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cor_to_pcor.R
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cor_to_pcor.R
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#' Correlation Matrix to (Semi) Partial Correlations
#'
#' Convert a correlation matrix to a (semi)partial correlation matrix. Partial
#' correlations are a measure of the correlation between two variables that
#' remains after controlling for (i.e., "partialling" out) all the other
#' relationships. They can be used for graphical Gaussian models, as they
#' represent the direct interactions between two variables, conditioned on all
#' remaining variables. This means that the squared partial correlation between
#' a predictor X1 and a response variable Y can be interpreted as the proportion
#' of (unique) variance accounted for by X1 relative to the residual or
#' unexplained variance of Y that cannot be accounted by the other variables.
#'
#' The semi-partial correlation is similar to the partial correlation statistic.
#' However, it represents (when squared) the proportion of (unique) variance
#' accounted for by the predictor X1, relative to the total variance of Y. Thus,
#' it might be seen as a better indicator of the "practical relevance" of a
#' predictor, because it is scaled to (i.e., relative to) the total variability
#' in the response variable.
#'
#' @param cor A correlation matrix, or a partial or a semipartial
#' correlation matrix.
#' @param pcor A correlation matrix, or a partial or a semipartial
#' correlation matrix.
#' @param cov A covariance matrix (or a vector of the SD of the variables).
#' Required for semi-partial correlations.
#' @param tol Relative tolerance to detect zero singular values.
#'
#' @return The (semi) partial correlation matrix.
#'
#' @examples
#' cor <- cor(iris[1:4])
#'
#' # Partialize
#' cor_to_pcor(cor)
#' cor_to_spcor(cor, cov = sapply(iris[1:4], sd))
#'
#' # Inverse
#' round(pcor_to_cor(cor_to_pcor(cor)) - cor, 2) # Should be 0
#' @export
cor_to_pcor <- function(cor, tol = .Machine$double.eps^(2 / 3)) {
UseMethod("cor_to_pcor")
}
#' @export
cor_to_pcor.matrix <- function(cor, tol = .Machine$double.eps^(2 / 3)) {
cor <- .get_cor(cor, cov = NULL)
.cor_to_pcor(cor)
}
#' @export
cor_to_pcor.easycormatrix <- function(cor, tol = .Machine$double.eps^(2 / 3)) {
if (inherits(cor, "matrix")) {
NextMethod()
} else {
.cor_to_pcor_easycormatrix(cor = cor, tol = tol)
}
}
#' @export
cor_to_pcor.easycorrelation <- function(cor, tol = .Machine$double.eps^(2 / 3)) {
.cor_to_pcor_easycorrelation(cor = cor, tol = tol)
}
# pcor to cor -------------------------------------------------------------
#' @rdname cor_to_pcor
#' @export
pcor_to_cor <- function(pcor, tol = .Machine$double.eps^(2 / 3)) {
UseMethod("pcor_to_cor")
}
#' @export
pcor_to_cor.matrix <- function(pcor, tol = .Machine$double.eps^(2 / 3)) {
pcor <- .get_cor(pcor, cov = NULL)
.pcor_to_cor(pcor)
}
#' @export
pcor_to_cor.easycormatrix <- function(pcor, tol = .Machine$double.eps^(2 / 3)) {
if (inherits(pcor, "matrix")) {
NextMethod()
} else {
.cor_to_pcor_easycormatrix(pcor = pcor, tol = tol)
}
}
#' @export
pcor_to_cor.easycorrelation <- function(pcor, tol = .Machine$double.eps^(2 / 3)) {
.cor_to_pcor_easycorrelation(pcor = pcor, tol = tol)
}
# Convenience Functions --------------------------------------------------------
#' @keywords internal
.cor_to_pcor_easycorrelation <- function(pcor = NULL, cor = NULL, tol = .Machine$double.eps^(2 / 3)) {
if (is.null(cor)) {
r <- .pcor_to_cor(.get_cor(summary(pcor, redundant = TRUE), cov = NULL))
cor <- pcor
} else {
r <- .cor_to_pcor(.get_cor(summary(cor, redundant = TRUE), cov = NULL))
}
# Extract info
p_adjust <- attributes(cor)$p_adjust
number_obs <- as.matrix(attributes(summary(cor, redundant = TRUE))$n_Obs[-1])
# Get Statistics
p <- cor_to_p(r, n = number_obs, method = "pearson")
ci_vals <- cor_to_ci(r, n = number_obs, ci = attributes(cor)$ci)
# Replace
newdata <- data.frame()
for (i in seq_len(nrow(cor))) {
row_index <- row.names(r) == cor[i, "Parameter1"]
col_index <- colnames(r) == cor[i, "Parameter2"]
newdata <- rbind(
newdata,
data.frame(
r = r[row_index, col_index],
CI_low = ci_vals$CI_low[row_index, col_index],
CI_high = ci_vals$CI_high[row_index, col_index],
t = p$statistic[row_index, col_index],
df_error = number_obs[row_index, col_index] - 2,
p = p$p[row_index, col_index],
Method = "Pearson",
n_Obs = number_obs[row_index, col_index],
stringsAsFactors = FALSE
)
)
}
# Fix for spearman
if (any(cor$Method %in% c("Spearman", "Kendall"))) {
newdata$df <- NULL
if (any(cor$Method == "Spearman")) {
names(newdata)[names(newdata) == "t"] <- "S"
newdata$Method <- "Spearman"
} else {
names(newdata)[names(newdata) == "t"] <- "z"
newdata$Method <- "Kendall"
}
}
# Format
newdata <- cbind(cor[1:2], newdata)
cor <- cor[, seq_len(ncol(newdata))]
cor[, ] <- newdata
names(cor) <- names(newdata)
# P-values adjustments
cor$p <- stats::p.adjust(cor$p, method = p_adjust, n = nrow(cor))
attributes(cor)$p_adjust <- p_adjust
cor
}
#' @keywords internal
.cor_to_pcor_easycormatrix <- function(pcor = NULL, cor = NULL, tol = .Machine$double.eps^(2 / 3)) {
if (is.null(cor)) {
r <- .pcor_to_cor(.get_cor(pcor, cov = NULL))
cor <- pcor
} else {
r <- .cor_to_pcor(.get_cor(cor, cov = NULL))
}
# Extract info
if (inherits(cor, "matrix")) {
return(r)
}
p_adjust <- attributes(cor)$p_adjust
number_obs <- as.matrix(attributes(cor)$n_Obs[-1])
p <- cor_to_p(r, n = number_obs, method = "pearson")
ci_vals <- cor_to_ci(r, n = number_obs, ci = attributes(cor)$ci)
r <- cbind(data.frame(Parameter = row.names(r)), r)
row.names(r) <- NULL
# P-values adjustments
n_comp <- sum(upper.tri(p$p))
p$p[upper.tri(p$p)] <- stats::p.adjust(p$p[upper.tri(p$p)], method = p_adjust, n = n_comp)
p$p[lower.tri(p$p)] <- stats::p.adjust(p$p[lower.tri(p$p)], method = p_adjust, n = n_comp)
attributes(cor)$p_adjust <- p_adjust
# Statistic and p-value
attributes(cor)$pd <- attributes(cor)$BF <- NULL
attributes(cor)$p[-1] <- p$p
attributes(cor)$t[-1] <- p$statistic
attributes(cor)$CI_low[-1] <- ci_vals$CI_low
attributes(cor)$CI_high[-1] <- ci_vals$CI_high
attributes(r) <- attributes(cor)
r
}
#' @keywords internal
.cor_to_pcor <- function(cor, tol = .Machine$double.eps^(2 / 3)) {
# Get cor
cor <- .get_cor(cor, cov = NULL)
# Partial
inverted <- .invert_matrix(cor, tol = tol)
out <- -stats::cov2cor(inverted)
diag(out) <- 1
out
}
#' @keywords internal
.pcor_to_cor <- function(pcor, tol = .Machine$double.eps^(2 / 3)) {
# negate off-diagonal entries, then invert
m <- -pcor
diag(m) <- -diag(m)
inverted <- .invert_matrix(m, tol = tol)
out <- stats::cov2cor(inverted)
out
}
# Internals ---------------------------------------------------------------
#' @keywords internal
.get_cor <- function(cor = NULL, cov = NULL) {
# Get Cormatrix
if (is.null(cor)) {
if (is.null(cov)) {
insight::format_error("A correlation or covariance matrix is required.")
}
cor <- stats::cov2cor(cov)
} else if (inherits(cor, "easycormatrix") && colnames(cor)[1] == "Parameter") {
row.names(cor) <- cor$Parameter
cor <- as.matrix(cor[-1])
}
cor
}