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R/center.R
In misty: Miscellaneous Functions 'T. Yanagida'
Defines functions
center
Documented in
center
#' Centering Predictor Variables in Single-Level and Multilevel Data
#'
#' This function centers predictor variables in single-level data, two-level
#' data, and three-level data at the grand mean (CGM, i.e., grand mean centering)
#' or within cluster (CWC, i.e., group mean centering).
#'
#' @param data a numeric vector for centering a predictor variable, or a
#' data frame for centering more than one predictor variable.
#' @param ... an expression indicating the variable names in \code{data} e.g.,
#' \code{center(dat, x1, x2)} for centering the variables \code{x1}
#' and \code{x2} in the data frame \code{dat}. Note that the
#' operators \code{.}, \code{+}, \code{-}, \code{~}, \code{:},
#' \code{::}, and \code{!} can also be used to select variables,
#' see 'Details' in the \code{\link{df.subset}} function.
#' @param cluster a character string indicating the name of the cluster variable
#' in \code{data} for a two-level model, a character vector
#' indicating the names of the cluster variables in \code{data}
#' for a three-level model, or a vector or data frame representing
#' the nested grouping structure (i.e., group or cluster variables).
#' Alternatively, a character string or character vector indicating
#' the variable name(s) of the cluster variable(s) in \code{data}.
#' Note that the cluster variable at Level 3 come first in a
#' three-level model, i.e., \code{cluster = c("level3", "level2")}.
#' @param type a character string indicating the type of centering, i.e.,
#' \code{"CGM"} for centering at the grand mean (i.e., grand mean
#' centering, default when \code{cluster = NULL}) or \code{"CWC"}
#' for centering within cluster (i.e., group mean centering, default
#' when specifying the argument \code{cluster}).
#' @param cwc.mean a character string indicating the type of centering of a level-1
#' predictor variable in a three-level model, i.e., \code{L2}
#' (default) for centering the predictor variable at the level-2
#' cluster means, and \code{L3} for centering the predictor
#' variable at the level-3 cluster means.
#' @param value a numeric value for centering on a specific user-defined value.
#' Note that this option is only available when specifying a
#' single-level predictor variable, i.e., \code{cluster = NULL}.
#' @param name a character string or character vector indicating the names of
#' the centered predictor variables. By default, centered predictor
#' variables are named with the ending \code{".c"} resulting in
#' e.g. \code{"x1.c"} and \code{"x2.c"}. Variable names can also
#' be specified by using a character vector matching the number
#' of variables specified in \code{...} (e.g.,
#' \code{name = c("center.x1", "center.x2")}).
#' @param append logical: if \code{TRUE} (default), centered predictor variable(s)
#' are appended to the data frame specified in the argument \code{data}.
#' @param as.na a numeric vector indicating user-defined missing values, i.e.
#' these values are converted to \code{NA} before conducting the
#' analysis. Note that \code{as.na()} function is only applied to
#' \code{...} but not to \code{cluster}.
#' @param check logical: if \code{TRUE} (default), argument specification is
#' checked.
#'
#' @details
#' \describe{
#' \item{\strong{Single-Level Data}}{\strong{Predictor variables in single-level
#' data} can only be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"}:
#'
#' \deqn{x_{i} - \bar{x}_{.}}
#'
#' where \eqn{x_{i}} is the predictor value of observation \eqn{i} and
#' \eqn{\bar{x}_{.}} is the average \eqn{x} score. Note that predictor variables
#' can be centered on any meaningful value specifying the argument \code{value},
#' e.g., a predictor variable centered at 5 by applying following formula:
#'
#' \deqn{x_{i} - \bar{x}_{.} + 5}
#'
#' resulting in a mean of the centered predictor variable of 5.
#' }
#' \item{\strong{Two-Level Data}}{\strong{Level-1 (L1) predictor variables} in
#' two-level data can be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"}:
#'
#' \deqn{x_{ij} - \bar{x}_{..}}
#'
#' where \eqn{x_{ij}} is the predictor value of observation \eqn{i} in L2 cluster
#' \eqn{j} and \eqn{\bar{x}_{..}} is the average \eqn{x} score.
#'
#' L1 predictor variables are centered at the group mean (CWC) by specifying
#' \code{type = "CWC"} (Default):
#'
#' \deqn{x_{ij} - \bar{x}_{.j}}
#'
#' where \eqn{\bar{x_{.j}}} is the average \eqn{x} score in cluster \eqn{j}.
#'
#' \strong{Level-2 (L1) predictor variables} in two-level data can only be
#' centered at the grand mean:
#'
#' \deqn{x_{.j} - \bar{x}_{..}}
#'
#' where \eqn{x_{.j}} is the predictor value of Level 2 cluster \eqn{j} and
#' \eqn{\bar{x}_{..}} is the average Level-2 cluster score. Note that the cluster
#' membership variable needs to be specified when centering a L2 predictor variable
#' in two-level data. Otherwise the average \eqn{x_{ij}} individual score instead
#' of the average \eqn{x_{.j}} cluster score is used to center the predictor
#' variable.
#' }
#' \item{\strong{Three-Level Data}}{\strong{Level-1 (L1) predictor variables} in
#' three-level data can be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"} (Default):
#'
#' \deqn{x_{ijk} - \bar{x}_{...}}
#'
#' where \eqn{x_{ijk}} is the predictor value of observation \eqn{i} in Level-2
#' cluster \eqn{j} within Level-3 cluster \eqn{k} and \eqn{\bar{x}_{...}} is the
#' average \eqn{x} score.
#'
#' L1 predictor variables are centered within cluster (CWC) by specifying
#' \code{type = "CWC"} (Default). However, L1 predictor variables can be either
#' centered within Level-2 clusters (\code{cwc.mean = "L2"}, Default,
#' see Brincks et al., 2017):
#'
#' \deqn{x_{ijk} - \bar{x}_{.jk}}
#'
#' or within Level-3 clusters (\code{cwc.mean = "L3"}, see Enders, 2013):
#'
#' \deqn{x_{ijk} - \bar{x}_{..k}}
#'
#' where \eqn{\bar{x}_{.jk}} is the average \eqn{x} score in Level-2 cluster
#' \eqn{j} within Level-3 cluster \eqn{k} and \eqn{\bar{x}_{..k}} is the average
#' \eqn{x} score in Level-3 cluster \eqn{k}.
#'
#' \strong{Level-2 (L2) predictor variables} in three-level data can be centered
#' at the grand mean (CGM) by specifying \code{type = "CGM"}:
#'
#' \deqn{x_{.jk} - \bar{x}_{...}}
#'
#' where \eqn{x_{.jk}} is the predictor value of Level-2 cluster \eqn{j} within
#' Level-3 cluster \eqn{k} and \eqn{\bar{x}_{...}} is the average Level-2 cluster
#' score.
#'
#' L2 predictor variables are centered within cluster (CWC) by specifying
#' \code{type = "CWC"} (Default):
#'
#' \deqn{x_{.jk} - \bar{x}_{..k}}
#'
#' where \eqn{\bar{x}_{..k}} is the average \eqn{x} score in Level-3 cluster
#' \eqn{k}.
#'
#' \strong{Level-3 (L3) predictor variables} in three-level data can only be
#' centered at the grand mean:
#'
#' \deqn{x_{..k} - \bar{x}_{...}}
#'
#' where \eqn{x_{..k}} is the predictor value of Level-3 cluster \eqn{k} and
#' \eqn{\bar{x}_{...}} is the average Level-3 cluster score. Note that the cluster
#' membership variables at Level 2 and Level 3 need to be specified when centering
#' a L3 predictor variable in three-level data.}
#' }
#'
#' @author
#' Takuya Yanagida \email{takuya.yanagida@@univie.ac.at}
#'
#' @seealso
#' \code{\link{coding}}, \code{\link{cluster.scores}}, \code{\link{rec}},
#' \code{\link{item.reverse}}, \code{\link{rwg.lindell}}, \code{\link{item.scores}}.
#'
#' @references
#' Brincks, A. M., Enders, C. K., Llabre, M. M., Bulotsky-Shearer, R. J., Prado, G.,
#' & Feaster, D. J. (2017). Centering predictor variables in three-level contextual
#' models. \emph{Multivariate Behavioral Research, 52}(2), 149–163.
#' https://doi.org/10.1080/00273171.2016.1256753
#'
#' Chang, C.-N., & Kwok, O.-M. (2022) Partitioning Variance for a Within-Level
#' Predictor in Multilevel Models. \emph{Structural Equation Modeling: A
#' Multidisciplinary Journal}. Advance online publication.
#' https://doi.org/10.1080/10705511.2022.2051175
#'
#' Enders, C. K. (2013). Centering predictors and cont
#' extual effects. In M. A.
#' Scott, J. S. Simonoff, & B. D. Marx (Eds.), \emph{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. \emph{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. \emph{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.
#' \emph{Psychological Methods}. Advance online publication.
#' https://doi.org/10.1037/met0000434
#'
#' @return
#' Returns a numeric vector or data frame with the same length or same number of
#' rows as \code{data} containing the centered variable(s).
#'
#' @export
#'
#' @examples
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Single-Level Data
#'
#' # Example 1a: Center predictor 'disp' at the grand mean
#' center(mtcars, disp, append = FALSE)
#'
#' # Alternative specification without using the '...' argument
#' center(mtcars$disp)
#'
#' # Example 1b: Center predictors 'disp' and 'hp' at the grand mean and append to 'mtcars'
#' center(mtcars, disp, hp)
#'
#' # Alternative specification without using the '...' argument
#' cbind(mtcars, center(mtcars[, c("disp", "hp")]))
#'
#' # Example 1c: Center predictor 'disp' at the value 3
#' center(mtcars, disp, value = 3)
#'
#' # Example 1d: Center predictors 'disp' and 'hp' and label with the suffix ".v"
#' center(mtcars, disp, hp, name = ".v")
#'
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Two-Level Data
#'
#' # Load data set "Demo.twolevel" in the lavaan package
#' data("Demo.twolevel", package = "lavaan")
#'
#' # Example 2a: Center L1 predictor 'y1' within cluster
#' center(Demo.twolevel, y1, cluster = "cluster")
#'
#' # Alternative specification without using the '...' argument
#' center(Demo.twolevel$y1, cluster = Demo.twolevel$cluster)
#'
#' # Example 2b: Center L2 predictor 'w2' at the grand mean
#' center(Demo.twolevel, w1, cluster = "cluster")
#'
#' # Example 2c: Center L1 predictor 'y1' within cluster and L2 predictor 'w1' at the grand mean
#' center(Demo.twolevel, y1, w1, cluster = "cluster")
#'
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Three-Level Data
#'
#' # Create arbitrary three-level data
#' Demo.threelevel <- data.frame(Demo.twolevel, cluster2 = Demo.twolevel$cluster,
#' cluster3 = rep(1:10, each = 250))
#'
#' # Example 3a: Center L1 predictor 'y1' within L2 cluster
#' center(Demo.threelevel, y1, cluster = c("cluster3", "cluster2"))
#'
#' # Example 3b: Center L1 predictor 'y1' within L3 cluster
#' center(Demo.threelevel, y1, cluster = c("cluster3", "cluster2"), cwc.mean = "L3")
#'
#' # Example 3c: Center L1 predictor 'y1' within L2 cluster and L2 predictor 'w1' within L3 cluster
#' center(Demo.threelevel, y1, w1, cluster = c("cluster3", "cluster2"))
center <- function(data, ..., cluster = NULL, type = c("CGM", "CWC"),
cwc.mean = c("L2", "L3"), value = NULL, append = TRUE,
name = ".c", as.na = NULL, check = TRUE) {
#_____________________________________________________________________________
#
# Initial Check --------------------------------------------------------------
# Check if input 'data' is missing
if (isTRUE(missing(data))) { stop("Please specify a numeric vector or data frame for the argument 'data'", call. = FALSE) }
# Check if input 'data' is NULL
if (isTRUE(is.null(data))) { stop("Input specified for the argument 'data' is NULL.", call. = FALSE) }
#_____________________________________________________________________________
#
# Data -----------------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Data using the argument 'data' ####
if (isTRUE(!missing(...))) {
# Variable names
var.names <- .var.names(..., data = data, cluster = cluster)
# Extract data and convert tibble into data frame or vector
x <- data[, var.names] |> (\(y) if (isTRUE("tbl" %in% substr(class(y), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(y)) == 1L)) { unname(unlist(y)) } else { as.data.frame(y) } } else { y })()
# Cluster variable
if (isTRUE(!is.null(cluster))) { cluster <- data[, cluster] }
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Data without using the argument 'data' ####
} else {
# Convert 'data' as tibble into data frame
x <- data |> (\(y) if (isTRUE("tbl" %in% substr(class(y), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(y)) == 1L)) { unname(unlist(y)) } else { as.data.frame(y) } } else { y })()
# Data and cluster
var.group <- .var.group(data = x, cluster = cluster)
# Data
if (isTRUE(!is.null(var.group$data))) { x <- var.group$data }
# Cluster variable
if (isTRUE(!is.null(var.group$cluster))) { cluster <- var.group$cluster }
# Convert 'cluster' as tibble into data frame
if (isTRUE(!is.null(cluster) && "tbl" %in% substr(class(cluster), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(cluster)) == 1L)) { cluster <- unname(unlist(cluster)) } else { cluster <- as.data.frame(cluster) } }
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Convert user-missing values into NA ####
if (isTRUE(!is.null(as.na))) { x <- .as.na(x, na = as.na) }
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Cluster variables ####
if (isTRUE(!is.null(cluster))) {
# Two cluster variables
if (isTRUE(ncol(as.data.frame(cluster)) == 2L)) {
l3.cluster <- cluster[, 1L]
l2.cluster <- cluster[, 2L]
no.clust <- "two"
# One cluster variables
} else {
no.clust <- "one"
}
}
#_____________________________________________________________________________
#
# Input Check ----------------------------------------------------------------
# Check inputs
.check.input(logical = "append", numeric = list(value = 1L), s.character = list(type = c("CGM", "CWC"), cwc.mean = c("L2", "L3")), envir = environment(), input.check = check)
# Additional checks
if (isTRUE(check)) {
# Check input 'name'
if (isTRUE(!is.null(dim(x)))) {
if (isTRUE(!is.character(name))) { stop("Please specify a character string or vector for the argument 'name'.", call. = FALSE) }
if (isTRUE(length(name) > 1L && length(name) != ncol(as.data.frame(x)))) { stop("Length of the vector specified in 'name' does not match with the number of variables.", call. = FALSE) }
}
}
#_____________________________________________________________________________
#
# Arguments ------------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Type of centering ####
if (isTRUE(all(c("L2", "L3") %in% cwc.mean))) { cwc.mean <- "L2" }
#_____________________________________________________________________________
#
# Main Function --------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Single variable ####
if (isTRUE(is.null(dim(x)))) {
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Variable ####
if (isTRUE(!is.null(cluster))) {
##### One cluster variable
if (isTRUE(no.clust == "one")) {
# Level 1 Variable
if (isTRUE(any(na.omit(as.vector(tapply(x, cluster, var, na.rm = TRUE))) != 0L))) {
vartype <- "L1"
# Level 2 Variable
} else {
vartype = "L2"
}
##### Two cluster variable s
} else if (isTRUE(no.clust == "two")) {
# Level 1 Variable
if (isTRUE(any(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) != 0L))) {
vartype <- "L1"
# Level 2 Variable
} else if (isTRUE(all(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) == 0L) && any(as.vector(tapply(x, cluster[, 1L], var, na.rm = TRUE)) != 0L))) {
vartype <- "L2"
# Level 3 Variable
} else if (isTRUE(all(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) == 0L) && all(na.omit(as.vector(tapply(x, cluster[, 1L], var, na.rm = TRUE))) == 0L))) {
vartype <- "L3"
}
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Type of centering ####
if (isTRUE(all(c("CGM", "CWC") %in% type))) {
#...................
### Single-level ####
if (isTRUE(is.null(cluster))) {
type <- "CGM"
#...................
### Multilevel ####
} else {
##### One cluster variable
if (isTRUE(no.clust == "one")) {
type <- switch(vartype, L1 = "CWC", L2 = "CGM")
##### Two cluster variable s
} else if (isTRUE(no.clust == "two")) {
type <- switch(vartype, L1 = "CWC", L2 = "CWC", L3 = "CGM")
}
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Centering ####
#...................
### No cluster variable ####
if (isTRUE(is.null(cluster))) {
##### Mean centering
if (isTRUE(is.null(value))) {
object <- as.numeric(scale(x, scale = FALSE))
##### Centering on a user-defined value
} else {
object <- x - mean(x, na.rm = TRUE) + value
}
#...................
### One cluster variable ####
} else if (isTRUE(no.clust == "one")) {
##### Centering at the grand mean (CGM)
if (isTRUE(type == "CGM")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- as.numeric(scale(x, scale = FALSE))
# Level 2 predictor
}, L2 = {
object <- x - mean(x[which(!duplicated(cluster))], na.rm = TRUE)
})
##### Centering within cluster (CWC)
} else if (isTRUE(type == "CWC")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- unname(x - misty::cluster.scores(x, cluster = cluster, fun = "mean", check = FALSE, expand = TRUE))
# Level 2 predictor
}, L2 = {
# Note, level 2 predictor can only be centered at the grand mean
object <- x - mean(x[which(!duplicated(cluster))], na.rm = TRUE)
})
}
#...................
### Two cluster variables ####
} else if (isTRUE(no.clust == "two")) {
##### Centering at the grand mean (CGM)
if (isTRUE(type == "CGM")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- as.numeric(scale(x, scale = FALSE))
# Level 2 predictor
}, L2 = {
object <- x - mean(x[which(!duplicated(apply(cluster, 1L, paste, collapse = "")))], na.rm = TRUE)
# Level 3 predictor
}, L3 = {
object <- x - mean(x[which(!duplicated(cluster[, 1L]))], na.rm = TRUE)
})
##### Centering within cluster (CWC)
} else if (isTRUE(type == "CWC")) {
switch(vartype,
# Level 1 predictor
L1 = {
switch(cwc.mean,
# Deviation from the Level-2 cluster mean
L2 = {
object <- unname(x - misty::cluster.scores(x, cluster = apply(cluster, 1L, paste, collapse = ""), fun = "mean", check = FALSE, expand = TRUE))
# Deviation from the Level-3 cluster mean
}, L3 = {
object <- x - misty::cluster.scores(x, cluster = cluster[, 1L])
})
# Level 2 predictor
}, L2 = {
object <- (data.frame(x, cluster3 = cluster[, 1L], cluster2 = cluster[, 2]) |>
(\(y) misty::cluster.scores(y[!duplicated(y$cluster2), ], x, cluster = "cluster3"))() |>
(\(z) data.frame(z, object = z$x - z$x.a))() |>
(\(q) merge(data.frame(by = apply(cluster[, c("cluster3", "cluster2")], 1L, paste, collapse = "")),
data.frame(object = q$object, by = apply(q[, c("cluster3", "cluster2")], 1L, paste, collapse = "")), by = "by", sort = FALSE))())[, "object"]
# Level 3 predictor
}, L3 = {
# Note, level 3 predictor can only be centered at the grand mean
object <- x - mean(x[which(!duplicated(cluster[, 1L]))], na.rm = TRUE)
})
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Multiple variables ####
} else {
object <- data.frame(vapply(x, misty::center, cluster = cluster, type = type, cwc.mean = cwc.mean, value = value, as.na = as.na, check = FALSE, FUN.VALUE = double(nrow(x))))
#...................
### Variable names ####
if (isTRUE(length(name) == 1L)) {
colnames(object) <- paste0(colnames(object), name)
} else {
colnames(object) <- name
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Append ####
if (isTRUE(!missing(...) && append)) {
if (isTRUE(is.null(dim(x)))) {
#...................
### Variable names ####
if (isTRUE(name == ".c")) {
object <- setNames(as.data.frame(object), nm = paste0(var.names, ".c"))
} else {
object <- setNames(as.data.frame(object), nm = name)
}
}
object <- data.frame(data, object)
}
#_____________________________________________________________________________
#
# Return Object --------------------------------------------------------------
return(object)
}
#_______________________________________________________________________________
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Defines functions center
Documented in center
#' Centering Predictor Variables in Single-Level and Multilevel Data
#'
#' This function centers predictor variables in single-level data, two-level
#' data, and three-level data at the grand mean (CGM, i.e., grand mean centering)
#' or within cluster (CWC, i.e., group mean centering).
#'
#' @param data a numeric vector for centering a predictor variable, or a
#' data frame for centering more than one predictor variable.
#' @param ... an expression indicating the variable names in \code{data} e.g.,
#' \code{center(dat, x1, x2)} for centering the variables \code{x1}
#' and \code{x2} in the data frame \code{dat}. Note that the
#' operators \code{.}, \code{+}, \code{-}, \code{~}, \code{:},
#' \code{::}, and \code{!} can also be used to select variables,
#' see 'Details' in the \code{\link{df.subset}} function.
#' @param cluster a character string indicating the name of the cluster variable
#' in \code{data} for a two-level model, a character vector
#' indicating the names of the cluster variables in \code{data}
#' for a three-level model, or a vector or data frame representing
#' the nested grouping structure (i.e., group or cluster variables).
#' Alternatively, a character string or character vector indicating
#' the variable name(s) of the cluster variable(s) in \code{data}.
#' Note that the cluster variable at Level 3 come first in a
#' three-level model, i.e., \code{cluster = c("level3", "level2")}.
#' @param type a character string indicating the type of centering, i.e.,
#' \code{"CGM"} for centering at the grand mean (i.e., grand mean
#' centering, default when \code{cluster = NULL}) or \code{"CWC"}
#' for centering within cluster (i.e., group mean centering, default
#' when specifying the argument \code{cluster}).
#' @param cwc.mean a character string indicating the type of centering of a level-1
#' predictor variable in a three-level model, i.e., \code{L2}
#' (default) for centering the predictor variable at the level-2
#' cluster means, and \code{L3} for centering the predictor
#' variable at the level-3 cluster means.
#' @param value a numeric value for centering on a specific user-defined value.
#' Note that this option is only available when specifying a
#' single-level predictor variable, i.e., \code{cluster = NULL}.
#' @param name a character string or character vector indicating the names of
#' the centered predictor variables. By default, centered predictor
#' variables are named with the ending \code{".c"} resulting in
#' e.g. \code{"x1.c"} and \code{"x2.c"}. Variable names can also
#' be specified by using a character vector matching the number
#' of variables specified in \code{...} (e.g.,
#' \code{name = c("center.x1", "center.x2")}).
#' @param append logical: if \code{TRUE} (default), centered predictor variable(s)
#' are appended to the data frame specified in the argument \code{data}.
#' @param as.na a numeric vector indicating user-defined missing values, i.e.
#' these values are converted to \code{NA} before conducting the
#' analysis. Note that \code{as.na()} function is only applied to
#' \code{...} but not to \code{cluster}.
#' @param check logical: if \code{TRUE} (default), argument specification is
#' checked.
#'
#' @details
#' \describe{
#' \item{\strong{Single-Level Data}}{\strong{Predictor variables in single-level
#' data} can only be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"}:
#'
#' \deqn{x_{i} - \bar{x}_{.}}
#'
#' where \eqn{x_{i}} is the predictor value of observation \eqn{i} and
#' \eqn{\bar{x}_{.}} is the average \eqn{x} score. Note that predictor variables
#' can be centered on any meaningful value specifying the argument \code{value},
#' e.g., a predictor variable centered at 5 by applying following formula:
#'
#' \deqn{x_{i} - \bar{x}_{.} + 5}
#'
#' resulting in a mean of the centered predictor variable of 5.
#' }
#' \item{\strong{Two-Level Data}}{\strong{Level-1 (L1) predictor variables} in
#' two-level data can be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"}:
#'
#' \deqn{x_{ij} - \bar{x}_{..}}
#'
#' where \eqn{x_{ij}} is the predictor value of observation \eqn{i} in L2 cluster
#' \eqn{j} and \eqn{\bar{x}_{..}} is the average \eqn{x} score.
#'
#' L1 predictor variables are centered at the group mean (CWC) by specifying
#' \code{type = "CWC"} (Default):
#'
#' \deqn{x_{ij} - \bar{x}_{.j}}
#'
#' where \eqn{\bar{x_{.j}}} is the average \eqn{x} score in cluster \eqn{j}.
#'
#' \strong{Level-2 (L1) predictor variables} in two-level data can only be
#' centered at the grand mean:
#'
#' \deqn{x_{.j} - \bar{x}_{..}}
#'
#' where \eqn{x_{.j}} is the predictor value of Level 2 cluster \eqn{j} and
#' \eqn{\bar{x}_{..}} is the average Level-2 cluster score. Note that the cluster
#' membership variable needs to be specified when centering a L2 predictor variable
#' in two-level data. Otherwise the average \eqn{x_{ij}} individual score instead
#' of the average \eqn{x_{.j}} cluster score is used to center the predictor
#' variable.
#' }
#' \item{\strong{Three-Level Data}}{\strong{Level-1 (L1) predictor variables} in
#' three-level data can be centered at the grand mean (CGM) by specifying
#' \code{type = "CGM"} (Default):
#'
#' \deqn{x_{ijk} - \bar{x}_{...}}
#'
#' where \eqn{x_{ijk}} is the predictor value of observation \eqn{i} in Level-2
#' cluster \eqn{j} within Level-3 cluster \eqn{k} and \eqn{\bar{x}_{...}} is the
#' average \eqn{x} score.
#'
#' L1 predictor variables are centered within cluster (CWC) by specifying
#' \code{type = "CWC"} (Default). However, L1 predictor variables can be either
#' centered within Level-2 clusters (\code{cwc.mean = "L2"}, Default,
#' see Brincks et al., 2017):
#'
#' \deqn{x_{ijk} - \bar{x}_{.jk}}
#'
#' or within Level-3 clusters (\code{cwc.mean = "L3"}, see Enders, 2013):
#'
#' \deqn{x_{ijk} - \bar{x}_{..k}}
#'
#' where \eqn{\bar{x}_{.jk}} is the average \eqn{x} score in Level-2 cluster
#' \eqn{j} within Level-3 cluster \eqn{k} and \eqn{\bar{x}_{..k}} is the average
#' \eqn{x} score in Level-3 cluster \eqn{k}.
#'
#' \strong{Level-2 (L2) predictor variables} in three-level data can be centered
#' at the grand mean (CGM) by specifying \code{type = "CGM"}:
#'
#' \deqn{x_{.jk} - \bar{x}_{...}}
#'
#' where \eqn{x_{.jk}} is the predictor value of Level-2 cluster \eqn{j} within
#' Level-3 cluster \eqn{k} and \eqn{\bar{x}_{...}} is the average Level-2 cluster
#' score.
#'
#' L2 predictor variables are centered within cluster (CWC) by specifying
#' \code{type = "CWC"} (Default):
#'
#' \deqn{x_{.jk} - \bar{x}_{..k}}
#'
#' where \eqn{\bar{x}_{..k}} is the average \eqn{x} score in Level-3 cluster
#' \eqn{k}.
#'
#' \strong{Level-3 (L3) predictor variables} in three-level data can only be
#' centered at the grand mean:
#'
#' \deqn{x_{..k} - \bar{x}_{...}}
#'
#' where \eqn{x_{..k}} is the predictor value of Level-3 cluster \eqn{k} and
#' \eqn{\bar{x}_{...}} is the average Level-3 cluster score. Note that the cluster
#' membership variables at Level 2 and Level 3 need to be specified when centering
#' a L3 predictor variable in three-level data.}
#' }
#'
#' @author
#' Takuya Yanagida \email{takuya.yanagida@@univie.ac.at}
#'
#' @seealso
#' \code{\link{coding}}, \code{\link{cluster.scores}}, \code{\link{rec}},
#' \code{\link{item.reverse}}, \code{\link{rwg.lindell}}, \code{\link{item.scores}}.
#'
#' @references
#' Brincks, A. M., Enders, C. K., Llabre, M. M., Bulotsky-Shearer, R. J., Prado, G.,
#' & Feaster, D. J. (2017). Centering predictor variables in three-level contextual
#' models. \emph{Multivariate Behavioral Research, 52}(2), 149–163.
#' https://doi.org/10.1080/00273171.2016.1256753
#'
#' Chang, C.-N., & Kwok, O.-M. (2022) Partitioning Variance for a Within-Level
#' Predictor in Multilevel Models. \emph{Structural Equation Modeling: A
#' Multidisciplinary Journal}. Advance online publication.
#' https://doi.org/10.1080/10705511.2022.2051175
#'
#' Enders, C. K. (2013). Centering predictors and cont
#' extual effects. In M. A.
#' Scott, J. S. Simonoff, & B. D. Marx (Eds.), \emph{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. \emph{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. \emph{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.
#' \emph{Psychological Methods}. Advance online publication.
#' https://doi.org/10.1037/met0000434
#'
#' @return
#' Returns a numeric vector or data frame with the same length or same number of
#' rows as \code{data} containing the centered variable(s).
#'
#' @export
#'
#' @examples
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Single-Level Data
#'
#' # Example 1a: Center predictor 'disp' at the grand mean
#' center(mtcars, disp, append = FALSE)
#'
#' # Alternative specification without using the '...' argument
#' center(mtcars$disp)
#'
#' # Example 1b: Center predictors 'disp' and 'hp' at the grand mean and append to 'mtcars'
#' center(mtcars, disp, hp)
#'
#' # Alternative specification without using the '...' argument
#' cbind(mtcars, center(mtcars[, c("disp", "hp")]))
#'
#' # Example 1c: Center predictor 'disp' at the value 3
#' center(mtcars, disp, value = 3)
#'
#' # Example 1d: Center predictors 'disp' and 'hp' and label with the suffix ".v"
#' center(mtcars, disp, hp, name = ".v")
#'
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Two-Level Data
#'
#' # Load data set "Demo.twolevel" in the lavaan package
#' data("Demo.twolevel", package = "lavaan")
#'
#' # Example 2a: Center L1 predictor 'y1' within cluster
#' center(Demo.twolevel, y1, cluster = "cluster")
#'
#' # Alternative specification without using the '...' argument
#' center(Demo.twolevel$y1, cluster = Demo.twolevel$cluster)
#'
#' # Example 2b: Center L2 predictor 'w2' at the grand mean
#' center(Demo.twolevel, w1, cluster = "cluster")
#'
#' # Example 2c: Center L1 predictor 'y1' within cluster and L2 predictor 'w1' at the grand mean
#' center(Demo.twolevel, y1, w1, cluster = "cluster")
#'
#' #----------------------------------------------------------------------------
#' # Predictor Variables in Three-Level Data
#'
#' # Create arbitrary three-level data
#' Demo.threelevel <- data.frame(Demo.twolevel, cluster2 = Demo.twolevel$cluster,
#' cluster3 = rep(1:10, each = 250))
#'
#' # Example 3a: Center L1 predictor 'y1' within L2 cluster
#' center(Demo.threelevel, y1, cluster = c("cluster3", "cluster2"))
#'
#' # Example 3b: Center L1 predictor 'y1' within L3 cluster
#' center(Demo.threelevel, y1, cluster = c("cluster3", "cluster2"), cwc.mean = "L3")
#'
#' # Example 3c: Center L1 predictor 'y1' within L2 cluster and L2 predictor 'w1' within L3 cluster
#' center(Demo.threelevel, y1, w1, cluster = c("cluster3", "cluster2"))
center <- function(data, ..., cluster = NULL, type = c("CGM", "CWC"),
cwc.mean = c("L2", "L3"), value = NULL, append = TRUE,
name = ".c", as.na = NULL, check = TRUE) {
#_____________________________________________________________________________
#
# Initial Check --------------------------------------------------------------
# Check if input 'data' is missing
if (isTRUE(missing(data))) { stop("Please specify a numeric vector or data frame for the argument 'data'", call. = FALSE) }
# Check if input 'data' is NULL
if (isTRUE(is.null(data))) { stop("Input specified for the argument 'data' is NULL.", call. = FALSE) }
#_____________________________________________________________________________
#
# Data -----------------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Data using the argument 'data' ####
if (isTRUE(!missing(...))) {
# Variable names
var.names <- .var.names(..., data = data, cluster = cluster)
# Extract data and convert tibble into data frame or vector
x <- data[, var.names] |> (\(y) if (isTRUE("tbl" %in% substr(class(y), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(y)) == 1L)) { unname(unlist(y)) } else { as.data.frame(y) } } else { y })()
# Cluster variable
if (isTRUE(!is.null(cluster))) { cluster <- data[, cluster] }
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Data without using the argument 'data' ####
} else {
# Convert 'data' as tibble into data frame
x <- data |> (\(y) if (isTRUE("tbl" %in% substr(class(y), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(y)) == 1L)) { unname(unlist(y)) } else { as.data.frame(y) } } else { y })()
# Data and cluster
var.group <- .var.group(data = x, cluster = cluster)
# Data
if (isTRUE(!is.null(var.group$data))) { x <- var.group$data }
# Cluster variable
if (isTRUE(!is.null(var.group$cluster))) { cluster <- var.group$cluster }
# Convert 'cluster' as tibble into data frame
if (isTRUE(!is.null(cluster) && "tbl" %in% substr(class(cluster), 1L, 3L))) { if (isTRUE(ncol(as.data.frame(cluster)) == 1L)) { cluster <- unname(unlist(cluster)) } else { cluster <- as.data.frame(cluster) } }
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Convert user-missing values into NA ####
if (isTRUE(!is.null(as.na))) { x <- .as.na(x, na = as.na) }
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Cluster variables ####
if (isTRUE(!is.null(cluster))) {
# Two cluster variables
if (isTRUE(ncol(as.data.frame(cluster)) == 2L)) {
l3.cluster <- cluster[, 1L]
l2.cluster <- cluster[, 2L]
no.clust <- "two"
# One cluster variables
} else {
no.clust <- "one"
}
}
#_____________________________________________________________________________
#
# Input Check ----------------------------------------------------------------
# Check inputs
.check.input(logical = "append", numeric = list(value = 1L), s.character = list(type = c("CGM", "CWC"), cwc.mean = c("L2", "L3")), envir = environment(), input.check = check)
# Additional checks
if (isTRUE(check)) {
# Check input 'name'
if (isTRUE(!is.null(dim(x)))) {
if (isTRUE(!is.character(name))) { stop("Please specify a character string or vector for the argument 'name'.", call. = FALSE) }
if (isTRUE(length(name) > 1L && length(name) != ncol(as.data.frame(x)))) { stop("Length of the vector specified in 'name' does not match with the number of variables.", call. = FALSE) }
}
}
#_____________________________________________________________________________
#
# Arguments ------------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Type of centering ####
if (isTRUE(all(c("L2", "L3") %in% cwc.mean))) { cwc.mean <- "L2" }
#_____________________________________________________________________________
#
# Main Function --------------------------------------------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Single variable ####
if (isTRUE(is.null(dim(x)))) {
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Variable ####
if (isTRUE(!is.null(cluster))) {
##### One cluster variable
if (isTRUE(no.clust == "one")) {
# Level 1 Variable
if (isTRUE(any(na.omit(as.vector(tapply(x, cluster, var, na.rm = TRUE))) != 0L))) {
vartype <- "L1"
# Level 2 Variable
} else {
vartype = "L2"
}
##### Two cluster variable s
} else if (isTRUE(no.clust == "two")) {
# Level 1 Variable
if (isTRUE(any(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) != 0L))) {
vartype <- "L1"
# Level 2 Variable
} else if (isTRUE(all(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) == 0L) && any(as.vector(tapply(x, cluster[, 1L], var, na.rm = TRUE)) != 0L))) {
vartype <- "L2"
# Level 3 Variable
} else if (isTRUE(all(na.omit(as.vector(tapply(x, apply(cluster, 1L, paste, collapse = ""), var, na.rm = TRUE))) == 0L) && all(na.omit(as.vector(tapply(x, cluster[, 1L], var, na.rm = TRUE))) == 0L))) {
vartype <- "L3"
}
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Type of centering ####
if (isTRUE(all(c("CGM", "CWC") %in% type))) {
#...................
### Single-level ####
if (isTRUE(is.null(cluster))) {
type <- "CGM"
#...................
### Multilevel ####
} else {
##### One cluster variable
if (isTRUE(no.clust == "one")) {
type <- switch(vartype, L1 = "CWC", L2 = "CGM")
##### Two cluster variable s
} else if (isTRUE(no.clust == "two")) {
type <- switch(vartype, L1 = "CWC", L2 = "CWC", L3 = "CGM")
}
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Centering ####
#...................
### No cluster variable ####
if (isTRUE(is.null(cluster))) {
##### Mean centering
if (isTRUE(is.null(value))) {
object <- as.numeric(scale(x, scale = FALSE))
##### Centering on a user-defined value
} else {
object <- x - mean(x, na.rm = TRUE) + value
}
#...................
### One cluster variable ####
} else if (isTRUE(no.clust == "one")) {
##### Centering at the grand mean (CGM)
if (isTRUE(type == "CGM")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- as.numeric(scale(x, scale = FALSE))
# Level 2 predictor
}, L2 = {
object <- x - mean(x[which(!duplicated(cluster))], na.rm = TRUE)
})
##### Centering within cluster (CWC)
} else if (isTRUE(type == "CWC")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- unname(x - misty::cluster.scores(x, cluster = cluster, fun = "mean", check = FALSE, expand = TRUE))
# Level 2 predictor
}, L2 = {
# Note, level 2 predictor can only be centered at the grand mean
object <- x - mean(x[which(!duplicated(cluster))], na.rm = TRUE)
})
}
#...................
### Two cluster variables ####
} else if (isTRUE(no.clust == "two")) {
##### Centering at the grand mean (CGM)
if (isTRUE(type == "CGM")) {
switch(vartype,
# Level 1 predictor
L1 = {
object <- as.numeric(scale(x, scale = FALSE))
# Level 2 predictor
}, L2 = {
object <- x - mean(x[which(!duplicated(apply(cluster, 1L, paste, collapse = "")))], na.rm = TRUE)
# Level 3 predictor
}, L3 = {
object <- x - mean(x[which(!duplicated(cluster[, 1L]))], na.rm = TRUE)
})
##### Centering within cluster (CWC)
} else if (isTRUE(type == "CWC")) {
switch(vartype,
# Level 1 predictor
L1 = {
switch(cwc.mean,
# Deviation from the Level-2 cluster mean
L2 = {
object <- unname(x - misty::cluster.scores(x, cluster = apply(cluster, 1L, paste, collapse = ""), fun = "mean", check = FALSE, expand = TRUE))
# Deviation from the Level-3 cluster mean
}, L3 = {
object <- x - misty::cluster.scores(x, cluster = cluster[, 1L])
})
# Level 2 predictor
}, L2 = {
object <- (data.frame(x, cluster3 = cluster[, 1L], cluster2 = cluster[, 2]) |>
(\(y) misty::cluster.scores(y[!duplicated(y$cluster2), ], x, cluster = "cluster3"))() |>
(\(z) data.frame(z, object = z$x - z$x.a))() |>
(\(q) merge(data.frame(by = apply(cluster[, c("cluster3", "cluster2")], 1L, paste, collapse = "")),
data.frame(object = q$object, by = apply(q[, c("cluster3", "cluster2")], 1L, paste, collapse = "")), by = "by", sort = FALSE))())[, "object"]
# Level 3 predictor
}, L3 = {
# Note, level 3 predictor can only be centered at the grand mean
object <- x - mean(x[which(!duplicated(cluster[, 1L]))], na.rm = TRUE)
})
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Multiple variables ####
} else {
object <- data.frame(vapply(x, misty::center, cluster = cluster, type = type, cwc.mean = cwc.mean, value = value, as.na = as.na, check = FALSE, FUN.VALUE = double(nrow(x))))
#...................
### Variable names ####
if (isTRUE(length(name) == 1L)) {
colnames(object) <- paste0(colnames(object), name)
} else {
colnames(object) <- name
}
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## Append ####
if (isTRUE(!missing(...) && append)) {
if (isTRUE(is.null(dim(x)))) {
#...................
### Variable names ####
if (isTRUE(name == ".c")) {
object <- setNames(as.data.frame(object), nm = paste0(var.names, ".c"))
} else {
object <- setNames(as.data.frame(object), nm = name)
}
}
object <- data.frame(data, object)
}
#_____________________________________________________________________________
#
# Return Object --------------------------------------------------------------
return(object)
}
#_______________________________________________________________________________
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