misty (version 0.5.0)

center: Centering at the Grand Mean and Centering Within Cluster

Description

This function is used to center predictors at the grand mean (CGM, i.e., grand mean centering) or within cluster (CWC, i.e., group-mean centering).

Usage

center(x, type = c("CGM", "CWC"), cluster = NULL, value = NULL, names = ".c",
       as.na = NULL, check = TRUE)

Value

Returns a numeric vector or data frame with the same length or same number of rows as x containing centered values or variable.

Arguments

x

a numeric vector for centering a predictor, matrix or data frame for centering more than one predictor.

type

a character string indicating the type of centering, i.e., "CGM" for centering at the grand mean (i.e., grand mean centering) or "CWC" for centering within cluster (i.e., group-mean centering).

cluster

a vector representing the nested grouping structure (i.e., group or cluster variable) of each unit in x. Note, this argument is required for centering at the grand mean (CGM) of a level-2 predictor or centering within cluster (CWC) of a level-1 predictor.

value

a numeric value for centering on a specific user-defined value.

names

a character string or character vector indicating the names of the centered variables when centering more than one variable. By default, centered variables are named with the ending ".c" resulting in e.g. "x1.c" and "x2.c". Variable names can also be specified using a character vector matching the number of variables specified in x (e.g. names = c("center.x1", "center.x2")).

as.na

a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to x but not to cluster.

check

logical: if TRUE, argument specification is checked.

Author

Takuya Yanagida

Details

Predictors in a single-level regression can only be centered at the grand mean (CGM) by specifying type = "CGM" (default) in conjunction with cluster = NULL (default).

Level-1 (L1) predictors in a multilevel regression can be centered at the grand mean (CGM) by specifying type = "CGM" (default) in conjunction with codecluster = NULL (default) or within cluster (CWC) by specifying type = "CWC" in conjunction with specifying a cluster membership variable using the cluster argument.

Level-2 (L2) predictors in a multilevel regression can only be centered at the grand mean (CGM) by specifying type = "CGM" (default) in conjunction with specifying a cluster membership variable using the cluster argument.

Note that predictors can be centered on any meaningful value using the argument value.

References

Chang, C.-N., & Kwok, O.-M. (2022) Partitioning Variance for a Within-Level Predictor in Multilevel Models. Structural Equation Modeling: A Multidisciplinary Journal. Advance online publication. https://doi.org/10.1080/10705511.2022.2051175#'

Enders, C. K. (2013). Centering predictors and contextual effects. In M. A. Scott, J. S. Simonoff, & B. D. Marx (Eds.), The Sage handbook of multilevel modeling (pp. 89-109). Sage. https://dx.doi.org/10.4135/9781446247600

Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12, 121-138. https://doi.org/10.1037/1082-989X.12.2.121

Rights, J. D., Preacher, K. J., & Cole, D. A. (2020). The danger of conflating level-specific effects of control variables when primary interest lies in level-2 effects. British Journal of Mathematical & Statistical Psychology, 73, 194-211. https://doi.org/10.1111/bmsp.12194

Yaremych, H. E., Preacher, K. J., & Hedeker, D. (2021). Centering categorical predictors in multilevel models: Best practices and interpretation. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000434

See Also

dummy.c, cluster.scores, rec, item.reverse, coderwg.lindell, item.scores.

Examples

#--------------------------------------
# Predictors in a single-level regression
dat.sl <- data.frame(x1 = c(4, 2, 5, 6, 3, 4, 1, 3, 4),
                     x2 = c(3, 1, 2, 6, 4, 8, 3, 2, 1),
                     y = c(5, 3, 6, 3, 4, 5, 2, 6, 5))

# Center predictor at the sample mean
center(dat.sl$x1)

# Center predictors at the sample mean and attach to 'dat.sl'
dat.sl <- data.frame(dat.sl,
                     center(dat.sl[, c("x1", "x2")]))

# Center predictor at the value 3
center(dat.sl$x1, value = 3)

# Center predictors at the value 3 and attach to 'dat.sl'
dat.sl <- data.frame(dat.sl,
                     center(dat.sl[, c("x1", "x2")], value = 3, names = ".v"))

#--------------------------------------
# Predictors in a multilevel regression
dat.ml <- data.frame(id = c(1, 2, 3, 4, 5, 6, 7, 8, 9),
                     cluster = c(1, 1, 1, 2, 2, 2, 3, 3, 3),
                     x1.l1 = c(4, 2, 5, 6, 3, 4, 1, 3, 4),
                     x2.l1 = c(1, 4, 2, 3, 5, 7, 8, 7, 5),
                     x1.l2 = c(4, 4, 4, 1, 1, 1, 3, 3, 3),
                     x2.l2 = c(5, 5, 5, 2, 2, 2, 7, 7, 7),
                     y = c(5, 3, 6, 3, 4, 5, 2, 6, 5))

# Center level-1 predictor at the grand mean (CGM)
center(dat.ml$x1.l1)

# Center level-1 predictors at the grand mean (CGM) and attach to 'dat.ml'
dat.ml<- cbind(dat.ml,
              center(dat.ml[, c("x1.l1", "x2.l1")], names = ".cgm"))

# Center level-1 predictor within cluster (CWC)
center(dat.ml$x1.l1, type = "CWC", cluster = dat.ml$cluster)

# Center level-1 predictors within cluster (CWC) and attach to 'dat.ml'
dat.ml <- cbind(dat.ml,
                center(dat.ml[, c("x1.l1", "x2.l1")], type = "CWC",
                cluster = dat.ml$cluster, names = ".cwc"))

# Center level-2 predictor at the grand mean (CGM)
center(dat.ml$x1.l2, type = "CGM", cluster = dat.ml$cluster)

# Center level-2 predictors at the grand mean (CGM) and attach to 'dat.ml'
dat.ml <- cbind(dat.ml,
                center(dat.ml[, c("x1.l2", "x2.l2")], type = "CGM",
                cluster = dat.ml$cluster, names = ".cgm"))