distancePlot: Distance Plot for Multivariate Model Diagnosis

In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Distance Plot for Multivariate Model Diagnosis

Description

This plot, suggested by Rousseeuw & van Zomeren (1991), Rousseeuw et al. (2004) typically plots Mahalanobis distances (D) of the Y response variables against the distances of the X variables in a multivariate linear model (MLM). When applied to a multivariate linear model itself, it plots the distances of the residuals for the Y variables against the predictor terms in the model.matrix X. The motivation behind this plot was to contribute to understanding robust methods for multivariate linear models, such as implemented here in robmlm().

This diagnostic plot combines the information on regression outliers and leverage points, and often more useful than either distance separately, because it shows WHY observations are unusual, either in X or Y space or both. In spirit, it is similar to the ideas behind influence plots for univariate models, such as car::influencePlot() and the multivariate analogs provided in the mvinfluence package via influencePlot().

Usage

distancePlot(X, Y, ...)

## Default S3 method:
distancePlot(
  X,
  Y,
  method = c("classical", "mcd", "mve"),
  level = 0.975,
  ids = rownames(X),
  pch = c(1, 16),
  col = c("black", "red"),
  label.pos = 2,
  xlab,
  ylab,
  verbose = FALSE,
  ...
)

## S3 method for class 'formula'
distancePlot(X, Y, data, ...)

## S3 method for class 'mlm'
distancePlot(X, ...)

Arguments

X	A multivariate linear model fit by lm, or a numeric data frame giving the predictors in the MLM
Y	A numeric data frame giving the responses in the MLM or the residuals
...	Other arguments passed to methods
method	Estimation method used for center and covariance, one of: "classical" (product-moment), "mcd" (minimum covariance determinant), or "mve" (minimum volume ellipsoid).
level	Lower-tail probability beyond which observations will be labeled.
ids	Labels for observations
pch	A vector of two point symbols, for the regular points and those beyond the cutoffs
col	A vector of two colors, for the regular points and those beyond the cutoffs
label.pos	Position of the label relative to the point; see text
xlab	Label stub for horizontal axis
ylab	Label stub for vertical axis
verbose	Logical; if TRUE print the cutoff values to the console
data	For the formula method, the dataset containing the variables

Details

Observations with "large" distances on X or Y are labeled with their ids. The cutoffs are calculated as \sqrt{\chi^2_{k, \text{level}}}.

The method argument provides a specification the covariance matrix used to calculate the Mahalanobis distances shown in this plot.

Value

   Returns invisibly a data frame containing the distances, `distX`, `distY`

References

Rousseeuw, P. J., & van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85(411), 633-639. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1990.10474920")}.

Rousseeuw P. J. & van Zomeren B. C. (1991). “Robust Distances: Simulation and Cutoff Values.” In W Stahel, S Weisberg (eds.), Directions in Robust Statistics and Diagnostics, Part II. Springer-Verlag, New York.

Rousseeuw, P. J., Van Driessen, K., Van Aelst, S., & Agullo, J. (2004). Robust multivariate regression. Technometrics, 46(3), 293–305. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/004017004000000329")}.

See Also

Mahalanobis, robmlm

Other diagnostic plots: cqplot(), eigstatCI(), plot.boxM()

Examples

if(require("robustbase")) {
  # Examples from Rousseeuw etal (2004)
  data(pulpfiber, package="robustbase")
  # Figure 1
  distancePlot(pulpfiber[, 1:4], pulpfiber[, 5:8])   
  # Figure 3
  pulp.mod <- lm(cbind(Y1, Y2, Y3, Y4) ~ X1 + X2 + X3 + X4, data = pulpfiber)
  distancePlot(pulp.mod, method = "mcd")
}

# NLSY data
data(NLSY, package = "heplots")
NLSY.mlm <- lm(cbind(math, read) ~ income + educ + antisoc + hyperact,
               data = NLSY)

distancePlot(NLSY.mlm)

# gives the same result
distancePlot(NLSY[, 3:6], residuals(NLSY.mlm), level = 0.975)

distancePlot(NLSY.mlm, method ="mve")

# distancePlot(cbind(math, read) ~ income + educ + antisoc + hyperact,
#                data = NLSY)

# schooldata dataset
data(schooldata)
school.mod <- lm(cbind(reading, mathematics, selfesteem) ~ ., data=schooldata)
distancePlot(school.mod, cex = 1.5, cex.lab = 1.2)

data(Hernior)
Hern.mod <- lm(cbind(leave, nurse, los) ~
               age + sex +  pstat +  build + cardiac + resp, data=Hernior)
distancePlot(Hern.mod)

heplots documentation built on Aug. 23, 2026, 5:07 p.m.