covariate mean-centering

[Elisa Cargnelutti]

Dear SwE experts,

I am wondering how to mean center covariates in my design. I have a group of healthy controls and a group of patients with brain tumor. For instance, I want to include tumor volume as a covariate. How could I mean center it, considering that for healthy controls it is obviously 0?

Further, I would like to know if – and in case how – center categorical variables. In the case of two categories, I can use -0.5 and +0.5, but what if the categories are three or more? Is it better to model different categories as subgroups?

Thank you in advance for any help.

Elisa

[Manfred Klöbl]

Dear Elisa,

you mean-center the tumor volume only within the group of patients. The covariate stays 0 for the controls.

For categorical variables, the meaning of the covariate changes with mean centering. If you consider gender as a categorical variable and you code "female" as 0 and "male" as 1, "female" would be your reference category. So, your results would assume a female population with any male influence regressed out. If you mean-center gender, your results would assume the gender distribution as it is found in your sample. If you code the genders as -0.5 and +0.5, the results would assume a person with average female and male traits (if there are any in your data). If you mean-center all factors/covariates, you need to include a constant term in your model. You can find more on this topic when searching for "effect coding" and "dummy coding".

Best,

    Manfred