# Predictive model & standardized variables

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.

• What do you mean by rescore? Sep 14 '12 at 0:18
• In the context of this post, 'rescore' means computing the predicted dependent values using new readings of the predictor variables. Sep 14 '12 at 1:23

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 $sd(x)$.
• 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 $\hat{y}$ ? Sep 14 '12 at 1:32
• @user14075 No, if the model can't be rebuilt, then you have to use the original $\bar{x}$ and $sd(x)$ values. Sep 14 '12 at 1:42
• @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. Sep 14 '12 at 16:50