'Function Factory' for Box-Cox Transformation of Data
boxcox3.RdFunction factory to create functions that take \(\lambda\) as an argument for performing the Box-Cox transformation on a given dataset. Adapted from Wickham (2019) Section 10.4.4 Exercises.
Value
Returns a function taking a single argument \(\lambda\) that performs the Box-Cox
transformation on data x.
Details
A numeric vector containing the data to be transformed is provided as an argument to this 'function factory', which returns a function performing the Box-Cox transformation on those data for any given value of \(\lambda\). The Box-Cox transformation takes the following form: -
if \(\lambda \ne 0\) $$y(\lambda) = \displaystyle \frac{y^\lambda - 1}{\lambda}$$
if \(\lambda = 0\) $$y(\lambda) = \log(y)$$
If labile_data is TRUE, data are represented in the boxcox3() function environment as a
quosure, and functions returned by will automatically refer to the current version of
data in its original environment, usually the calling environment i.e., typically but not
necessarily the global environment. If labile_data is FALSE, returned functions refer to a copy of data
saved in the function environment at the time of execution of boxcox3(), and will not reflect any subsequent
changes to the original data.
References
Wickham, Hadley (2019) Advanced R 2nd edition. CRC Press. adv-r.hadley.nz
See also
Other boxcox:
opt_bc()
Examples
## Create skewed data
(d <- rlnorm(20))
#> [1] 0.24658623 1.29087083 0.08739968 0.99444420 1.86181668 3.15318044
#> [7] 0.16173151 0.78088663 0.78333126 0.75374177 0.57481939 1.87570022
#> [13] 7.88549421 0.19573582 1.66933768 0.15520453 0.59332527 0.94875763
#> [19] 1.72115632 0.40088734
## Calculate skewness using BitsnBobs::skew()
d |> skew()
#> [1] 3.16996
## Box-Cox function for these data
bc_func <- boxcox3(d)
## Box-Cox transform data with various values of lambda
bc_func(-1)
#> [1] -3.055376440 0.225329154 -10.441688958 -0.005586835 0.462890192
#> [6] 0.682859887 -5.183086998 -0.280595625 -0.276599123 -0.326714319
#> [11] -0.739676861 0.466865767 0.873184867 -4.108927002 0.400960027
#> [16] -5.443110962 -0.685416164 -0.054009971 0.418995248 -1.494466372
bc_func(0)
#> [1] -1.400043517 0.255317055 -2.437263611 -0.005571287 0.621552721
#> [6] 1.148411606 -1.821817661 -0.247325302 -0.244199607 -0.282705449
#> [11] -0.553699384 0.628982042 2.065024895 -1.630989402 0.512426950
#> [16] -1.863011492 -0.522012515 -0.052601910 0.542996343 -0.914074827
bc_func(1)
#> [1] -0.753413767 0.290870833 -0.912600316 -0.005555796 0.861816681
#> [6] 2.153180437 -0.838268489 -0.219113372 -0.216668740 -0.246258229
#> [11] -0.425180605 0.875700223 6.885494207 -0.804264183 0.669337681
#> [16] -0.844795471 -0.406674730 -0.051242372 0.721156318 -0.599112655
bc_func(2)
#> [1] -0.469597615 0.333173754 -0.496180648 -0.005540362 1.233180677
#> [6] 4.471273434 -0.486921459 -0.195108037 -0.193196068 -0.215936672
#> [11] -0.334791332 1.259125664 30.590509448 -0.480843745 0.893344147
#> [16] -0.487955777 -0.323982562 -0.049929481 0.981189535 -0.419644668
## bc_func(0) same as log(d)
identical(bc_func(0), log(d))
#> [1] TRUE
seq(-3, 3, 1) |> ## Create a sequence from -3 to 3
set_names(\(x) paste("lambda", x)) |> ## Name sequence vector using rlang::set_names()
print_lf() |> ## Print with line feed
lapply(bc_func) |> ## Box-Cox transform data using each lambda value
print_lf() |> ## in sequence and print the named list
map_dbl(skewness) |> ## Calculate skewness for each element of the list
print_lf() |> ## and print the numeric vector
abs() |> ## Absolute skewness...
which.min() ## ...which lambda gives minimum?
#> lambda -3 lambda -2 lambda -1 lambda 0 lambda 1 lambda 2 lambda 3
#> -3 -2 -1 0 1 2 3
#>
#> $`lambda -3`
#> [1] -2.189835e+01 1.783695e-01 -4.989524e+02 -5.618106e-03 2.816836e-01
#> [6] 3.227009e-01 -7.846097e+01 -3.666937e-01 -3.601601e-01 -4.450813e-01
#> [11] -1.421697e+00 2.828220e-01 3.326535e-01 -4.411626e+01 2.616784e-01
#> [16] -8.882575e+01 -1.262547e+00 -5.697956e-02 2.679574e-01 -4.840491e+00
#>
#> $`lambda -2`
#> [1] -7.723039034 0.199942540 -64.956123103 -0.005602442 0.355756527
#> [6] 0.449711074 -18.615282412 -0.319962578 -0.314852660 -0.380085442
#> [11] -1.013237790 0.357883945 0.491958961 -12.550567555 0.320575555
#> [16] -20.256839433 -0.920313822 -0.055468509 0.331216739 -2.611181240
#>
#> $`lambda -1`
#> [1] -3.055376440 0.225329154 -10.441688958 -0.005586835 0.462890192
#> [6] 0.682859887 -5.183086998 -0.280595625 -0.276599123 -0.326714319
#> [11] -0.739676861 0.466865767 0.873184867 -4.108927002 0.400960027
#> [16] -5.443110962 -0.685416164 -0.054009971 0.418995248 -1.494466372
#>
#> $`lambda 0`
#> [1] -1.400043517 0.255317055 -2.437263611 -0.005571287 0.621552721
#> [6] 1.148411606 -1.821817661 -0.247325302 -0.244199607 -0.282705449
#> [11] -0.553699384 0.628982042 2.065024895 -1.630989402 0.512426950
#> [16] -1.863011492 -0.522012515 -0.052601910 0.542996343 -0.914074827
#>
#> $`lambda 1`
#> [1] -0.753413767 0.290870833 -0.912600316 -0.005555796 0.861816681
#> [6] 2.153180437 -0.838268489 -0.219113372 -0.216668740 -0.246258229
#> [11] -0.425180605 0.875700223 6.885494207 -0.804264183 0.669337681
#> [16] -0.844795471 -0.406674730 -0.051242372 0.721156318 -0.599112655
#>
#> $`lambda 2`
#> [1] -0.469597615 0.333173754 -0.496180648 -0.005540362 1.233180677
#> [6] 4.471273434 -0.486921459 -0.195108037 -0.193196068 -0.215936672
#> [11] -0.334791332 1.259125664 30.590509448 -0.480843745 0.893344147
#> [16] -0.487955777 -0.323982562 -0.049929481 0.981189535 -0.419644668
#>
#> $`lambda 3`
#> [1] -0.328335460 0.383679798 -0.333110793 -0.005524986 1.817909798
#> [6] 10.116881427 -0.331923192 -0.174609295 -0.173113926 -0.190593069
#> [11] -0.270023236 1.866394933 163.109354770 -0.330833623 1.217307926
#> [16] -0.332087121 -0.263709604 -0.048661441 1.366239150 -0.311857710
#>
#>
#> lambda -3 lambda -2 lambda -1 lambda 0 lambda 1 lambda 2
#> -4.08779986 -3.36358910 -2.00565188 -0.04650773 3.16995968 4.27696463
#> lambda 3
#> 4.44244689
#>
#> lambda 0
#> 4
## Usually, lambda 0 has least absolute skewness as data were sampled from lognormal distribution
rm(d, bc_func)