RE: Centering (was Re: Missing covariates)

From: "Perez Ruixo, Juan Jose [JanBe]" <JPEREZRU@janbe.jnj.com> Subject: RE: Centering (was Re: Missing covariates) Date: Thu, 12 Jul 2001 10:13:07 +0200 Dear all, We must take care with the centering approach for categorical data. Following the example of Mat (TVCL = THETA(1) + Xi * THETA(2)), the parametrizations Xi = 1 for females, and Xi = -1 for males, allow to get the population average when Xi=0 and there is equal proportion of males and females. In this case, we have a null correlation between intercept and slope, but the intercept SE is the same that slope SE and, both equal to residual standard error divided by SQRT(N). In other words, you don't know directly the males population parameter and the difference with females, because THETA(2) is affected by the Xi codification. In this case THETA(2) is a half of the real difference between males and females and its absolute standard error (not relative standard error) is affected. It means t-test is the same, but confidence interval building needs previous transformation in order to get the precision of the real difference between males and females. I can show you a simple example (with S+ code) weight <- c(rnorm(50, mean = 60, sd = 6),rnorm(50, mean = 50, sd = 5)) gender0 <- c( rep(1,50),rep(0,50)) gender1 <- c( rep(1,50),rep(-1,50)) G0 <- lm(weight~gender0) G1 <- lm(weight~gender1) summary(G0) summary(G1) ....... Coefficients G0: Value Std. Error t value Pr(>|t|) (Intercept) 50.7279 0.7918 64.0675 0.0000 gender0 7.9107 1.1198 7.0647 0.0000 Residual standard error: 5.599 on 98 degrees of freedom Multiple R-Squared: 0.3374 F-statistic: 49.91 on 1 and 98 degrees of freedom, the p-value is 2.362e-010 Correlation Intercept, gender: -0.7071 Coefficients G1: Value Std. Error t value Pr(>|t|) (Intercept) 54.6832 0.5599 97.6698 0.0000 gender1 3.9554 0.5599 7.0647 0.0000 Residual standard error: 5.599 on 98 degrees of freedom Multiple R-Squared: 0.3374 F-statistic: 49.91 on 1 and 98 degrees of freedom, the p-value is 2.362e-010 Correlation Intercept, gender: 0 For this reasons, I suggest don't use centering approach for categorical data (here, I don't include ordinal data). With first approach the intercept have a useful meaning, and I don't need to center the variable. Thanks, Juan Jose Perez Ruixo Global Pharmacokinetics and Clinical Pharmacology Division. Janssen Research Foundation Turnhoutseweg, 30 B-2340 Beerse Belgium Tel: (+32) 14 60 75 08 Email: jperezru@janbe.jnj.com