Linear Statistical Models: Regression


Updated for Stata 11

Centering a variable involves subtracting the mean from each of the scores, that is, creating deviation scores. Centering can be done two ways; 1) centering using the grand mean and 2) centering using group means, which is also known as context centering.

Centering using the grand mean

We will illustrate issues surrounding centering using using the hsb2 dataset. We will begin by interpreting the constant in simple linear regression.

Now, let's examine a model that includes an interaction. Next, let's examine a polynomial regression. Centering scores is a technique that is recommended by some (Aiken & West, 1991; Bryk & Raudenbush, 1991) and viewed as unnecessary by others (Kromrey & Foster-Johnson, 1998; Pedhazur, 1997). Katrichis (1992) views centering negatively and has argued that this technique produces systematically biased estimates of main effects.

The arguments in favor of centering revolve primarily around 1) the greater ease of interpreting the coefficients and 2) reducing collinearity. As to reducing collinearity, modern statistical packages have sufficient numerical accuracy to estimate parameters for product and power variables.

Centering using group means

In this section we will center the socst variable using the means group means for males and females.

Linear Statistical Models Course

Phil Ender, 18feb02, 22dec00