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...

Full description

Saved in:
Bibliographic Details
Published in:Biometrics Vol. 78; no. 3; pp. 974 - 987
Main Authors: Fiksel, Jacob, Zeger, Scott, Datta, Abhirup
Format: Journal Article
Language:English
Published: United States Blackwell Publishing Ltd 01.09.2022
Subjects:
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
Kullback-Leibler distance loss function
compositional data
expectation-maximization algorithm
transformation-free
estimating equation
ISSN:0006-341X, 1541-0420, 1541-0420
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0006-341X
1541-0420
1541-0420
DOI:10.1111/biom.13465