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Thread: Why do you subtract the mean of a predictor variable from that variable..

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    Why do you subtract the mean of a predictor variable from that variable..




    An author using temperature as a predictor subtracted its mean value from each temperature data point to deal with "scaling issues."

    I don't understand what that is, or why you do this. Is this to make the intercept make more substantive sense?
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    Re: Why do you subtract the mean of a predictor variable from that variable..

    i have seen and done this to get a model to converge. i just assumed it get large numbers out of equations, say during factorials or something like that but in realty i was being ignorant.
    Stop cowardice, ban guns!

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    Re: Why do you subtract the mean of a predictor variable from that variable..

    I thought there might be some theoretical reason like when you center the data to make the intercept make substantive sense.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Why do you subtract the mean of a predictor variable from that variable..

    If the predictor that is being mean-centered is involved in an interaction with another predictor, then mean-centering can help a lot with interpreting the regression coefficient for that other predictor. If the predictor that is being mean-centered is NOT involved in interactions with any other variables, then the only effect this will have, as you note, will be to change the value of the estimated intercept -- which is probably not of much interest in many cases, but there certainly may be cases where the intercept is of interest.
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    Re: Why do you subtract the mean of a predictor variable from that variable..

    Hi,
    to add to what Jake said, often the intercept is not interesting exactly because it is the meyn Y value at X=0 where X=0 might not make sense or be of any larticular interest. If the variable is centered then the intercept is the mean Y at the mean X - which, at least makes practical sense and has more chance of being a practically interesting value as we sampled around it.

    Also, I think but am not sure, the requirement to build hierachical models is moot if the IVs are centered. Any opinion on that?

    regards

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    Re: Why do you subtract the mean of a predictor variable from that variable..


    Quote Originally Posted by noetsi View Post
    I thought there might be some theoretical reason like when you center the data to make the intercept make substantive sense.
    Simply put, it's a way to deal with the so-called problem of multicollinearity, which is what Jake was alluding to when you have an interaction (or moderating variable). Outside of that, subtracting the mean of X from each value of X_i just makes the intercept term equal to the means of both the predicted values of Y (Y-hats) and the actual observations of Y. In short, without subtracting the mean of X from the values of the X_i just changes the intercept term so that it still ensures that the mean of the predicted scores of Y (Y-hats) is still equal to the mean of the actual observations of Y. That really all there is to say.

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