fsmult {fsdaR}

Gives an automatic outlier detection procedure in multivariate analysis

Description

Gives an automatic outlier detection procedure in multivariate analysis and performs forward search in multivariate analysis with exploratory data

Usage

fsmult(
  x,
  bsb,
  monitoring = FALSE,
  crit = c("md", "biv", "uni"),
  rf = 0.95,
  init,
  plot = FALSE,
  bonflev,
  msg = TRUE,
  nocheck = FALSE,
  scaled = FALSE,
  trace = FALSE,
  ...
)

Arguments

x

An n x p data matrix (n observations and p variables). Rows of x represent observations, and columns represent variables.

Missing values (NA's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

bsb

List of units forming the initial subset or size of the initial subset. If monitoring=FALSE the default is to start the search with p+1 units, containing those observations which are not outlying on any scatterplot, found as the intersection of all points lying within a robust contour containing a specified portion of the data (Riani and Zani 1997) and inside the univariate boxplot.

Remark: if bsb is a vector, the option crit is ignored.

monitoring

Wheather to perform monitoring of Mahalanobis distances and other specific quantities

crit

If specified, the criterion to be used to initialize the search.

• If crit="md" the units which form initial subset are those which have the smallest m0 pseudo Mahalanobis distances computed using procedure unibiv() (bivariate robust ellipses).

• If crit="biv" sorting is done first in terms of times units fell outside robust bivariate ellipses and then in terms of pseudoMD. In other words, the units forming initial subset are chosen first among the set of those which never fell outside robust bivariate ellipses then among those which fell only once outside bivariate ellipses ... up to reach m0.

• If crit="uni" sorting is done first in terms of times units fell outside univariate boxplots and then in terms of pseudoMD. In other words, the units forming initial subset are chosen first among the set of those which never fell outside univariate boxplots then among those which fell only once outside univariate boxplots... up to reach m0.

Remark: as the user can see the starting point of the search is not going to affect at all the results of the analysis. The user can explore this point with his own datasets.

Remark: if crit="biv" the user can also supply in scalar rf (see below) the confidence level of the bivariate ellipses.

rf

Confidence level for bivariate ellipses. The default is 0.95. This option is useful only if crit='biv'.

init

Point where to start monitoring required diagnostics. Note that if a vector m0 is supplied, init >= length(m0). If init is not specified it will be set equal to floor(n*0.6).

plot

Plots the minimum Mahalanobis distance. If plot=FALSE (default) or plot=0 no plot is produced. If plot=TRUE the plot of minimum MD with envelopes based on n observations and the scatterplot matrix with the outliers highlighted is produced. If plot=2 the additional plots of envelope resuperimposition are produced. If plot is a list it may contain the following fields:

• ylim vector with two elements controlling minimum and maximum on the y axis. Default value is ” (automatic scale)

• xlim vector with two elements controlling minimum and maximum on the x axis. Default value is ” (automatic scale)

• resuper vector which specifies for which steps it is necessary to show the plots of resuperimposed envelopes if resuper is not supplied a plot of each step in which the envelope is resuperimposed is shown. Example: if resuper = c(85 87) plots of resuperimposedenvelopes are shown at steps m=85 and m=87

• ncoord If ncoord=1 plots are shown in normal coordinates else (default) plots are shown in traditional mmd coordinates

• labeladd If labeladd=1, the outliers in the spm are labelled with the unit row index. The default value is labeladd="", i.e. no label is added

• nameY character vector containing the labels of the variables. As default value, the labels which are added are Y1, ...Yp.

• lwd controls line width of the curve which contains the monitoring of minimum Mahalanobis distance. Default is lwd=2.

• lwdenv Controls linewidth of the envelopes. Default is lwdenv=2.

bonflev

Option that might be used to identify extreme outliers when the distribution of the data is strongly non normal. In these circumstances, the general signal detection rule based on consecutive exceedances cannot be used. In this case bonflev can be:

1. a scalar smaller than 1, which specifies the confidence level for a signal and a stopping rule based on the comparison of the minimum deletion residual with a Bonferroni bound. For example if bonflev=0.99 the procedure stops when the trajectory exceeds for the first time the 99 per cent bonferroni bound.

2. a scalar value greater than 1. In this case the procedure stops when the residual trajectory exceeds for the first time this value.

Default value is empty, which means to rely on general rules based on consecutive exceedances.

msg

It controls whether to display or not messages on the screen. If msg=TRUE (default) messages about the progression of the search are displayed on the screen otherwise only error messages will be displayed.

nocheck

It controls whether to perform checks on matrix Y. If nocheck=TRUE, no check is performed.

scaled

Controls whether to monitor scaled Mahalanobis distances (only if monitoring=TRUE). If scaled=TRUE Mahalanobis distances monitored during the search are scaled using ratio of determinant. If scaled=2 Mahalanobis distances monitored during the search are scaled using asymptotic consistency factor. The default is scaled=FALSE, that is Mahalanobis distances are not scaled.

trace

Whether to print intermediate results. Default is trace=FALSE.

...

potential further arguments passed to lower level functions.

Value

Depending on the input parameter monitoring, one of the following objects will be returned:

1. fsmult.object

2. fsmeda.object

Author(s)

FSDA team, [e-mail]

References

Riani, M., Atkinson A.C., Cerioli A. (2009). Finding an unknown number of multivariate outliers. Journal of the Royal Statistical Society Series B, Vol. 71, pp. 201-221.

Cerioli A., Farcomeni A., Riani M., (2014). Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter, Journal of Multivariate Analysis, Vol. 126, pp. 167-183, http://dx.doi.org/10.1016/j.jmva.2013.12.010.

Atkinson Riani and Cerioli (2004), Exploring multivariate data with the forward search Springer Verlag, New York.

Examples

 ## Not run: 

 data(hbk, package="robustbase")
 (out <- fsmult(hbk[,1:3]))
 class(out)
 summary(out)

 ##  Generate contaminated data (200,3)
 n <- 200
 p <- 3
 set.seed(123456)
 X <- matrix(rnorm(n*p), nrow=n)
 Xcont <- X
 Xcont[1:5, ] <- Xcont[1:5,] + 3

 out1 <- fsmult(Xcont, trace=TRUE)           # no plots (plot defaults to FALSE)
 names(out1)

 (out1 <- fsmult(Xcont, trace=TRUE, plot=TRUE))    # identical to plot=1

 ## plot=1 - minimum MD with envelopes based on n observations
 ##  and the scatterplot matrix with the outliers highlighted
 (out1 <- fsmult(Xcont, trace=TRUE, plot=1))

 ## plot=2 - additional plots of envelope resuperimposition
 (out1 <- fsmult(Xcont, trace=TRUE, plot=2))

 ## plots is a list: plots showing envelope superimposition in normal coordinates.
 (out1 <- fsmult(Xcont, trace=TRUE, plot=list(ncoord=1)))

 ##  Choosing an initial subset formed by the three observations with
 ##  the smallest Mahalanobis Distance.

 (out1 <- fsmult(Xcont, m0=5, crit="md", trace=TRUE))

 ## fsmult() with monitoring
 (out2 <- fsmult(Xcont, monitoring=TRUE, trace=TRUE))
 names(out2)

 ## Monitor the exceedances from m=200 without showing plots.
 n <- 1000
 p <- 10
 Y <- matrix(rnorm(10000), ncol=10)
 (out <- fsmult(Y, init=200))

 ##  Forgery Swiss banknotes examples.

 data(swissbanknotes)

 ## Monitor the exceedances of Minimum Mahalanobis Distance
 (out1 <- fsmult(swissbanknotes[101:200,], plot=1))

 ##  Control minimum and maximum on the x axis
 (out1 <- fsmult(swissbanknotes[101:200,], plot=list(xlim=c(60,90))))

 ##  Monitor the exceedances of Minimum Mahalanobis Distance using
 ##  normal coordinates for mmd.
 (out1 <- fsmult(swissbanknotes[101:200,], plot=list(ncoord=1)))
 
## End(Not run)