A transformation‐free linear regression for compositional outcomes and predictors
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 u...
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| Vydáno v: | Biometrics Ročník 78; číslo 3; s. 974 - 987 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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United States
Blackwell Publishing Ltd
01.09.2022
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| ISSN: | 0006-341X, 1541-0420, 1541-0420 |
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| Abstract | 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 log‐ratio 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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| AbstractList | 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 log‐ratio 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. 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 log‐ratio 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. 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 log-ratio 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.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 log-ratio 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. |
| Author | Fiksel, Jacob Zeger, Scott Datta, Abhirup |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33788259$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.6339/JDS.201901_17(1).0010 10.1080/02664763.2016.1157145 10.1177/0962280217710835 10.17713/ajs.v47i5.718 10.1002/9781119976462.ch25 10.1080/01621459.2021.1909599 10.1007/BF00891269 10.1177/0962280214560047 10.1111/j.1467-9876.2008.00627.x 10.1080/02664763.2011.644268 10.1016/j.apgeochem.2008.03.004 10.1111/j.2517-6161.1977.tb01600.x 10.1515/jem-2012-0006 10.1007/978-3-319-96422-5 10.2307/1913471 10.32614/RJ-2017-016 10.1198/016214501753381850 10.1111/j.2517-6161.1982.tb01195.x 10.1353/mpq.0.0030 10.1023/A:1023818214614 10.1093/biomet/71.2.323 10.1007/BF00048682 10.18637/jss.v087.c03 10.1093/biomet/asu031 10.1080/07474938.2013.806849 10.1007/978-3-642-36809-7 10.2307/1913295 10.1007/978-94-009-4109-0 10.1093/biomet/86.2.351 10.1002/(SICI)1099-1255(199611)11:6<619::AID-JAE418>3.0.CO;2-1 |
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| SubjectTerms | biomedical research compositional data data collection education estimating equation expectation‐maximization algorithm Genetic transformation inventories Kullback–Leibler distance loss function Medical research Permutations Regression analysis Regression models Transformations transformation‐free |
| Title | A transformation‐free linear regression for compositional outcomes and predictors |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fbiom.13465 https://www.ncbi.nlm.nih.gov/pubmed/33788259 https://www.proquest.com/docview/2719652209 https://www.proquest.com/docview/2507724532 https://www.proquest.com/docview/2811972135 |
| Volume | 78 |
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