Log contrast models for experiments with mixtures

Aitchison, J.; Bacon‐Shone, John

doi:10.1093/biomet/71.2.323

Cited by 169 publications

(117 citation statements)

References 16 publications

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“…Model (1) exempts us from choosing the reference component, as it was necessary in the aforementioned standard log-contrast model by Aitchison and Bacon-Shone (1984) , while gaining interpretability. Note that the zero-sum constraint in (1) is crucial for an estimator of regression coefficients to fulfill the desirable properties of compositional data analysis, namely the scale invariance, the permutation invariance, and the subcompositional coherence properties (Aitchison 1986). The scale invariance property guarantees that the regression coefficient β is independent from an arbitrary scaling of the basis count from which the composition is obtained, i.e.…”

Section: Sparse Logistic Regression Models With Compositional Covariatesmentioning

confidence: 99%

Robust logistic zero-sum regression for microbiome compositional data

Monti

Filzmoser

2021

Adv Data Anal Classif

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We introduce the Robust Logistic Zero-Sum Regression (RobLZS) estimator, which can be used for a two-class problem with high-dimensional compositional covariates. Since the log-contrast model is employed, the estimator is able to do feature selection among the compositional parts. The proposed method attains robustness by minimizing a trimmed sum of deviances. A comparison of the performance of the RobLZS estimator with a non-robust counterpart and with other sparse logistic regression estimators is conducted via Monte Carlo simulation studies. Two microbiome data applications are considered to investigate the stability of the estimators to the presence of outliers. Robust Logistic Zero-Sum Regression is available as an R package that can be downloaded at https://github.com/giannamonti/RobZS.

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Section: Sparse Logistic Regression Models With Compositional Covariatesmentioning

confidence: 99%

Robust logistic zero-sum regression for microbiome compositional data

Monti

Filzmoser

2021

Adv Data Anal Classif

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“…∑ ∈ (̂+̂) [14] are the Schoenfeld residuals at time , defined in the usual manner in terms of the difference between the covariates of the individual with an event at time and the weighted average of covariates over all individuals exposed to risk at time (but we have made the distinction between the ilr-coordinates and the non-compositional covariates explicit),…”

Section: As ( ) = (∑ =mentioning

confidence: 99%

“…The Gramsch-Therneau test statistic was defined in Eq. [13][14][15][16][17][18][19][20] with reference to hypothesized timedependence G, defined in Eq. [9,12].…”

Section: Fundingmentioning

confidence: 99%

“…represented with an arbitrary but fixed sum of the parts, commonly 1 or 100), a multicollinearity problem arises in regression analysis as a consequence of the singularity of the raw covariance matrix between compositional variables, which was already recognised in early approaches to mixture experiments (11)(12)(13)(14). Although for model fitting purposes this could be technically overcome using e.g.…”

Section: Introductionmentioning

confidence: 99%

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Cox regression survival analysis with compositional covariates: Application to modelling mortality risk from 24-h physical activity patterns

McGregor

Palarea‐Albaladejo

Dall

et al. 2019

Stat Methods Med Res

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Survival analysis is commonly conducted in medical and public health research to assess the association of an exposure or intervention with a hard end outcome such as mortality. The Cox (proportional hazards) regression model is probably the most popular statistical tool used in this context. However, when the exposure includes compositional covariables (that is, variables representing a relative makeup such as a nutritional or physical activity behaviour composition), some basic assumptions of the Cox regression model and associated significance tests are violated. Compositional variables involve an intrinsic interplay between one another which precludes results and conclusions based on considering them in isolation as is ordinarily done. In this work, we introduce a formulation of the Cox regression model in terms of log-ratio coordinates which suitably deals with the constraints of compositional covariates, facilitates the use of common statistical inference methods, and allows for scientifically meaningful interpretations. We illustrate its practical application to a public health problem: the estimation of the mortality hazard associated with the composition of daily activity behaviour (physical activity, sitting time and sleep) using data from the U.S. National Health and Nutrition Examination Survey (NHANES).

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“…They develop a reparameterized model that permits the experimenter to separate the effects of the process 22 variables from the mixture variables. From such a model it is demonstrated that reduced model forms can be obtained through the use of a variable selection procedure.. Aitchison and Bacon-Slone (1984) show that the constant sum constraint, i.e.…”

Section: 'I /mentioning

confidence: 99%

Response Surface Methodology

Myers¹,

Montgomery²

1996

IIE Transactions

1,108

525

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Approved for Public Release: Distribution Unlimited 17. OiSTAiSuTiON STATEMENT (of the ob.trocl -ntoted IA Block 20, It different 1-m. Roporl) If. SUPPLEMENTARY NOTES 19. KEY *ORDS (Comntin~ue onrvrse 00.... It necateottv aid Identity by block number) Response Surface, Review, Design, Analysis. 20 ABSTRACT (Contln..e an roers*9 old* It flec*esorYan id hentity by block number)This paper provides a thorough review of response surface methodology since 1966. The review covers topics pertaining to the design and analysis of response surfaces. Multirespone techniques associated with optimization and lack of fit testing are also covered.

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Log contrast models for experiments with mixtures

Cited by 169 publications

References 16 publications

Robust logistic zero-sum regression for microbiome compositional data

Robust logistic zero-sum regression for microbiome compositional data

Cox regression survival analysis with compositional covariates: Application to modelling mortality risk from 24-h physical activity patterns

Response Surface Methodology

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