Select among correlated variables based on a given criterion

Correlations among variables are problematic in multivariate models, as they inflate the variance of coefficients and thus may bias the interpretation of the effects of those variables on the response. One of the strategies to circumvent this problem is to eliminate a priori one from each pair of correlated variables, but it is not always straightforward to pick the right variable among these. The corSelect function selects among correlated variables based either on their (stepwise) variance inflation factor (VIF); or on their relationship with the response variable, by building a bivariate model of each individual variable against the response and choosing, among each of two correlated variables, the one with the best p-value, AIC or BIC.

This function is now included in fuzzySim and depends on other functions in the package, such as FDR and multicol. It is also included as a new option within function multGLM in this package, so that multiple models can be built based on uncorrelated variables chosen appropriately for each species.

corSelect <- function(data, sp.cols = NULL, var.cols, cor.thresh = 0.8, select = "p.value", ...) {

# version 1.6 (6 Jul 2017)

if (length(sp.cols) > 1) stop ("Sorry, 'corSelect' is currently implemented for only one 'sp.col' at a time.")

univar.criteria <- c("VIF")
 bivar.criteria <- c("p.value", "AIC", "BIC")

if (!(select %in% c(univar.criteria, bivar.criteria))) stop ("Invalid 'select' criterion.")

if (!is.null(sp.cols) & select %in% bivar.criteria) { <- nrow(data)
 data <- data[is.finite(data[ , sp.cols]), ]
 n.out <- nrow(data)
 if (n.out < warning ( - n.out, " observations removed due to missing data in 'sp.cols'; ", n.out, " observations actually evaluated.")

cor.mat <- cor(data[ , var.cols], ...)
 cor.mat[upper.tri(cor.mat, diag = TRUE)] <- NA
 high.cor.mat <- bivar.mat <- numeric(0)

if (max(abs(cor.mat), na.rm = TRUE) >= cor.thresh) {
 high.cor.rowcol <- as.matrix(which(abs(cor.mat) >= cor.thresh, arr.ind = TRUE))
 high.cor.inds <- sort(unique(as.vector(high.cor.rowcol)))
 high.cor.mat <- data.frame(var1 = rownames(cor.mat)[high.cor.rowcol[ , "row"]], var2 = colnames(cor.mat)[high.cor.rowcol[ , "col"]])
 high.cor.mat$corr <- NULL
 for (r in 1:nrow(high.cor.mat)) high.cor.mat$corr[r] <- cor.mat[high.cor.rowcol[ ,"row"][r], high.cor.rowcol[ ,"col"][r]]
 high.cor.mat <- high.cor.mat[order(abs(high.cor.mat$corr), decreasing = TRUE), ]

if (is.null(sp.cols) & select %in% bivar.criteria) {
 message("Bivariate relationships not assessable without a response variable ('sp.cols'). Returning high pairwise correlations among 'var.cols'.")
 return (high.cor.mat)

high.cor.vars <- unique(rownames(cor.mat[high.cor.inds, high.cor.inds]))

if (select %in% bivar.criteria) {
 bivar.mat <- FDR(data = data, sp.cols = sp.cols, var.cols = match(high.cor.vars, colnames(data)), simplif = TRUE)[ , c("p.value", "AIC", "BIC")]
 if (all.equal(order(bivar.mat[ , c("p.value")]), order(bivar.mat[ , c("AIC")]), order(bivar.mat[ , c("BIC")]))) message("Results identical using whether p-value, AIC or BIC to select variables.\n")
 else message("Results NOT identical using whether p-value, AIC or BIC to select variables.\n")
 } # end if select in bivar

data.remaining <- data[ , var.cols]
 while (max(abs(cor.mat), na.rm = TRUE) >= cor.thresh) {
 max.cor.ind <- which(abs(cor.mat) == max(abs(cor.mat), na.rm = TRUE), arr.ind = TRUE)
 v1 <- rownames(cor.mat)[max.cor.ind[1]]
 v2 <- colnames(cor.mat)[max.cor.ind[2]]
 if (select %in% univar.criteria) {
 vif <- multicol(data.remaining)
 targets <- vif[c(v1, v2), "VIF", drop = FALSE]
 } # end if univar
 else if (select %in% bivar.criteria) {
 targets <- bivar.mat[c(v1, v2), select, drop = FALSE]
 } # end if bivar

exclude <- which.max(as.matrix(targets)) <- rownames(targets)[exclude]
 excl.ind <- match(, colnames(cor.mat))
 data.remaining <- data.remaining[ , -excl.ind, drop = FALSE]
 cor.mat <- cor.mat[-excl.ind, -excl.ind, drop = FALSE]
 if (all( cor.mat <- numeric(0)
 if (length(cor.mat) == 0) break
 } # end while max

} # end if max > thresh

selected.vars <- colnames(cor.mat)
 selected.var.cols <- match(colnames(cor.mat), colnames(data))
 excluded.vars <- colnames(data)[var.cols][!(colnames(data)[var.cols] %in% colnames(cor.mat))]

vif2 <- multicol(data[ , selected.var.cols])

list(high.correlations = high.cor.mat,
 bivariate.significance = bivar.mat,
 excluded.vars = excluded.vars,
 selected.vars = selected.vars,
 selected.var.cols = selected.var.cols,
 strongest.remaining.corr = cor.mat[which.max(abs(cor.mat))],
 remaining.multicollinearity = vif2
} # end corSelect function


You can install and load fuzzySim (>=version 1.5) and then check help(corSelect) for reproducible usage examples.



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