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Tukey's resistant line

Source: R/eda_rline.R
eda_rline.Rd

eda_rline is an R implementation of Hoaglin, Mosteller and Tukey's resistant line technique outlined in chapter 5 of "Understanding Robust and Exploratory Data Analysis" (Wiley, 1983).

Usage

eda_rline(dat, x, y, px = 1, py = 1, tukey = FALSE, maxiter = 20)

Arguments

dat

Data frame.

x

Column assigned to the x axis.

y

Column assigned to the y axis.

px

Power transformation to apply to the x-variable.

py

Power transformation to apply to the y-variable.

tukey

Boolean determining if a Tukey transformation should be adopted. (FALSE adopts a Box-Cox transformation)

maxiter

Maximum number of iterations to run.

Value

Returns a list of class eda_rline with the following named components:

  • a: Intercept

  • b: Slope

  • residuals: Residuals sorted on x-values

  • x: Sorted x values

  • y: y values following sorted x-values

  • xmed: Median x values for each third

  • ymed: Median y values for each third

  • index: Index of sorted x values defining upper boundaries of each thirds

  • xlab: X label name

  • ylab: Y label name

  • iter: Number of iterations

  • fitted.values: Fitted values

Details

This is an R implementation of the RLIN.F FORTRAN code in Velleman et. al's book. This function fits a robust line using a three-point summary strategy whereby the data are split into three equal length groups along the x-axis and a line is fitted to the medians defining each group via an iterative process. This function should mirror the built-in stat::line function in its fitting strategy but it outputs additional parameters.


See the accompanying resistant line article for a detailed breakdown of the resistant line technique.

References

  • Velleman, P. F., and D. C. Hoaglin. 1981. Applications, Basics and Computing of Exploratory Data Analysis. Boston: Duxbury Press.

  • D. C. Hoaglin, F. Mosteller, and J. W. Tukey. 1983. Understanding Robust and Exploratory Data Analysis. Wiley.

Examples


# This first example uses breast cancer data from "ABC's of EDA" page 127.
# The output model's  parameters should closely match:  Y = -46.19 + 2.89X
# The plots shows the original data with a fitted resistant line (red)
# and a regular lm fitted line (dashed line), and the modeled residuals.
# The 3-point summary dots are shown in red.

M <- eda_rline(neoplasms, Temp, Mortality)
M
#> $b
#> [1] 2.890173
#> 
#> $a
#> [1] -46.20241
#> 
#> $residuals
#>  [1] 45.57582 24.41744 22.09836 33.10703 13.02900 16.66079 24.13767 29.03651
#>  [9] 15.26830 22.07813 27.03304 17.00992 23.88680 30.46368 26.07466 24.41744
#> 
#> $x
#>  [1] 31.8 34.0 40.2 42.1 42.3 43.5 44.2 45.1 46.3 47.3 47.8 48.5 49.2 49.9 50.0
#> [16] 51.3
#> 
#> $y
#>  [1]  67.3  52.5  68.1  84.6  65.1  72.2  81.7  89.2  78.9  88.6  95.0  87.0
#> [13]  95.9 104.5 100.4 102.5
#> 
#> $xmed
#> [1] 40.2 45.7 49.9
#> 
#> $ymed
#> [1]  67.30  85.15 100.40
#> 
#> $index
#> [1]  5 11 16
#> 
#> $xlab
#> [1] "Temp"
#> 
#> $ylab
#> [1] "Mortality"
#> 
#> $px
#> [1] 1
#> 
#> $py
#> [1] 1
#> 
#> $iter
#> [1] 4
#> 
#> $fitted.values
#>  [1]  45.70511  52.06349  69.98256  75.47389  76.05193  79.52013  81.54326
#>  [8]  84.14441  87.61262  90.50279  91.94788  93.97100  95.99412  98.01724
#> [15]  98.30626 102.06349
#> 
#> attr(,"class")
#> [1] "eda_rline"

# Plot the output (red line is the resistant line)
plot(M)

# Add a traditional OLS regression line (dashed line)
abline(lm(Mortality ~ Temp, neoplasms), lty = 3)


# Plot the residuals
plot(M, type = "residuals")


# This next example uses Andrew Siegel's pathological 9-point dataset to test
# for model stability when convergence cannot be reached.
M <- eda_rline(nine_point, X, Y)
plot(M)