A matrix with the compositional data. Zero values are allowed.

The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to
be greater than 0. If \(\lambda=0\) the additive log-ratio transformation (<code><a rd-options="" href="/link/alr?package=Compositional&version=5.4" data-mini-rdoc="Compositional::alr">alr</a></code>) is applied.
If zero values are present \(\lambda\) must be strictly positive.

lambda

The folded power transformation

Regression, classification, contour plots, hypothesis testing and fitting of distributions for compositional data are some of the functions included.
The standard textbook for such data is John Aitchison's (1986) "The statistical analysis of compositional data". Relevant papers include:
a) Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. Fourth International International Workshop on Compositional Data Analysis.
b) Tsagris M. (2014). The k-NN algorithm for compositional data: a revised approach with and without zero values present. Journal of Data Science, 12(3):519--534.
c) Tsagris M. (2015). A novel, divergence based, regression for compositional data. Proceedings of the 28th Panhellenic Statistics Conference, 15-18 April 2015, Athens, Greece, 430--444.
d) Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2):47--57.
e) Tsagris M., Preston S. and Wood A.T.A. (2016). Improved supervised classification for compositional data using the alpha-transformation. Journal of Classification, 33(2):243--261. <doi:10.1007/s00357-016-9207-5>.
f) Tsagris M., Preston S. and Wood A.T.A. (2017). Nonparametric hypothesis testing for equality of means on the simplex. Journal of Statistical Computation and Simulation, 87(2): 406--422. <doi:10.1080/00949655.2016.1216554>.
g) Tsagris M. and Stewart C. (2018). A Dirichlet regression model for compositional data with zeros. Lobachevskii Journal of Mathematics, 39(3): 398--412. <doi:10.1134/S1995080218030198>.
h) Alenazi A. (2019). Regression for compositional data with compositional data as predictor variables with or without zero values. Journal of Data Science, 17(1): 219--238. <doi:10.6339/JDS.201901_17(1).0010>.
i) Tsagris M. and Stewart C. (2020). A folded model for compositional data analysis. Australian and New Zealand Journal of Statistics, 62(2):249--277. <doi:10.1111/anzs.12289>.
j) Tsagris M., Alenazi A. and Stewart C. (2021). Non-parametric regression models for compositional data. <arXiv:2002.05137>.
We further include functions for percentages (or proportions).

Michail Tsagris

Compositional

Compositional Data Analysis

Giorgos Athineou

Abdulaziz Alenazi

Christos Adam

The folded power transformation function

The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to
be greater than 0. If \(\lambda=0\) the additive log-ratio transformation (<code><a rd-options='' href='alr'>alr</a></code>) is applied.
If zero values are present \(\lambda\) must be strictly positive.

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The folded power transformation: The folded power transformation

Description

Usage

Arguments

Value

Details

References

See Also

Examples