scholarly journals Impact of Covariates in Compositional Models and Simplicial Derivatives

2021 ◽  
Vol 50 (2) ◽  
pp. 1-15 ◽  
Author(s):  
Joanna Morais ◽  
Christine Thomas-Agnan
Keyword(s):  
Data Analysis ◽  
Regression Models ◽  
Compositional Data ◽  
Explanatory Variable ◽  
Regression Equation ◽  
Compositional Data Analysis ◽  
Linear Regression Models ◽  
Explanatory Variables ◽  
Relative Information ◽  
Single Side

In the framework of Compositional Data Analysis, vectors carrying relative information, also called compositional vectors, can appear in regression models either as dependent or as explanatory variables. In some situations, they can be on both sides of the regression equation. Measuring the marginal impacts of covariates in these types of models is not straightforward since a change in one component of a closed composition automatically affects the rest of the composition. Previous work by the authors has shown how to measure, compute and interpret these marginal impacts in the case of linear regression models with compositions on both sides of the equation. The resulting natural interpretation is in terms of an elasticity, a quantity commonly used in econometrics and marketing applications. They also demonstrate the link between these elasticities and simplicial derivatives. The aim of this contribution is to extend these results to other situations, namely when the compositional vector is on a single side of the regression equation. In these cases, the marginal impact is related to a semi-elasticity and also linked to some simplicial derivative. Moreover we consider the possibility that a total variable is used as an explanatory variable, with several possible interpretations of this total and we derive the elasticity formulas in that case.

scholarly journals Interpretation of Explanatory Variables Impacts in Compositional Regression Models

2018 ◽  
Vol 47 (5) ◽  
pp. 1-25 ◽  
Author(s):  
Joanna Morais ◽  
Christine Thomas-Agnan ◽  
Michel Simioni
Keyword(s):  
Data Analysis ◽  
Regression Models ◽  
Compositional Data ◽  
Selection Procedure ◽  
Original Model ◽  
Compositional Data Analysis ◽  
Explanatory Variables ◽  
Market Shares ◽  
Share Model ◽  
The Impact

We are interested in modeling the impact of media investments on automobile manufacturer's market shares. Regression models have been developed for the case where the dependent variable is a vector of shares. Some of them, from the marketing literature, are easy to interpret but quite simple (Model A). Alternative models, from the compositional data analysis literature, allow a large complexity but their interpretation is not straightforward (Model B).  This paper combines both approaches in order to obtain a performing market share model and develop relevant interpretations for practical use.We prove that Model A is a particular case of Model B, and that an intermediate specification is possible (Model AB). A model selection procedure is proposed. Several impact measures are presented and we show that elasticities are particularly useful: they can be computed from the transformed or from the original model, and they are linked to the simplicial derivatives.

Individual categorisation of glucose profiles using compositional data analysis

2018 ◽  
Vol 28 (12) ◽  
pp. 3550-3567 ◽  
Author(s):  
Lyvia Biagi ◽  
Arthur Bertachi ◽  
Marga Giménez ◽  
Ignacio Conget ◽  
Jorge Bondia ◽  
...  
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Glucose Monitoring ◽  
Glucose Variability ◽  
Compositional Data Analysis ◽  
Relative Information ◽  
Glucose Profiles ◽  
Patient Groups ◽  
The Times

The aim of this study was to apply a methodology based on compositional data analysis (CoDA) to categorise glucose profiles obtained from continuous glucose monitoring systems. The methodology proposed considers complete daily glucose profiles obtained from six patients with type 1 diabetes (T1D) who had their glucose monitored for eight weeks. The glucose profiles were distributed into the time spent in six different ranges. The time in one day is finite and limited to 24 h, and the times spent in each of these different ranges are co-dependent and carry only relative information; therefore, CoDA is applied to these profiles. A K-means algorithm was applied to the coordinates obtained from the CoDA to obtain different patterns of days for each patient. Groups of days with relatively high time in the hypo and/or hyperglycaemic ranges and with different glucose variability were observed. Using CoDA of time in different ranges, individual glucose profiles were categorised into groups of days, which can be used by physicians to detect the different conditions of patients and personalise patient's insulin therapy according to each group. This approach can be useful to assist physicians and patients in managing the day-to-day variability that hinders glycaemic control.

scholarly journals Associations of movement behaviors and body mass index: comparison between a report-based and monitor-based method using Compositional Data Analysis

2020 ◽  
Vol 45 (1) ◽  
pp. 266-275 ◽  
Author(s):  
Youngwon Kim ◽  
Ryan D. Burns ◽  
Duck-chul Lee ◽  
Gregory J. Welk
Keyword(s):  
Physical Activity ◽  
Body Mass Index ◽  
Data Analysis ◽  
Body Mass ◽  
Compositional Data ◽  
Activity Measurement ◽  
Compositional Data Analysis ◽  
Lifestyle Behaviors ◽  
Linear Regression Models ◽  
Index Comparison

Abstract Background/objectives Evidence on the associations between lifestyle movement behaviors and obesity has been established without taking into account the time-constrained nature of categorized, time-based lifestyle behaviors. We examined the associations of sleep, sedentary behavior (SED), light-intensity physical activity (LPA), and moderate-to-vigorous PA (MVPA) with body mass index (BMI) using Compositional Data Analysis (CoDA), and compared the associations between a report-based method (24-h Physical Activity Recall; 24PAR) and a monitor-based method (SenseWear Armband; SWA). Subjects/methods Replicate data from a representative sample of 1247 adults from the Physical Activity Measurement Survey (PAMS) were used in the study. Participants completed activity monitoring on two randomly selected days, each of which required wearing a SWA for a full day, and then completing a telephone-administered 24PAR the following day. Relationships among behavioral compositional parts and BMI were analyzed using CoDA via multiple linear regression models with both 24PAR and SWA data. Results Using 24PAR, time spent in sleep (γ = −3.58, p = 0.011), SED (γ = 3.70, p = 0.002), and MVPA (γ = −0.53, p = 0.018) was associated with BMI. Using SWA, time spent in sleep (γ = −5.10, p < 0.001), SED (γ = 8.93, p < 0.001), LPA (γ = −3.12, p < 0.001), and MVPA (γ = −1.43, p < 0.001) was associated with BMI. The SWA models explained more variance in BMI (R2 = 0.28) compared with the 24PAR models (R2 = 0.07). The compositional isotemporal substitution models revealed reductions in BMI when replacing SED by MVPA, LPA (not with 24PAR) or sleep for both 24PAR and SWA, but the effect estimates were larger with SWA. Conclusions Favorable levels of relative time spent in lifestyle movement behaviors were, in general, associated with decreased BMI. The observed associations were stronger using the monitor-based SWA method compared with the report-based 24PAR method.

Analysing body composition as compositional data: An exploration of the relationship between body composition, body mass and bone strength

2020 ◽  
pp. 096228022095522
Author(s):  
D Dumuid ◽  
JA Martín-Fernández ◽  
S Ellul ◽  
RS Kenett ◽  
M Wake ◽  
...  
Keyword(s):  
Body Composition ◽  
Data Analysis ◽  
Health Outcomes ◽  
Bone Strength ◽  
Body Mass ◽  
Statistical Approach ◽  
Compositional Data ◽  
Fat Free Mass ◽  
Compositional Data Analysis ◽  
Relative Information

Human body composition is made up of mutually exclusive and exhaustive parts (e.g. %truncal fat, %non-truncal fat and %fat-free mass) which are constrained to sum to the same total (100%). In statistical analyses, individual parts of body composition (e.g. %truncal fat or %fat-free mass) have traditionally been used as proxies for body composition, and have been linked with a range of health outcomes. But analysis of individual parts omits information about the other parts, which are intrinsically co-dependent because of the constant sum constraint of 100%. Further, body mass may be associated with health outcomes. We describe a statistical approach for body composition based on compositional data analysis. The body composition data are expressed as logratios to allow relative information about all the compositional parts to be explored simultaneously in relation to health outcomes. We describe a recent extension to the logratio approach to compositional data analysis which allows absolute information about the total of the compositional parts (body mass) to be considered alongside relative information about body composition. The statistical approach is illustrated by an example that explores the relationships between adults’ body composition, body mass and bone strength.

Compositional data analysis in epidemiology

2016 ◽  
Vol 27 (6) ◽  
pp. 1878-1891 ◽  
Author(s):  
Mehmet C Mert ◽  
Peter Filzmoser ◽  
Gottfried Endel ◽  
Ingrid Wilbacher
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Statistical Analyses ◽  
Analysis Approach ◽  
Compositional Data Analysis ◽  
Data Sets ◽  
Multivariate Statistical Analyses ◽  
Multivariate Statistical ◽  
Data Set ◽  
Relative Information

Compositional data analysis refers to analyzing relative information, based on ratios between the variables in a data set. Data from epidemiology are usually treated as absolute information in an analysis. We outline the differences in both approaches for univariate and multivariate statistical analyses, using illustrative data sets from Austrian districts. Not only the results of the analyses can differ, but in particular the interpretation differs. It is demonstrated that the compositional data analysis approach leads to new and interesting insights.

Insights on the characteristics and sources of gas from an underground coal mine using compositional data analysis

2021 ◽  
pp. 103767
Author(s):  
C. Özgen Karacan ◽  
Josep Antoni Martín-Fernández ◽  
Leslie F. Ruppert ◽  
Ricardo A. Olea
Keyword(s):  
Data Analysis ◽  
Coal Mine ◽  
Compositional Data ◽  
Compositional Data Analysis ◽  
Underground Coal Mine

scholarly journals Effects of Two Randomized and Controlled Multi-Component Interventions Focusing On 24-Hour Movement Behavior among Office Workers: A Compositional Data Analysis

2021 ◽  
Vol 18 (8) ◽  
pp. 4191
Author(s):  
Lisa-Marie Larisch ◽  
Emil Bojsen-Møller ◽  
Carla F. J. Nooijen ◽  
Victoria Blom ◽  
Maria Ekblom ◽  
...  
Keyword(s):  
Physical Activity ◽  
Data Analysis ◽  
Cardiorespiratory Fitness ◽  
Leisure Time ◽  
Compositional Data ◽  
Office Workers ◽  
Movement Behavior ◽  
Compositional Data Analysis ◽  
Intervention Effects ◽  
Time In Bed

Intervention studies aiming at changing movement behavior have usually not accounted for the compositional nature of time-use data. Compositional data analysis (CoDA) has been suggested as a useful strategy for analyzing such data. The aim of this study was to examine the effects of two multi-component interventions on 24-h movement behavior (using CoDA) and on cardiorespiratory fitness among office workers; one focusing on reducing sedentariness and the other on increasing physical activity. Office workers (n = 263) were cluster randomized into one of two 6-month intervention groups, or a control group. Time spent in sedentary behavior, light-intensity, moderate and vigorous physical activity, and time in bed were assessed using accelerometers and diaries, both for 24 h in total, and for work and leisure time separately. Cardiorespiratory fitness was estimated using a sub-maximal cycle ergometer test. Intervention effects were analyzed using linear mixed models. No intervention effects were found, either for 24-h behaviors in total, or for work and leisure time behaviors separately. Cardiorespiratory fitness did not change significantly. Despite a thorough analysis of 24-h behaviors using CoDA, no intervention effects were found, neither for behaviors in total, nor for work and leisure time behaviors separately. Cardiorespiratory fitness did not change significantly. Although the design of the multi-component interventions was based on theoretical frameworks, and included cognitive behavioral therapy counselling, which has been proven effective in other populations, issues related to implementation of and compliance with some intervention components may have led to the observed lack of intervention effect.

scholarly journals The Gut Microbiota of Healthy Aged Chinese Is Similar to That of the Healthy Young

mSphere ◽  
2017 ◽  
Vol 2 (5) ◽  
Author(s):  
Gaorui Bian ◽  
Gregory B. Gloor ◽  
Aihua Gong ◽  
Changsheng Jia ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Data Analysis ◽  
Gut Microbiota ◽  
Large Scale ◽  
Compositional Data ◽  
Healthy Lifestyle ◽  
Compositional Data Analysis ◽  
Surprising Result ◽  
Microbiota Composition ◽  
Cross Sectional ◽  
Age Cohorts

ABSTRACT We report the large-scale use of compositional data analysis to establish a baseline microbiota composition in an extremely healthy cohort of the Chinese population. This baseline will serve for comparison for future cohorts with chronic or acute disease. In addition to the expected difference in the microbiota of children and adults, we found that the microbiota of the elderly in this population was similar in almost all respects to that of healthy people in the same population who are scores of years younger. We speculate that this similarity is a consequence of an active healthy lifestyle and diet, although cause and effect cannot be ascribed in this (or any other) cross-sectional design. One surprising result was that the gut microbiota of persons in their 20s was distinct from those of other age cohorts, and this result was replicated, suggesting that it is a reproducible finding and distinct from those of other populations. The microbiota of the aged is variously described as being more or less diverse than that of younger cohorts, but the comparison groups used and the definitions of the aged population differ between experiments. The differences are often described by null hypothesis statistical tests, which are notoriously irreproducible when dealing with large multivariate samples. We collected and examined the gut microbiota of a cross-sectional cohort of more than 1,000 very healthy Chinese individuals who spanned ages from 3 to over 100 years. The analysis of 16S rRNA gene sequencing results used a compositional data analysis paradigm coupled with measures of effect size, where ordination, differential abundance, and correlation can be explored and analyzed in a unified and reproducible framework. Our analysis showed several surprising results compared to other cohorts. First, the overall microbiota composition of the healthy aged group was similar to that of people decades younger. Second, the major differences between groups in the gut microbiota profiles were found before age 20. Third, the gut microbiota differed little between individuals from the ages of 30 to >100. Fourth, the gut microbiota of males appeared to be more variable than that of females. Taken together, the present findings suggest that the microbiota of the healthy aged in this cross-sectional study differ little from that of the healthy young in the same population, although the minor variations that do exist depend upon the comparison cohort. IMPORTANCE We report the large-scale use of compositional data analysis to establish a baseline microbiota composition in an extremely healthy cohort of the Chinese population. This baseline will serve for comparison for future cohorts with chronic or acute disease. In addition to the expected difference in the microbiota of children and adults, we found that the microbiota of the elderly in this population was similar in almost all respects to that of healthy people in the same population who are scores of years younger. We speculate that this similarity is a consequence of an active healthy lifestyle and diet, although cause and effect cannot be ascribed in this (or any other) cross-sectional design. One surprising result was that the gut microbiota of persons in their 20s was distinct from those of other age cohorts, and this result was replicated, suggesting that it is a reproducible finding and distinct from those of other populations.

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