Benchmarking (version 0.27)

outlier.ap: Detection of outliers in benchmark models

Description

The functions implements the Wilson (1993) outlier detection method using only R functions.

Usage

outlier.ap(X, Y, NDEL = 3, NLEN = 25, TRANSPOSE = FALSE)
outlier.ap.plot(ratio, NLEN = 25, xlab = "r", ylab = "Log ratio", 
                ..., ylim)

Arguments

X

Input as a firms times goods matrix, see TRANSPOSE.

Y

Output as a firms times goods matrix, see TRANSPOSE.

NDEL

The maximum number of firms to be considered as a group of outliers, i.e. the maximum number of firms to be deleted.

NLEN

The number of ratios to save for each level or removal, the number of rows in ratio used.

TRANSPOSE

Input and output matrices are treated as firms times goods matrices for the default value TRANSPOSE=FALSE corresponding to the standard in R for statistical models. When TRUE data matrices are transposed to good times firms matrices as is normally used in LP formulation of the problem.

ratio

The ratio component from the list as output from outlier.ap.

xlab

Label for the x-axis.

ylab

Label for the y-axis

ylim

The y limits (y1, y2) of the plot, an array/vector of length 2.

…

Usual options for the methods plot and lines.

Value

ratio

A min(NLEN,K) x NDEL matrix with the log-ratios to be plotted.

imat

A NDEL x NDEL matrix with indicies for deleted firms.

r0

A NDEL array with the minimum value \(R^{i}\) of the for each number of deleted firms.

Details

An implementation of the method in Wilson (1993) using only R functions and especially the function det to calculate \(R^{(i)}_{\min}\).

An elementary presentation of the method is found in Bogetoft and Otto (2011), Sect. 5.13 on outliers.

References

Bogetoft and Otto; Benchmarking with DEA, SFA, and R; Springer 2011

Wilson (1993), “Detecing outliers in deterministic nonparametric frontier models with multiple outputs,” Journal of Business and Economic Statistics 11, 319-323.

Wilson (2008), “FEAR 1.0: A Software Package for Frontier Efficiency Analysis with R,” Socio-Economic Planning Sciences 42, 247--254

See Also

The function ap in the package FEAR.

Examples

# NOT RUN {
n <- 25
x <- matrix(rnorm(n))
y <- .5 + 2.5*x + 2*rnorm(25)
tap <- outlier.ap(x,y, NDEL=2)
print(cbind(tap$imat,tap$rmin), na.print="", digit=2)
outlier.ap.plot(tap$ratio)
# }