# interpreting regression coefficients

### Concepts in Linear Regression you need to know before learning Multilevel Models

January 30th, 2009 by

It seems very many researchers are needing to learn multilevel and mixed models, and I have to say, it’s not so easy on your own.

I too went to graduate school before it was taught in classes–we did learn mixed models as in Split Plot designs, but things have progressed a bit since then.  So I too have had to learn them without benefit of a class, or teacher.  So I feel your pain.  But I’ve struggled through and learned a (more…)

### Centering and Standardizing Predictors

December 5th, 2008 by

I was recently asked about whether centering (subtracting the mean) a predictor variable in a regression model has the same effect as standardizing (converting it to a Z score).  My response:

They are similar but not the same.

In centering, you are changing the values but not the scale.  So a predictor that is centered at the mean has new values–the entire scale has shifted so that the mean now has a value of 0, but one unit is still one unit.  The intercept will change, but the regression coefficient for that variable will not.  Since the regression coefficient is interpreted as the effect on the mean of Y for each one unit difference in X, it doesn’t change when X is centered.

And incidentally, despite the name, you don’t have to center at the mean.  It is often convenient, but there can be advantages of choosing a more meaningful value that is also toward the center of the scale.

But a Z-score also changes the scale.  A one-unit difference now means a one-standard deviation difference.  You will interpret the coefficient differently.  This is usually done so you can compare coefficients for predictors that were measured on different scales.  I can’t think of an advantage for doing this for an interaction.