You can use a categorical moderator variable in meta-regression only if the variable is dichotomous. In your situation, it would make sense to run the meta-regression with W only, with both W and M (if M is dichotomous), and with W, M, and W*M (again if M is dichotomous). Even though you can run a meta-regression using only one dichotomous categorical moderator variable, one traditionally uses a subgroup analysis for comparing the levels of the variable and with subgroup analysis you are not limited to a dichotomous variable.

Dear Joane,

Assuming you are working with R or something, you can fit meta-regression models with continuous (W) and categorical (M) moderators in the same model (note: M doesn't have to be necessarily dichotomous!). The interpretation of the model estimates (of the fixed effect) is the same in linear models. The choice to analyze your moderators separately in two models or together (with or without their interaction) largely depend on your aim and hypotheses. You can scale the continuous moderator (W) if you want, but this is normally done when you have more than one continuous moderators in multiple regression to better interpretate the estimates of the model.

A categorical moderator variable used in meta-regression must be dichotomous. If you use a categorical variable with three or more levels in a meta-regression, the variable is no longer categorical. It has been arbitrarily transformed into an interval variable. The numbers arbitrarily assigned to represent the three or more levels (e.g., 0, 2, 1) in the meta-regression make an assumption of order (e.g., 1 > 2 > 0) and equal distance between adjacent levels (e.g., 1-2 = 2-0), which are not correct. This holds for any kind of regression, not just meta-regression.

@ Gabriele Midolo, Thank you for your reply. In my case, my categorical variable is indeed a dichotomous one. But my main concern is that as X is entered in the analysis as its interaction with Y, I was wondering if it makes sense to only enter M and W as moderator with their interaction, as well as using the centered mean and the product centered mean*dichotomous variables in the model. Because As far as I understood for regression, usually the dependent variable is a continuous variable and not the correlation between two other variables.

Gordon L Warren Thank you for your explanations. Yes, I was also thinking to just use subgroups to make it easier but was not sure if it was the right way to do it. And as I mentioned in my previous post, my main concern is also the fact that I am using a correlation as my dependent variables (the relationship between X and Y) so I was wondering if it is possible to use a continuous variable with a centered mean. And Yes, my categorical variable is a dichotomous one.

Hi Joane,

Thanks for replying. Unfortunately I'm not sure what you mean with "X is entered in the analysis as its interaction with Y". From your initial question I thought you had the correlation coefficient of X and Y ('r') as effect size (response variable) in your meta-regression. Can you confirm this is the effect size you are working with? In that case, I still think it is fine to fit a model as you described before (with 'W+M+W:M' as moderators).

This is not the main issue here, but note that there is no problem to use categorical variables with more than two levels as explanatory variables, just like any linear model.

Gabriele Midolo Hi Gabriele and thank you for your reply. Yes, as you mentioned I am using the correlation coefficient of X and Y and somehow I thought that it was not the right way to do it. I will then proceed with my analysis. Thank you so much.