meanCenter: meanCenter

In rockchalk: Regression Estimation and Presentation

meanCenter

Description

meanCenter selectively centers or standarizes variables in a regression model.

Usage

meanCenter(
  model,
  centerOnlyInteractors = TRUE,
  centerDV = FALSE,
  standardize = FALSE,
  terms = NULL
)

## Default S3 method:
meanCenter(
  model,
  centerOnlyInteractors = TRUE,
  centerDV = FALSE,
  standardize = FALSE,
  terms = NULL
)

Arguments

model	a fitted regression model (presumably from lm)
centerOnlyInteractors	Default TRUE. If FALSE, all numeric predictors in the regression data frame are centered before the regression is conducted.
centerDV	Default FALSE. Should the dependent variable be centered? Do not set this option to TRUE unless the dependent variable is a numeric variable. Otherwise, it is an error.
standardize	Default FALSE. Instead of simply mean-centering the variables, should they also be "standardized" by first mean-centering and then dividing by the estimated standard deviation.
terms	Optional. A vector of variable names to be centered. Supplying this argument will stop meanCenter from searching for interaction terms that might need to be centered.

Details

Works with "lm" class objects, objects estimated by glm(). This centers some or all of the the predictors and then re-fits the original model with the new variables. This is a convenience to researchers who are often urged to center their predictors. This is sometimes suggested as a way to ameliorate multi-collinearity in models that include interaction terms (Aiken and West, 1991; Cohen, et al 2002). Mean-centering may enhance interpretation of the regression intercept, but it actually does not help with multicollinearity. (Echambadi and Hess, 2007). This function facilitates comparison of mean-centered models with others by calculating centered variables. The defaults will cause a regression's numeric interactive variables to be mean centered. Variations on the arguments are discussed in details.

Suppose the user's formula that fits the original model is m1 <- lm(y ~ x1*x2 + x3 + x4, data = dat). The fitted model will include estimates for predictors x1, x2, x1:x2, x3 and x4. By default, meanCenter(m1) scans the output to see if there are interaction terms of the form x1:x2. If so, then x1 and x2 are replaced by centered versions (m1-mean(m1)) and (m2-mean(m2)). The model is re-estimated with those new variables. model (the main effect and the interaction). The resulting thing is "just another regression model", which can be analyzed or plotted like any R regression object.

The user can claim control over which variables are centered in several ways. Most directly, by specifying a vector of variable names, the user can claim direct control. For example, the argument terms=c("x1","x2","x3") would cause 3 predictors to be centered. If one wants all predictors to be centered, the argument centerOnlyInteractors should be set to FALSE. Please note, this WILL NOT center factor variables. But it will find all numeric predictors and center them.

The dependent variable will not be centered, unless the user explicitly requests it by setting centerDV = TRUE.

As an additional convenience to the user, the argument standardize = TRUE can be used. This will divide each centered variable by its observed standard deviation. For people who like standardized regression, I suggest this is a better approach than the standardize function (which is brain-dead in the style of SPSS). meanCenter with standardize = TRUE will only try to standardize the numeric predictors.

To be completely clear, I believe mean-centering is not helpful with the multicollinearity problem. It doesn't help, it doesn't hurt. Only a misunderstanding leads its proponents to claim otherwise. This is emphasized in the vignette "rockchalk" that is distributed with this package.

Value

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

Author(s)

Paul E. Johnson [e-mail]

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

standardize residualCenter

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)

## Make a bigger dataset to see effects better
N <- 500
dat <- genCorrelatedData(N = N, means = c(200,200), sds = c(60,30),
                         rho = 0.2, stde = 10)
dat$x3 <- rnorm(100, m = 40, s = 4)
dat$x3 <- gl(4, 25, labels = c("none", "some", "much", "total"))
dat$y2 <- with(dat,
               0.4 - 0.15 * x1 + 0.04 * x1^2 -
               drop(contrasts(dat$x3)[dat$x3, ] %*% c(-1.9, 0, 5.1))  +
               1000* rnorm(nrow(dat)))
dat$y2 <- drop(dat$y2)

m4literal <- lm(y2 ~ x1 + I(x1*x1) + x2 + x3, data = dat)
summary(m4literal)
plotCurves(m4literal, plotx="x1")
## Superficially, there is multicollinearity (omit the intercept)
cor(model.matrix(m4literal)[ -1 , -1 ])

m4literalmc <- meanCenter(m4literal, terms = "x1")
summary(m4literalmc)

m4literalmcs <- meanCenter(m4literal, terms = "x1", standardize = TRUE)
summary(m4literalmcs)

m4 <- lm(y2 ~ poly(x1, 2, raw = TRUE) + x2 + x3, data = dat)
summary(m4)
plotCurves(m4, plotx="x1")

m4mc1 <- meanCenter(m4, terms = "x1")
summary(m4mc1)

m4mc2 <- meanCenter(m4, terms = "x1", standardize = TRUE)
summary(m4mc2)

m4mc3 <- meanCenter(m4, terms = "x1", centerDV = TRUE, standardize = TRUE)
summary(m4mc3)

rockchalk documentation built on Aug. 6, 2022, 5:05 p.m.