A Review of Flexible Transformations for Modeling Compositional Data

Tsagris, Michail; Stewart, Connie

doi:10.1007/978-3-031-08329-7_10

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…The benefit of the α-transformation over the alr and clr transformations is that it can be applied even when zero values are present in the data (using strictly positive values of α), offer more flexibility and yield better results (Tsagris, 2015b, Tsagris et al, 2016, Tsagris and Stewart, 2022.…”

Section: Kullback-leibler Divergence Principal Component Regressionmentioning

confidence: 99%

Constrained least squares simplicial-simplicial regression

Tsagris

2024

Preprint

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Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression coefficients themselves lie within the simplex, is proposed. The model is transformation-free but the adoption of a power transformation is straightforward, it can treat more than one compositional datasets as predictors and offers the possibility of weights among the simplicial predictors. Among the model’s advantages are its ability to treat zeros in a natural way and a highly computationally efficient algorithm to estimate its coefficients. Resampling based hypothesis testing procedures are employed regarding inference, such as linear independence, and equality of the regression coefficients to some pre-specified values. The strategy behind the formulation new model is implemented to a an existing methodology, that is of the same spirit, showcasing how other similar models can be employed as well. Finally, the performance of the proposed technique and its comparison to the existing methodology takes place using simulation studies and real data examples.

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Section: Kullback-leibler Divergence Principal Component Regressionmentioning

confidence: 99%

Constrained least squares simplicial-simplicial regression

Tsagris

2024

Preprint

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Flexible non-parametric regression models for compositional response data with zeros

Tsagris¹,

Alenazi²,

Stewart³

2023

Stat Comput

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Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical k- Nearest Neighbours (k-NN) regression, that yields a highly flexible non-parametric regression model for compositional data. A similar extension of kernel regression is proposed by adopting the Nadaraya–Watson estimator. Both extensions involve a power transformation termed the $$\alpha $$ α -transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between compositional response data and Euclidean predictor variables. Both the extended K-NN and kernel regressions can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the extended k-NN regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large sample data sets.

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Compositional: Compositional Data Analysis

Tsagris,

Athineou

2016

CRAN: Contributed Packages

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A Review of Flexible Transformations for Modeling Compositional Data

Cited by 3 publications

References 21 publications

Constrained least squares simplicial-simplicial regression

Constrained least squares simplicial-simplicial regression

Flexible non-parametric regression models for compositional response data with zeros

Compositional: Compositional Data Analysis

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