Distance Plot for Multivariate Model Diagnosis

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, ...)

# 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

Value

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

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. doi:10.1198/004017004000000329 .

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")
}
#> Loading required package: robustbase
#> 0.975 distance cutoffs: 3.338156 3.338156 

#> 0.975 distance cutoffs: 3.338156 3.338156 


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

distancePlot(NLSY.mlm)
#> 0.975 distance cutoffs: 3.338156 2.716203 


# gives the same result
distancePlot(NLSY[, 3:6], residuals(NLSY.mlm), level = 0.975)
#> 0.975 distance cutoffs: 3.338156 2.716203 


distancePlot(NLSY.mlm, method ="mve")
#> 0.975 distance cutoffs: 3.338156 2.716203 


# 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)
#> 0.975 distance cutoffs: 3.582248 3.057516 


data(Hernior)
Hern.mod <- lm(cbind(leave, nurse, los) ~
               age + sex +  pstat +  build + cardiac + resp, data=Hernior)
distancePlot(Hern.mod)
#> 0.975 distance cutoffs: 3.801233 3.057516