Dear Community,
I want to center (subtract the mean) my data in order to lower my intercept (as close as possible to zero). However, as I have categorical data as well, which I don't know how I can possibly center, I can't seem to lower my intercept.
And the thing is that my dummy variable drive up the intercept... So I don't know to fix the issue.
When I enter only continuous variables that are centered, the intercept is close to zero.
I thank you in advance?
Not sure why you want the intercept being zero, but one way you could easily achieve this is by first finding the (non-zero) intercept and the subtract this value from the response variable.
The answer of Jochem is the most simplest and perhaps the most appropriate. But, I was curious what would happen if you would weigh the model. First apply a model, weigh all residuals < 0 and < mean of the response by 1 and weigh all residuals >= 0 and >= mean of the response by 1 all others are set to 0. Hence, you regress only 50% of the data. Then you shift both the intercept and estimate of the model. The first approach basically approximates 0, whereas the weighted approach reaches 2.25. Yet, If the latter is my option, the question is why?
Minor edit: the later seems to work poorly with increasing complexity and categories.
Yuko -
It sounded to me as if you had been trying to do what Jochen said. Centering that way is sometimes used to reduce some collinearity situations.
Could you perhaps have a random intercept model with two intercepts? Perhaps then the difference in intercepts is the point. I'm not really familiar with this. Centering can help with collinearity. Do you really have a problem with that? Would centering actually help?
Sometimes intercepts are used when they should not be. If y should be zero when all predictors are zero, then there should be no intercept term, i.e. the intercept is zero.
I saw an otherwise nice paper which used a random intercept for small area estimation as just an adjustment between each small area which otherwise used a ratio estimator. But because the physical relationship modeled was just a ratio, no nonzero intercept made any sense.
Are you sure of your model from a subject matter perspective?
You can compare performances of models, which can also be used to see what happens with only one change at a time, by comparing "graphical residual analyses." (A graphical residual analysis can also be used to consider heteroscedasticity.) But especially if you look at many models, one may only appear better for your particular sample. "Cross-validation" can be used to try to avoid too tightly fitting to one particular sample which may not work well in general for the population or subpopulation you wish to model.
Perhaps the near-centering you have done already is all you can do. But this is not really something I can say for certain.
Perhaps something in my babbling above might be of some use to you.
Best wishes - Jim
Centering leads to zero intercepts. But, I can not understand what is your reason.
Generally people don't centre categorical predictors, but it is very common to use effect coding, particularly in interaction models) and this can help interpretation.
E.g., replace 0,1 dummy coding with -1,1 or -0.5, 0.5
This can be extended to multiple groups (e.g., see https://talklab.psy.gla.ac.uk/tvw/catpred /).
If the design is perfectly balanced (equal n per cell/group) then -0.5,0.5 coding is equivalent to centering, but will not be if there is imbalance.
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