Outlier Map of a Robust PCA or Robust PLS Model

Plots the orthogonal distance of each observation against its score distance, for a robust PCA fitted by robpca(), rospca(), macropca() or cellpca() (Hubert, Rousseeuw and Vanden Branden, 2005). For cellpca(), the vertical axis is the norm of the standardized residuals, as in the enhanced outlier map of Centofanti, Hubert and Rousseeuw. For a robust calibration model fitted by rsimpls() or rpcr(), it is by default the regression outlier map of Hubert and Vanden Branden (2003): the residual distance (with one response, the absolute standardized residual) against the score distance. With map = "score", it is the score outlier map of the predictors: the orthogonal distance of each spectrum to the model against its score distance, as for a robust PCA.

Usage

plot_outlier_map(
  object,
  newdata = NULL,
  labels = 3,
  relative = FALSE,
  shade = FALSE,
  log = FALSE,
  colour_by = c("type", "distance"),
  title = NULL,
  map = c("regression", "score"),
  ...
)

Arguments

object: An object returned by robpca(), rospca(), macropca(), cellpca(), rsimpls() or rpcr().
newdata: Optional new observations to add to the map (a numeric matrix or data frame with the calibration variables). Not available for the regression outlier map of rsimpls() and rpcr() fits.
labels: The number of most outlying observations to label (by their row names, or row numbers). Default is 3; use 0 for no labels.
relative: If TRUE, plot the reduced distances (divided by their cut-offs). Default is FALSE.
shade: If TRUE, shade the three outlying regions in grey, darker for more harmful observations (good leverage, orthogonal outliers, bad leverage), and name them in their corners. The region of regular observations stays white. Default is FALSE.
log: If TRUE, use logarithmic axes, which spread out the regular observations when a few are far away. Zero distances are drawn at the smallest positive distance. Default is FALSE.
colour_by: The colors of the points: "type" (default), by outlier type, or "distance", by their reduced distance from the origin, \(\max(SD/c_{SD}, OD/c_{OD})\), on a rainbow scale from dark red (the closest) to blue (the farthest). With relative = TRUE, where both cut-offs are at 1, yellow marks the cut-offs: dark red through orange for the regular observations, then green and blue for the outlying ones. Otherwise, the colors spread evenly over the distances.
title: The plot title.
map: For rsimpls() and rpcr() fits, the map to draw: "regression" (default), the regression outlier map, or "score", the score outlier map of the predictors. Not used for robust PCA fits.
...: Further arguments passed to ggplot2::geom_point() to style the points, such as alpha (default 0.85), size (2.2), stroke (0.4) or colour (the outline, "black"). size can also be a numeric vector with one value per sample (the calibration samples, then those of newdata), such as the concentration of an element, to vary the size of the points, with a legend.

Value

A ggplot object.

Details

The dashed lines are the cut-offs of the two distances. They divide the map into four types of observations:

regular observations (bottom left);
good leverage points (bottom right): far from the center, but close to the PCA subspace, so they follow the structure of the data;
orthogonal outliers (top left): close to the center once projected, but far from the PCA subspace;
bad leverage points (top right): far on both counts, the most harmful outliers.

In the regression outlier map of rsimpls() or rpcr(), the top left region holds the vertical outliers: observations with a typical spectrum but a large residual, such as a wrong reference value. Bad leverage points have both an outlying spectrum and a large residual; good leverage points have an outlying spectrum that the model still fits.

New observations (newdata) are projected onto the model with predict() (or predict() for the score outlier map of an rsimpls() or rpcr() fit) and shown with the calibration cut-offs, which is how new spectra are screened before prediction.

With relative = TRUE, each distance is divided by its cut-off (the reduced score and orthogonal distances), so both cut-offs are at 1 whatever the model. This puts maps of different models (for example, with different numbers of components) on the same scale. A relative distance tells where an observation falls with respect to the cut-off, not how unlikely it is: twice the cut-off is not equally rare in every model.

Author

Christian L. Goueguel

Examples

spectra_id <- forageLIBS |> dplyr::select(1:2) |> names()
minerals <- forageLIBS |> dplyr::select(3:14) |> names()
set.seed(1)
fit <- forageLIBS |>
  dplyr::select(-dplyr::all_of(c(spectra_id, minerals))) |>
  center() |>
  robpca()

plot_outlier_map(fit, relative = TRUE, shade = TRUE, log = TRUE)

plot_outlier_map(fit, relative = TRUE, shade = TRUE, log = TRUE,
labels = 10, colour_by = "distance")