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In a predictive model, I have standardized variables as predictors. Say I have to rescore the model on fresh data at some point in the future: do I use the means/stds as they were when I built the model to center and scale the new data, or do I use the means/stds as they are with the data I'm scoring.

My take is to use the means/stds of the data I'm scoring, since I want the standardized variables to reflect distributions as they are at the time of scoring.

Pros & cons of original means/stds vs. current means/stds?

Thanks.

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    $\begingroup$ What do you mean by rescore? $\endgroup$
    – RioRaider
    Sep 14 '12 at 0:18
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    $\begingroup$ In the context of this post, 'rescore' means computing the predicted dependent values using new readings of the predictor variables. $\endgroup$
    – user14075
    Sep 14 '12 at 1:23
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This is one of the major problems with standardizing variables prior to regression. The entire meaning of the output is sample-dependent. I much prefer working with unstandardized variables so that this problem (and similar ones) do not arise.

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If one were to fit a model $y= \beta_1 + \beta_2z$ where $z=\frac{x-\bar{x}}{sd(x)}$ and use that model to predict $y$ for some given values of $x$, then use the original $\bar{x}$ and $sd(x)$ to standardize the new $x$ values being used for prediction.

However, if one has many new values of $y$ and $x$ and wants to refit the model then standardize $x$ based on the new values of $\bar{x}$ and $sd(x)$.

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  • $\begingroup$ But if the model can't be rebuilt (or re-estimated or refit) because all I have are fresh values for the predictors, no reading on the dependent variable yet: do I understand your answer as taking the mean of 'fresh' predictors to compute $z$, and then $\hat{y}$ ? $\endgroup$
    – user14075
    Sep 14 '12 at 1:32
  • $\begingroup$ @user14075 No, if the model can't be rebuilt, then you have to use the original $\bar{x}$ and $sd(x)$ values. $\endgroup$
    – RioRaider
    Sep 14 '12 at 1:42
  • $\begingroup$ @user14075 It seems silly to use $x$ values that are scaled one way (i.e., standardized based on new $\bar{x}$ and $sd(x)$) to predict $\hat{y}$ from a model that was built using $x$ values that were scaled differently (i.e., standardized based on the original $\bar{x}$ and $sd(x)$). This would be like using an $x$ value that was measured in say inches to build the model and then using $x$ values measured in centimeters (without transformation to inches) to predict $\hat{y}$ from that model. $\endgroup$
    – RioRaider
    Sep 14 '12 at 16:50
  • $\begingroup$ I think some would say they're scaled the same way, using the same z-transform. And once standardized, both cm and inch series become comparable, and the model is based on scaled deviations to the mean: agnostic to original scale. That's what's prompted this post: can't a case be made for using a predictor such as total dollars spent, which increases monotonously, to compute predictions once the field total dollar spent is scaled as deviation to its mean, and that at any given time? This has some traction, at least in my mind. $\endgroup$
    – user14075
    Sep 14 '12 at 19:26

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