RE: Centering (Impact on SE)

From: SMITH_BRIAN_P@Lilly.com Subject: RE: Centering (Impact on SE) Date: Mon, 09 Jul 2001 10:14:34 -0500 Unfortunately, this is a classic apples to oranges comparison. In the uncentered model the intercept is estimating the clearance for a person with an age of 0. In the centered model the intercept is estimating the clearance for a person with an age of 40. Obviously, your estimate of a person with an age of 40 will be more precise (this is where most of your data is) than an estimate of a person with age 0. Now, notice that the estimate of a person of age 0 with your non centered model is 9.0024 + 0*0.0249 = 9.0024 the estimate of a person of age 40 with your non centered model is 9.0024 + 40*0.0249 = 9.9984 the estimate of a person of age 0 with your centered model is 9.9994 - 40*0.0249 = 9.0034 the estimate of a person of age 40 with your centered model is 9.9994 + 0*0.0249 = 9.9994 The only difference of the estimates of these two models is completely due to rounding error. With this said, consider finding the standard error for a person with age 0 from your centered model. That is find the standard error of 9.9994 - 40*0.0249. It is a mathematical fact that the standard error will be exactly the same as the standard error for the intercept for the non centered model. Further notice that the estimate and standard error of the slopes of the two models are exactly the same. Thus, the 2 model give identical inference about the effect of age on clearance. As has been mentioned, there are numerical analysis advantages to centering. Centering also allows the intercept to be an estimate of something meaningful. As others have said and I reiterate, these advantages make centering useful. However, statistically (given that both models properly converge) there is no advantage to centering. Sincerely, Brian Smith Eli Lilly and Company