rockchalk (version 1.6.3)

meanCenter: meanCenter

Description

meanCenter selectively centers or standarizes variables in a regression model.

Usage

meanCenter(model, centerOnlyInteractors = TRUE,
    centerDV = FALSE, standardize = FALSE)
  ## S3 method for class 'default':
meanCenter(model,
    centerOnlyInteractors = TRUE, centerDV = FALSE,
    standardize = FALSE)

Arguments

model

a fitted regression model (presumably from lm)

centerOnlyInteractors

If false, all predictors in the regression data frame are centered before the regression is conducted.

centerDV

Should the dependent variable be centered?

standardize

Instead of simply mean-centering the variables, should they also be "standardized" by first mean-centering and then dividing by the estimated standard deviation.

Value

• A regression model of the same type as the input model, with attributes representing the names of the centered variables.

Details

Mean-centering has often been recommended as a way to ameliorate multi-collinearity in regression models that include interaction terms (Aiken and West, 1991; Cohen, et al 2002). While this claim may have been mistaken (Echambadi and Hess, 2007), mean-centering is still widely practiced. This function facilitates comparison of mean-centered models with others by automatically re-calculating centered variables. The defaults will cause a regression's numeric interactive variables to be mean centered. That is to say, if an interaction x1:x2 is present in the model, then x1 and x2 are replaced by (m1-mean(m1)) and (m2-mean(m2) in all of the terms in which they appear in the model (the main effect and the interaction). If one wants all predictors to be centered, the option centerOnlyInteractors should be set to FALSE. The dependent variable will not be centered, unless the user explicitly requests it by setting centerDV = TRUE. The centered variables can be standardized (optionally, of course).

References

Aiken, L. S. and West, S.G. (1991). Multiple Regression: Testing and Interpreting Interactions. Newbury Park, Calif: Sage Publications.

Cohen, J., Cohen, P., West, S. G., and Aiken, L. S. (2002). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (Third.). Routledge Academic.

Echambadi, R., and Hess, J. D. (2007). Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models. Marketing Science, 26(3), 438-445.

See Also

lmres

Examples

library(rockchalk)
N <- 100
dat <- genCorrelatedData(N=N, means=c(100,200), sds=c(20,30), rho=0.4, stde=10)
dat$x3 <- rnorm(100, m=40, s=4)

m1 <- lm(y ~ x1 * x2 + x3, data=dat)
summary(m1)
mcDiagnose(m1)

m1c <- meanCenter(m1)
summary(m1c)
mcDiagnose(m1c)

m2 <- lm(y ~ x1 * x2 + x3, data=dat)
summary(m2)
mcDiagnose(m2)

m2c <- meanCenter(m2, standardize = TRUE)
summary(m2c)
mcDiagnose(m2c)

m2c2 <- meanCenter(m2, centerOnlyInteractors = FALSE)
summary(m2c2)

m2c3 <- meanCenter(m2, centerOnlyInteractors = FALSE, centerDV = TRUE)
summary(m2c3)

dat <- genCorrelatedData(N=N, means=c(100,200), sds=c(20,30), rho=0.4, stde=10)
dat$x3 <- rnorm(100, m=40, s=4)
dat$x3 <- gl(4, 25, labels=c("none","some","much","total"))

m3 <- lm(y ~ x1 * x2 + x3, data=dat)
summary(m3)
## visualize, for fun
plotPlane(m3, "x1", "x2")

m3c1 <- meanCenter(m3)
summary(m3c1)

## Not exactly the same as a "standardized" regression because the
## interactive variables are centered in the model frame,
## and the term "x1:x2" is never centered again.
m3c2 <- meanCenter(m3, centerDV=TRUE, centerOnlyInteractors=FALSE, standardize=TRUE)
summary(m3c2)

m3st <- standardize(m3)
summary(m3st)