outlierplot {compositions}

Plot various graphics to analyse outliers.

Description

A collection of plots emphasing different aspects of possible outliers.

Usage

outlierplot(X,...)
## S3 method for class 'acomp'
outlierplot(X,colcode=colorsForOutliers1,
  pchcode=pchForOutliers1,
  type=c("scatter","biplot","dendrogram","ecdf","portion","nout","distdist"),
  legend.position,pch=19,...,clusterMethod="ward",
  myCls=classifier(X,alpha=alpha,type=class.type,corrected=corrected),
  classifier=OutlierClassifier1,
  alpha=0.05,
  class.type="best",
  Legend,pow=1,
  main=paste(deparse(substitute(X))),
  corrected=TRUE,robust=TRUE,princomp.robust=FALSE,
                              mahRange=exp(c(-5,5))^pow,
                              flagColor="red",
                              meanColor="blue",
                              grayColor="gray40",
                              goodColor="green",
                              mahalanobisLabel="Mahalanobis Distance"
                              )

Arguments

X

The dataset as an acomp object

colcode

A color palette for factor given by the myCls, or function to create it from the factor. Use colorForOutliers2 if class.method="all" is used.

pchcode

A function to create a plot character palette for the factor returned by the myCls call

type

The type of plot to be produced. See details for more precise definitions.

legend.position

The location of the legend. Must!!! be given to draw a classical legend.

pch

A default plotting char

...

Further arguments to the used plotting function

clusterMethod

The clustering method for hclust based outlier grouping.

myCls

A factor presenting the groups of outliers

classifier

The routine to create a factor presenting the groups of outliers heuristically. It is only used in the default argument to myCls.

alpha

The confidence level to be used for outlier classification tests

class.type

The type of classification that should be generated by classifier

Legend

The content will be substituted and stored as list entry legend in the result of the function. It can than be evaluated to actually create a seperate legend on another device (e.g. for publications).

pow

The power of Mahalanobis distances to be used.

main

The title of the graphic

corrected

Literature typically proposes to compare the Mahalanobis distances with the distribution of a random Mahalanobis distance. However it would be needed to correct this for (dependent) multiple testing, since we always test the whole dataset, which means comparing against the distribution of the maximum Mahalanobis distance. This argument switches to this second behavior, giving less outliers.

robust

A robustness description as define in robustnessInCompositions

princomp.robust

Either a logical determining wether or not the principal component analysis should be done robustly or a principal component object for the dataset.

mahRange

The range of Mahalanobis distances displayed. This is fixed to make views comparable among datasets. However if the preset default is not enough a warning is issued and a red mark is drawn in the plot

flagColor

The color to draw critical situations.

meanColor

The color to draw typical curves.

goodColor

The color to draw confidence bounds.

grayColor

The color to draw less important things.

mahalanobisLabel

The axis label to be used for axes displaying Mahalanobis distances.

Details

See outliersInCompositions for a comprehensive introduction into the outlier treatment in compositions.

type="scatter"

Produces an appropriate standard plot such as a tenary diagram with the outliers marked by there codes according to the given classifier and colorcoding and pch coding.
This shows the actual values of the identified outliers.

type="biplot"

Creates a biplot based on a nonrobust principal component analysis showing the outliers classified through outliers in the given color scheme. We use the nonrobust principal component analyis since it rotates according to a good visibility of the extreme values.
This shows the position of the outliers in the usual principal components analysis. However note that a coloredBiplot is used rather than the usual one.

type="dendrogram"

Shows a dendrogram based on robust Mahalanobis distance based hierachical clustering, where the observations are labeled with the identified outlier classes.
This plot can be used to see how good different categories of outliers cluster.

type="ecdf"

This plot provides a cummulated distribution function of the Mahalanobis distances along with an expeced curve and a lower confidence limit. The empirical cdf is plotted in the default color. The expected cdf is displayed in meanColor. The alpha-quantile – i.e. a lower prediction bound – for the cdf is given in goodColor. A line in grayColor show the minium portion of observations above some limit to be outliers, based on the portion of observations necessary to move down to make the empirical distribution function get above its lower prediction limit under the assumption of normality.
This plot shows the basic construction for the minimal number of outlier computation done in type="portion".

type="portion"

This plot focusses on numbers of outliers. The horizontal axis give Mahalanobis distances and the vertical axis number of observations. In meanColor we see a curve of an estimated number of outliers above some limit, generated by estimating the portion of outliers with a Mahalanobis distance over the given limit by max(0,1-ecdf/cdf). The minimum number of outliers is computed by replacing cdf by its lower confidence limit and displayed in goodColor. The Mahalanobis distances of the individual data points are added as a stacked stripchart, such that the influence of individual observations can be seen.
The true problem of outlier detection is to detect "near" outliers. Near outliers are outliers so near to the dataset that they could well be extrem observation. These near outliers would provide no problem unless they are not many showing up in groups. Graphic allows at least to count them and to show there probable Mahalanobis distance such, however it still does not allow to conclude that an individual observation is an outlier. However still the outlier candidates can be identified comparing their mahalanobis distance (returned by the plot as$mahalanobis) with a cutoff inferred from this graphic.

type="nout"

This is a simplification of the previous plot simply providing the number of outliers over a given limit.

type="distdist"

Plots a scatterplot of the the classical and robust Mahalanobis distance with the given classification for colors and plot symbols. Furthermore it plots a horizontal line giving the 0.95-Quantil of the distribution of the maximum robust Mahalanobis distance of normally distributed dataset.

Value

a list respresenting the criteria computed to create the plots. The content of the list depends on the plotting type selected.

Note

The package robustbase is required for using the robust estimations.

Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

See Also

OutlierClassifier1, ClusterFinder1

Examples

## Not run: 
data(SimulatedAmounts)
outlierplot(acomp(sa.outliers5))

datas <- list(data1=sa.outliers1,data2=sa.outliers2,data3=sa.outliers3,
                data4=sa.outliers4,data5=sa.outliers5,data6=sa.outliers6)

opar<-par(mfrow=c(2,3),pch=19,mar=c(3,2,2,1))  
tmp<-mapply(function(x,y) {
outlierplot(x,type="scatter",class.type="grade");
  title(y)
},datas,names(datas))


par(mfrow=c(2,3),pch=19,mar=c(3,2,2,1))  
tmp<-mapply(function(x,y) {
  myCls2 <- OutlierClassifier1(x,alpha=0.05,type="all",corrected=TRUE)
  outlierplot(x,type="scatter",classifier=OutlierClassifier1,class.type="best",
  Legend=legend(1,1,levels(myCls),xjust=1,col=colcode,pch=pchcode),
  pch=as.numeric(myCls2));
  legend(0,1,legend=levels(myCls2),pch=1:length(levels(myCls2)))
  title(y)
},datas,names(datas))
# To slow
par(mfrow=c(2,3),pch=19,mar=c(3,2,2,1))  
for( i in 1:length(datas) ) 
  outlierplot(datas[[i]],type="ecdf",main=names(datas)[i])
par(mfrow=c(2,3),pch=19,mar=c(3,2,2,1))  
for( i in 1:length(datas) ) 
  outlierplot(datas[[i]],type="portion",main=names(datas)[i])
par(mfrow=c(2,3),pch=19,mar=c(3,2,2,1))  
for( i in 1:length(datas) ) 
  outlierplot(datas[[i]],type="nout",main=names(datas)[i])
for( i in 1:length(datas) ) 
  outlierplot(datas[[i]],type="distdist",main=names(datas)[i])
par(opar)


## End(Not run)