Transformations

Functions used in quantile regression transformation models

Usage

ao(theta, lambda, symm = TRUE, omega = 0.001)
invao(x, lambda, symm = TRUE, replace = TRUE)
bc(x, lambda)
invbc(x, lambda, replace = TRUE)
mcjI(x, lambda, symm = TRUE, dbounded = FALSE, omega = 0.001)
invmcjI(x, lambda, symm = TRUE, dbounded = FALSE)
mcjII(x, lambda, delta, dbounded = FALSE, omega = 0.001)
invmcjII(x, lambda, delta, dbounded = FALSE)

Arguments

x, theta: numeric vector of singly (x) or doubly (theta) bounded observations; theta must be between 0 and 1 (see map to map generic [a,b] intervals to [0,1]).
lambda, delta: transformation parameters.
symm: logical flag. If TRUE (default) a symmetric transformation is used.
dbounded: logical flag. If TRUE the argument x is assumed to be bounded between 0 and 1.
omega: small constant to avoid numerical problems when theta is exactly 0 or 1.
replace: logical flag. If TRUE (default), values that are outside the admissible range after the Box-Cox or the Aranda-Ordaz back-transformations are replaced by the range bounds.

Details

These functions transform (back-transform) x or theta conditional on the parameters lambda and theta, using the Box–Cox (bc), Aranda-Ordaz (ao), Proposal I (mcjI) and Proposal II (mcjII) transformations.

Value

Transformed or back-transformed values.

References

Aranda-Ordaz FJ. On two families of transformations to additivity for binary response data. Biometrika 1981;68(2):357-363.

Box GEP, Cox DR. An analysis of transformations. Journal of the Royal Statistical Society Series B-Statistical Methodology 1964;26(2):211-252.

Dehbi H-M, Cortina-Borja M, and Geraci M. Aranda-Ordaz quantile regression for student performance assessment. Journal of Applied Statistics. 2016;43(1):58-71.

Geraci M and Jones MC. Improved transformation-based quantile regression. Canadian Journal of Statistics 2015;43(1):118-132.

Jones MC. Connecting distributions with power tails on the real line, the half line and the interval. International Statistical Review 2007;75(1):58-69.

Author

Marco Geraci