Robust Principal Component Analysis for Compositional Tables

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information would consist of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with a direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (PCA) is performed for dimension reduction, allowing to investigate the relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply robust PCA, which would otherwise suffer from the singularity of clr coefficients.Comment: 20 pages, 2 figure

Thurstonian Scaling of Compositional Questionnaire Data

To prevent response biases, personality questionnaires may use comparative response formats. These include forced choice, where respondents choose among a number of items, and quantitative comparisons, where respondents indicate the extent to which items are preferred to each other. The present article extends Thurstonian modeling of binary choice data (Brown & Maydeu-Olivares, 2011a) to “proportion-of-total” (compositional) formats. Following Aitchison (1982), compositional item data are transformed into log-ratios, conceptualized as differences of latent item utilities. The mean and covariance structure of the log-ratios is modelled using Confirmatory Factor Analysis (CFA), where the item utilities are first-order factors, and personal attributes measured by a questionnaire are second-order factors. A simulation study with two sample sizes, N=300 and N=1000, shows that the method provides very good recovery of true parameters and near-nominal rejection rates. The approach is illustrated with empirical data from N=317 students, comparing model parameters obtained with compositional and Likert scale versions of a Big Five measure. The results show that the proposed model successfully captures the latent structures and person scores on the measured traits

Convex hull method for the determination of vapour-liquid equilibria (VLE) phase diagrams for binary and ternary systems

Amieibibama Joseph wishes to thank Petroleum Technology Development Fund (PTDF) for their financial support which has made this research possible.Peer reviewedPostprin

Interactions between species introduce spurious associations in microbiome studies

Microbiota contribute to many dimensions of host phenotype, including disease. To link specific microbes to specific phenotypes, microbiome-wide association studies compare microbial abundances between two groups of samples. Abundance differences, however, reflect not only direct associations with the phenotype, but also indirect effects due to microbial interactions. We found that microbial interactions could easily generate a large number of spurious associations that provide no mechanistic insight. Using techniques from statistical physics, we developed a method to remove indirect associations and applied it to the largest dataset on pediatric inflammatory bowel disease. Our method corrected the inflation of p-values in standard association tests and showed that only a small subset of associations is directly linked to the disease. Direct associations had a much higher accuracy in separating cases from controls and pointed to immunomodulation, butyrate production, and the brain-gut axis as important factors in the inflammatory bowel disease.Comment: 4 main text figures, 15 supplementary figures (i.e appendix) and 6 supplementary tables. Overall 49 pages including reference

The impact of movement behaviors on bone health in elderly with adequate nutritional status: compositional data analysis depending on the frailty status

The aim of this study was to determine the relationship between bone mass (BM) and physical activity (PA) and sedentary behavior (SB) according to frailty status and sex using compositional data analysis. We analyzed 871 older people with an adequate nutritional status. Fried criteria were used to classify by frailty status. Time spent in SB, light intensity PA (LPA) and moderate-to-vigorous intensity PA (MVPA) was assessed from accelerometry for 7 days. BM was determined by dual-energy X-ray absorptiometry (DXA). The combined effect of PA and SB was significantly associated with BM in robust men and women (p ≤ 0.05). In relation to the other behaviors, SB was negatively associated with BM in robust men while BM was positively associated with SB and negatively with LPA and MVPA in robust women. Moreover, LPA also was positively associated with arm BM (p ≤ 0.01). Finally, in pre-frail women, BM was positively associated with MVPA. In our sample, to decrease SB could be a good strategy to improve BM in robust men. In contrast, in pre-frail women, MVPA may be an important factor to consider regarding bone health