mvTopCoding function

Detection and winsorization of multivariate outliers

Imputation and detection of outliers

mvTopCoding(x, maha = NULL, center = NULL, cov = NULL, alpha = 0.025)

Arguments

• x: an object coercible to a data.table containing numeric entries
• maha: squared mahalanobis distance of each observation
• center: center of data, needed for calculation of mahalanobis distance (if not provided)
• cov: covariance matrix of data, needed for calcualtion of mahalanobis distance (if not provided)
• alpha: significance level, determining the ellipsoide to which outliers should be placed upon

Returns

the imputed winsorized data

Details

Winsorizes the potential outliers on the ellipsoid defined by (robust) Mahalanobis distances in direction to the center of the data

Examples

set.seed(123)
x <- MASS::mvrnorm(20, mu = c(5,5), Sigma = matrix(c(1,0.9,0.9,1), ncol = 2))
x[1, 1] <- 3
x[1, 2] <- 6
plot(x)
ximp <- mvTopCoding(x)
points(ximp, col = "blue", pch = 4)

# more dimensions
Sigma <- diag(5)
Sigma[upper.tri(Sigma)] <- 0.9
Sigma[lower.tri(Sigma)] <- 0.9
x <- MASS::mvrnorm(20, mu = rep(5,5), Sigma = Sigma)
x[1, 1] <- 3
x[1, 2] <- 6
pairs(x)

ximp <- mvTopCoding(x)
xnew <- data.frame(rbind(x, ximp))
xnew$beforeafter <- rep(c(0,1), each = nrow(x))
pairs(xnew, col = xnew$beforeafter, pch = 4)

# by hand (non-robust)
x[2,2] <- NA
m <- colMeans(x, na.rm = TRUE)
s <- cov(x, use = "complete.obs")
md <- stats::mahalanobis(x, m, s)
ximp <- mvTopCoding(x, center = m, cov = s, maha = md)
plot(x)
points(ximp, col = "blue", pch = 4)

Author(s)

Johannes Gussenbauer, Matthias Templ