is based on 5 multiple choice questions. How can I combined them? Even though they are related somewhat, it does not justify combining unlike scales, am I right? Or should I just have multiple moderators?
Multiple moderator is definitely an option for you to consider, but remember a parsimonious model is always better than a complicated model. And interpretation of multiple moderators can be quite complicated. I highly encourage you to review Melanie's presentation on interactions: https://slideplayer.com/slide/3792435/
Another idea would be using some sort of latent approach to summarize all your measures into one variable. For example, dependent mixture modeling can include both categorical and continuous variables to create a latent variable (search for depmix). Or, you can convert your categorical variable into continuous variable via item response theory (theta score), then use everything as continuous scale. You can be creative as long as you can justify your approach.
If I were you, I would combine all variables into one summary variable then use that as a moderator.
https://www.google.com/url?sa=t&source=web&rct=j&url=http://web.pdx.edu/~newsomj/cdaclass/ho_interactions.pdf&ved=2ahUKEwiY3seporvzAhXDCewKHR7jBs0QFnoECBUQAQ&usg=AOvVaw1UhgpQvRvHe5DBDIhHUQP_
Well if there are other ways to transform the variables into one measurement, please do that to prevent complicated interpretations. I suggest you convert them all into binary.
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