heplots (version 1.7.8)

distancePlot: Distance Plot for Multivariate Model Diagnosis

Description

This plot, suggested by Rousseeuw & van Zomeren (1991), Rousseeu 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.

This diagnostic plot combines the information on regression outliers and leverage points, and often more useful than either distance separately.

Usage

distancePlot(X, Y, ...)
# S3 method for default
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 formula
distancePlot(X, Y, data, ...)
# S3 method for mlm
distancePlot(X, ...)

Value

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

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 \(\sqrt{\chi^2_{k, \text{level}}}\).

References

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. tools:::Rd_expr_doi("10.1198/004017004000000329").

See Also

Mahalanobis

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)

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