Josep A. Martín-Fernández

Dealing with zeros and missing values in compositional data sets using nonparametric imputation

The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature which can be used. In particular, substitution or imputation strategies are available for rounded zeros. In this paper, existing nonparametric imputation methods—both for the additive and the multiplicative approach—are revised and essential properties of the last method are given. For missing values a generalization of the multiplicative approach is proposed.

Logratio Analysis and Compositional Distance

The concept of distance between two compositions is important in the statistical analysis of compositional data, particularly in such activities as cluster analysis and multidimensional scaling. This paper exposes the fallacies in a recent criticism of logratio-based distance measures—in particular, the misstatements that logratio methods destroy distance structures and are denominator dependent. Emphasis is on ensuring that compositional data analysis involving distance concepts satisfies certain logically necessary invariance conditions. Logratio analysis and its associated distance measures satisfy these conditions.

Mapping Individual Variation in Male Mating Preference Space: Multiple Choice in a Color Polymorphic Cichlid Fish

Sexual selection theory largely rests on the assumption that populations contain individual variation in mating preferences and that individuals are consistent in their preferences. However, there are few empirical studies of within-population variation and even fewer have examined individual male mating preferences. Here, we studied a color polymorphic population of the Lake Victoria cichlid fish Neochromis omnicaeruleus, a species in which color morphs are associated with different sex-determining factors. Wild-caught males were tested in three-way choice trials with multiple combinations of different females belonging to the three color morphs. Compositional log-ratio techniques were applied to analyze individual male mating preferences. Large individual variation in consistency, strength, and direction of male mating preferences for female color morphs was found and hierarchical clustering of the compositional data revealed the presence of four distinct preference groups corresponding to the three color morphs in addition to a no-preference class. Consistency of individual male mating preferences was higher in males with strongest preferences. We discuss the implications of these findings for our understanding of the mechanisms underlying polymorphism in mating preferences.

Health-related quality of life and lifestyle behavior clusters in school-aged children from 12 countries

Objective To evaluate the relationship between childrens lifestyles and health‐related quality of life and to explore whether this relationship varies among children from different world regions. Study design This study used cross‐sectional data from the International Study of Childhood Obesity, Lifestyle and the Environment. Children (9‐11 years) were recruited from sites in 12 nations (n = 5759). Clustering input variables were 24‐hour accelerometry and self‐reported diet and screen time. Health‐related quality of life was self‐reported with KIDSCREEN‐10. Cluster analyses (using compositional analysis techniques) were performed on a site‐wise basis. Lifestyle behavior cluster characteristics were compared between sites. The relationship between cluster membership and health‐related quality of life was assessed with the use of linear models. Results Lifestyle behavior clusters were similar across the 12 sites, with clusters commonly characterized by (1) high physical activity (actives); (2) high sedentary behavior (sitters); (3) high screen time/unhealthy eating pattern (junk‐food screenies); and (4) low screen time/healthy eating pattern and moderate physical activity/sedentary behavior (all‐rounders). Health‐related quality of life was greatest in the all‐rounders cluster. Conclusions Children from different world regions clustered into groups of similar lifestyle behaviors. Cluster membership was related to differing health‐related quality of life, with children from the all‐rounders cluster consistently reporting greatest health‐related quality of life at sites around the world. Findings support the importance of a healthy combination of lifestyle behaviors in childhood: low screen time, healthy eating pattern, and balanced daily activity behaviors (physical activity and sedentary behavior). Trial registration ClinicalTrials.gov: NCT01722500.

Recycling of plastic waste: presence of phthalates in plastics from households and industry

Plastics recycling has the potential to substitute virgin plastics partially as a source of raw materials in plastic product manufacturing. Plastic as a material may contain a variety of chemicals, some potentially hazardous. Phthalates, for instance, are a group of chemicals produced in large volumes and are commonly used as plasticisers in plastics manufacturing. Potential impacts on human health require restricted use in selected applications and a need for the closer monitoring of potential sources of human exposure. Although the presence of phthalates in a variety of plastics has been recognised, the influence of plastic recycling on phthalate content has been hypothesised but not well documented. In the present work we analysed selected phthalates (DMP, DEP, DPP, DiBP, DBP, BBzP, DEHP, DCHP and DnOP) in samples of waste plastics as well as recycled and virgin plastics. DBP, DiBP and DEHP had the highest frequency of detection in the samples analysed, with 360μg/g, 460μg/g and 2700μg/g as the maximum measured concentrations, respectively. Among other, statistical analysis of the analytical results suggested that phthalates were potentially added in the later stages of plastic product manufacturing (labelling, gluing, etc.) and were not removed following recycling of household waste plastics. Furthermore, DEHP was identified as a potential indicator for phthalate contamination of plastics. Close monitoring of plastics intended for phthalates-sensitive applications is recommended if recycled plastics are to be used as raw material in production.

Gaussian kernels for density estimation with compositional data

Common simplifications of the bandwidth matrix cannot be applied to existing kernels for density estimation with compositional data. In this paper, kernel density estimation methods are modified on the basis of recent developments in compositional data analysis and bandwidth matrix selection theory. The isometric log-ratio normal kernel is used to define a new estimator in which the smoothing parameter is chosen from the most general class of bandwidth matrices on the basis of a recently proposed plug-in algorithm. Both simulated and real examples are presented in which the behaviour of our approach is illustrated, which shows the advantage of the new estimator over existing proposed methods.

Analysis of new diffusion tensor imaging anisotropy measures in the three-phase plot.

To evaluate diffusion anisotropy from diffusion tensor imaging using new measures derived from Hellinger divergences and from compositional data distances.

Criteria to Compare Estimation Methods of Regionalized Compositions

The additive logratio (alr) transformation has been used in several case studies to predict regionalized compositions using standard geostatistical estimation methods such as ordinary kriging and ordinary cokriging. It is a simple method that allows application to transformed data all the body of knowledge available for geostatistical analysis of coregionalizations without a constant sum constraint. To compare the performance of methods, it is customary to use a univariate crossvalidation approach based on the leaving-one-out technique to evaluate the performance for each attribute separately. For multivariate observations this approach is difficult to interpret in terms of overall performance. Therefore, we propose using appropriate distances in real space and in the simplex, to improve the crossvalidation approach and, going a step forward, to adapt the concept of stress from multidimensional scaling to obtain a global measure of performance for each method. The Lyons West oil field of Kansas is used to illustrate the impactof using different distances in the performance of ordinary kriging versus ordinary cokriging.

Advances in Principal Balances for Compositional Data

Compositional data analysis requires selecting an orthonormal basis with which to work on coordinates. In most cases this selection is based on a data driven criterion. Principal component analysis provides bases that are, in general, functions of all the original parts, each with a different weight hindering their interpretation. For interpretative purposes, it would be better to have each basis component as a ratio or balance of the geometric means of two groups of parts, leaving irrelevant parts with a zero weight. This is the role of principal balances, defined as a sequence of orthonormal balances which successively maximize the explained variance in a data set. The new algorithm to compute principal balances requires an exhaustive search along all the possible sets of orthonormal balances. To reduce computational time, the sets of possible partitions for up to 15 parts are stored. Two other suboptimal, but feasible, algorithms are also introduced: (i) a new search for balances following a constrained principal component approach and (ii) the hierarchical cluster analysis of variables. The latter is a new approach based on the relation between the variation matrix and the Aitchison distance. The properties and performance of these three algorithms are illustrated using a typical data set of geochemical compositions and a simulation exercise.

Statistical analysis of solid waste composition data: Arithmetic mean, standard deviation and correlation coefficients

Data for fractional solid waste composition provide relative magnitudes of individual waste fractions, the percentages of which always sum to 100, thereby connecting them intrinsically. Due to this sum constraint, waste composition data represent closed data, and their interpretation and analysis require statistical methods, other than classical statistics that are suitable only for non-constrained data such as absolute values. However, the closed characteristics of waste composition data are often ignored when analysed. The results of this study showed, for example, that unavoidable animal-derived food waste amounted to 2.21±3.12% with a confidence interval of (-4.03; 8.45), which highlights the problem of the biased negative proportions. A Pearsons correlation test, applied to waste fraction generation (kg mass), indicated a positive correlation between avoidable vegetable food waste and plastic packaging. However, correlation tests applied to waste fraction compositions (percentage values) showed a negative association in this regard, thus demonstrating that statistical analyses applied to compositional waste fraction data, without addressing the closed characteristics of these data, have the potential to generate spurious or misleading results. Therefore, ¨compositional data should be transformed adequately prior to any statistical analysis, such as computing mean, standard deviation and correlation coefficients.