Hello Alexandre,

If you're envisioning a regression model that incorporates one or more categorical IVs having more than two levels, then centering would have to be done separately for each of the dummy variates created to carry the information for a given categorical IV.

Is there some compelling reason for centering your categorical variables? Each dummy variate invokes a comparison of one category/condition to other(s).

Good luck with your work.

In addition to Prof Morse comments here are some good references I would suggest to you.

Jared Lander R for everyone and Frank Harrell's Regression modeling strategies and D C Montgomery.Design of experiments all are available from the z-library. Best wishes, David Booth

There is no unidimensional center when you have more than two groups. However, sum or deviation coding (in R obtained with contr.sum()) might about what you are looking for. See for instance

https://marissabarlaz.github.io/portfolio/contrastcoding/#sum-coding

https://rstudio-pubs-static.s3.amazonaws.com/84177_4604ecc1bae246c9926865db53b6cc29.html

If x is your original var and g is your grouping var

x - ave(x,g)

If you want to use something other than average, e.g.,

x - ave(x,g,FUN=median)

Do you need to centre them? Its helpful for some situations, but not always necessary. Its generally recommended for multilevel modeling and if you have interactions but in some cases you can just fit the model with default contrasts and obtain the tests and effects you need via other means (e.g., drop1, general linear hypothesis tests, plotting marginal effects).

Also, Dale Barr's page on deviation coding is very helpful in explaining how to handle multiple levels on a factor when you do need it.

https://talklab.psy.gla.ac.uk/tvw/catpred/