boxcox_itr_bias_cor {lidaRtRee}

Inverse Box-Cox transformation with bias correction

Description

Inverse Box-Cox transform with bias correction as suggested by Pu & Tiefelsdorf (2015). Here 'varmod' is not the local prediction variance as suggested in the paper but the model residuals variance. For variance computation, uses 'n-p' instead of 'n-1', with 'p' the number of variables in the model.

Usage

boxcox_itr_bias_cor(x, lambda, varmod)

Arguments

x

vector or raster values to be transformed

lambda

numeric. parameter of Box-Cox transformation

varmod

numeric. model residuals variance

Value

a vector or raster

References

Xiaojun Pu and Michael Tiefelsdorf, 2015. A variance-stabilizing transformation to mitigate biased variogram estimation in heterogeneous surfaces with clustered samples. doi:10.1007/978-3-319-22786-3_24

See Also

boxcox_tr Box-Cox transformation, boxcox_itr inverse Box-Cox transformation.

Examples

x <- 1:10
boxcox_itr(x, 0.3)
boxcox_itr_bias_cor(x, 0.3, 0)
boxcox_itr_bias_cor(x, 0.3, 2)

# plot functions
curve(boxcox_itr(x, 0.3), 0, 3,
  col = "blue",
  main = "inverse Box Cox transf., lambda = 0.3",
  xlab = "x", ylab = "inverse Boxcox(x, lambda = 0.3)"
)
curve(boxcox_itr_bias_cor(x, 0.3, 1), 0, 3, col = "red", add = TRUE)
curve(boxcox_itr_bias_cor(x, 0.3, 2), 0, 3, col = "black", add = TRUE)
legend("topleft",
  legend = c(
    "residuals variance  = 2",
    "residuals variance  = 1", "residuals variance not accounted for"
  ),
  col = c("black", "red", "blue"), lty = 1
)