TRC function

Transformed rank correlations for multivariate outlier detection

TRC starts from bivariate Spearman correlations and obtains a positive definite covariance matrix by back-transforming robust univariate medians and mads of the eigenspace. TRC can cope with missing values by a regression imputation using the a robust regression on the best predictor and it takes sampling weights into account.

TRC(
  data,
  weights,
  overlap = 3,
  mincor = 0,
  robust.regression = "rank",
  gamma = 0.5,
  prob.quantile = 0.75,
  alpha = 0.05,
  md.type = "m",
  monitor = FALSE
)

Arguments

• data: a data frame or matrix with the data.
• weights: sampling weights.
• overlap: minimum number of jointly observed values for calculating the rank correlation.
• mincor: minimal absolute correlation to impute.
• robust.regression: type of regression: "irls" is iteratively reweighted least squares M-estimator, "rank" is based on the rank correlations.
• gamma: minimal number of jointly observed values to impute.
• prob.quantile: if mads are 0, try this quantile of absolute deviations.
• alpha: (1 - alpha) Quantile of F-distribution is used for cut-off.
• md.type: type of Mahalanobis distance when missing values occur: "m" marginal (default), "c" conditional.
• monitor: if TRUE, verbose output.

Returns

TRC returns a list whose first component output is a sublist with the following components:

• sample.size: Number of observations
• number.of.variables: Number of variables
• number.of.missing.items: Number of missing values
• significance.level: 1 - alpha
• computation.time: Elapsed computation time
• medians: Componentwise medians
• mads: Componentwise mads
• center: Location estimate
• scatter: Covariance estimate
• robust.regression: Input parameter
• md.type: Input parameter
• cutpoint: The default threshold MD-value for the cut-off of outliers

The further components returned by TRC are:

• outind: Indicator of outliers
• dist: Mahalanobis distances (with missing values)

Details

TRC is similar to a one-step OGK estimator where the starting covariances are obtained from rank correlations and an ad hoc missing value imputation plus weighting is provided.

Examples

data(bushfirem, bushfire.weights)
det.res <- TRC(bushfirem, weights = bushfire.weights)
PlotMD(det.res$dist, ncol(bushfirem))
print(det.res)

References

Béguin, C. and Hulliger, B. (2004) Multivariate outlier detection in incomplete survey data: the epidemic algorithm and transformed rank correlations, JRSS-A, 167, Part 2, pp. 275-294.

Author(s)

Beat Hulliger