Regression for Compositional Data with Compositional Data as Predictor Variables with or without Zero Values

Alenazi, Abdulaziz

doi:10.6339/jds.201901_17(1).0010

Cited by 6 publications

(15 citation statements)

References 21 publications

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“…Here we used the composition of relative read abundance of each of the three plant species (RRA from faeces or meal mixtures) as response variables and the expected plant species composition ( i.e., known biomass composition) as predictor variables. This type of compositional analysis accounts for the fact that an increase in one taxon’s proportion will force a decrease in other taxon(s) proportion within the same sample ( Alenazi, 2019 ; Chen, Zhang & Li, 2017 ; Fiksel, Zeger & Datta, 2021 ). The model allows, without transformation, for direct interpretation of the relationship between expected and observed compositions through a Markov transition matrix “B” based on the estimated regression coefficients.…”

Section: Methodsmentioning

confidence: 99%

Issues of under-representation in quantitative DNA metabarcoding weaken the inference about diet of the tundra vole Microtus oeconomus

Neby

Kamenova

Devineau

et al. 2021

PeerJ

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During the last decade, methods based on high-throughput sequencing such as DNA metabarcoding have opened up for a range of new questions in animal dietary studies. One of the major advantages of dietary metabarcoding resides in the potential to infer a quantitative relationship between sequence read proportions and biomass of ingested food. However, this relationship’s robustness is highly dependent on the system under study, calling for case-specific assessments. Herbivorous small rodents often play important roles in the ecosystem, and the use of DNA metabarcoding for analyses of rodent diets is increasing. However, there has been no direct validation of the quantitative reliability of DNA metabarcoding for small rodents. Therefore, we used an experimental approach to assess the relationship between input plant biomass and sequence reads proportions from DNA metabarcoding in the tundra vole Microtus oeconomus. We found a weakly positive relationship between the number of high-throughput DNA sequences and the expected biomass proportions of food plants. The weak relationship was possibly caused by a systematic under-amplification of one of the three plant taxa fed. Generally, our results add to the growing evidence that case-specific validation studies are required to reliably make use of sequence read abundance as a proxy of relative food proportions in the diet.

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Section: Methodsmentioning

confidence: 99%

Issues of under-representation in quantitative DNA metabarcoding weaken the inference about diet of the tundra vole Microtus oeconomus

Neby

Kamenova

Devineau

et al. 2021

PeerJ

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“…Alenazi (2019) takes a different approach to compositional regression, as only the explanatory compositional variable

\mathbf {x}

is transformed. While Alenazi (2019) is more interested in prediction accuracy than interpretation and uses a complex principal components–based transformation, one can use any transformation t (e.g., the ALR or ILR transformations).…”

Section: Review Of Transformation‐based Compositional Regression Modelsmentioning

confidence: 99%

“…White cell composition analysis Aitchison (2003) and Alenazi (2019) consider a dataset provided in the ggtern R package (Hamilton and Ferry, 2018) in which the proportions of white blood cell types (granulocytes, lymphocytes, and monocytes) in 30 blood samples are determined by both a time-consuming microscopic analysis and an automated image analysis. The microscopic analysis is known to produce accurate results, while the accuracy of the image analysis is unknown.…”

Section: 2mentioning

confidence: 99%

“…Examples of problems with both compositional outcomes and explanatory variables include relating the per-centage of males and females with different education levels across countries (Filzmoser et al, 2018), modeling the relationship between age structure and consumption structure across economic areas (Chen et al, 2017), and understanding how different methods for estimating the composition of white blood cell types are related (Aitchison, 1986;Alenazi, 2019).…”

Section: Introductionmentioning

confidence: 99%

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A transformation‐free linear regression for compositional outcomes and predictors

2021

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Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited, and the existing models are often difficult to interpret in the compositional space, due to their use of complex logratio transformations. We develop a transformation-free linear regression model where the expected value of the compositional outcome is expressed as a single Markov transition from the compositional predictor. Our approach is based on estimating equations thereby not requiring complete specification of data likelihood and is robust to different data-generating mechanisms. Our model is simple to interpret, allows for 0s and 1s in both the compositional outcome and covariates, and subsumes several interesting subcases of interest. We also develop permutation tests for linear independence and equality of effect sizes of two components of the predictor. Finally, we show that despite its simplicity, our model accurately captures the relationship between compositional data using two datasets from education and medical research.

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“…Finally, Wang et al (2013) considered linear regression for compositional data as both dependent and independent variables, again using the isometric log-ratio transformation, whereas (Alenazi, 2019) suggested the use of principal components regression.…”

Section: Introductionmentioning

confidence: 99%

Non-parametric regression models for compositional data

Tsagris¹,

Alenazi²,

Stewart³

2020

Preprint

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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. This paper, through use of the α-transformation, extends the classical k-N N regression to what is termed α-k-N N regression, yielding a highly flexible non-parametric regression model for compositional data. 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 model without modification. Extensive simulation studies and real-life data analysis highlight the advantage of using α-k-N N regression for complex relationships between the response data and predictor variables for two cases, namely when the response data is compositional and predictor variables are continuous (or categorical) and vice versa. Both cases suggest that α-k-N N regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables.

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Regression for Compositional Data with Compositional Data as Predictor Variables with or without Zero Values

Cited by 6 publications

References 21 publications

Issues of under-representation in quantitative DNA metabarcoding weaken the inference about diet of the tundra vole Microtus oeconomus

Issues of under-representation in quantitative DNA metabarcoding weaken the inference about diet of the tundra vole Microtus oeconomus

A transformation‐free linear regression for compositional outcomes and predictors

Non-parametric regression models for compositional data

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