On the Interpretation of Orthonormal Coordinates for Compositional Data

2011 ◽  
Vol 43 (4) ◽  
pp. 455-468 ◽  
Author(s):  
Eva Fišerová ◽  
Karel Hron
2018 ◽  
Vol 47 (2) ◽  
pp. 3-19 ◽  
Author(s):  
Ivo Muller ◽  
Karel Hron ◽  
Eva Fiserova ◽  
Jan Smahaj ◽  
Panajotis Cakirpaloglu ◽  
...  

Regression with compositional response or covariates, or even regression between parts of a composition, is frequently employed in social sciences. Among other possible applications, it may help to reveal interesting features in time allocation analysis. As individual activities represent relative contributions to the total amount of time, statistical processing of raw data (frequently represented directly as proportions or percentages) using standard methods may lead to biased results. Specific geometrical features of time budget variables are captured by the logratio methodology of compositional data, whose aim is to build (preferably orthonormal) coordinates to be applied with popular statistical methods. The aim of this paper is to present recent tools of regression analysis within the logratio methodology and apply them to reveal potential relationships among psychometric indicators in a real-world data set. In particular, orthogonal logratio coordinates have been introduced to enhance the interpretability of coefficients in regression models.


2016 ◽  
Vol 16 (5) ◽  
pp. 235-243 ◽  
Author(s):  
Eva Fišerová ◽  
Sandra Donevska ◽  
Karel Hron ◽  
Ondřej Bábek ◽  
Kristýna Vaňkátová

AbstractRegression analysis with compositional response, observations carrying relative information, is an appropriate tool for statistical modelling in many scientific areas (e.g. medicine, geochemistry, geology, economics). Even though this technique has been recently intensively studied, there are still some practical aspects that deserve to be further analysed. Here we discuss the issue related to the coordinate representation of compositional data. It is shown that linear relation between particular orthonormal coordinates and centred log-ratio coordinates can be utilized to simplify the computation concerning regression parameters estimation and hypothesis testing. To enhance interpretation of regression parameters, the orthogonal coordinates and their relation with orthonormal and centred log-ratio coordinates are presented. Further we discuss the quality of prediction in different coordinate system. It is shown that the mean squared error (MSE) for orthonormal coordinates is less or equal to the MSE for log-transformed data. Finally, an illustrative real-world example from geology is presented.


Author(s):  
Lisa-Marie Larisch ◽  
Emil Bojsen-Møller ◽  
Carla F. J. Nooijen ◽  
Victoria Blom ◽  
Maria Ekblom ◽  
...  

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.


2020 ◽  
Vol 176 (1) ◽  
Author(s):  
W. D. Maier ◽  
S.-J. Barnes ◽  
D. Muir ◽  
D. Savard ◽  
Y. Lahaye ◽  
...  

AbstractBushveld anorthosites commonly contain the so-called “mottles” comprising irregular, typically centimetric domains of oikocrystic pyroxene or olivine enclosing small, embayed plagioclase grains. The mottles were traditionally interpreted to result from solidification of trapped intercumulus liquid or via in situ crystallisation at the top of the crystal mush. Here, we present microtextural and compositional data of a mottle to place further constraints on the formation of anorthosite layers. Element maps generated by scanning electron microscopy reveal that plagioclase within and around the mottle has markedly elevated An contents (up to An95) relative to the host anorthosite and is strongly reversely zoned. Other unusual features, some of which were reported previously, include a halo of sub-vertically oriented, acicular phlogopite around the mottle, elevated contents of disseminated sulfides, and relatively evolved yet Ni-rich olivine (Fo71–75, 3000 ppm Ni). These features are interpreted to result from reactive porous flow of hot, acidic fluid enriched in nickel and sulfur through proto norite. The fluids dissolved mafic minerals and leached alkalis from the outer rims of plagioclase grains. Reconnaissance studies suggest that reversed zoning of plagioclase is a common feature in Bushveld norite and anorthosite. This implies that reactive porous flow could have been far more pervasive than currently realised and that Bushveld anorthosite layers formed through recrystallisation of norites.


2019 ◽  
Vol 62 (1) ◽  
Author(s):  
Eun-Ha Kim ◽  
So-Young Lee ◽  
Da-Young Baek ◽  
Soo-Yun Park ◽  
Sang-Gu Lee ◽  
...  

Abstract Red peppers are a remarkable source of nutrients in the human diet. However, comprehensive studies have not reported on the effects of genotype, cultivation region, and year on pepper fruit characteristics. To address this, 12 commercial pepper varieties were grown at two locations in South Korea, during 2016 and 2017, representing four environments, and concentrations of proximate, minerals, amino acids, fatty acids, capsaicinoids, and free sugars in pepper pericarps were determined. Variation in most nutrients was observed among the 12 varieties grown within each location in each year, indicating a significant genotype effect. Statistical analysis of combined data showed significant differences among varieties, locations, and years for the measured components. The % variability analysis demonstrated that environment (location and year) and genotype-environment interaction contributed more to the nutritional contents than genotype alone. Particularly, variation in many amino acids, capsaicinoids, free sugars, and myristic acid was attributed to location. Year effect was significant for palmitoleic acid, ash, tryptophan, copper, linolenic acid, crude fiber, and tyrosine. Insoluble dietary fiber, soluble dietary fiber, sodium, sulfate, linoleic acid, and alanine were primarily varied by genotype–environment interaction. Palmitic acid was the trait the most highly affected by genotype. Cultivation and the genotype–environment interaction have a major role in determining the composition of 12 pepper varieties across four environments. The data from this study could explain the natural variation in the compositional data of peppers by genotypes and environments.


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