On stability of compositional canonical variate vector components

Abstract: Canonical variate analysis (aka discriminant coordinates) is viewed from the aspect of Aitchisonian compositional data analysis and the concept of stability in canonical vectors examined in relation to their reification (i.e. providing canonical vector components with a practical interpretation). The log-ratio transformation was found to have computational and interpretational advantages over the centred log-ratio transformation. The ad hoc application of N. A. Campbell's application of the method of shrinkage estimators to multiple discrimination, and the optimal retention of discrimination power, is exemplified by two cases, one drawn from quantitative sedimentology, the other from biomolecular palaeontology, with the intention of probing the effect of instability on interpreting the relative importance of standardized canonical variate coefficients in relation to the suppression of near-redundant directions of within-groups variation. Pronounced instability in canonical vectors may endanger the validity of an analysis

The Morphometric Synthesis for landmarks and edge-elements in images

Over the last decade, techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry, and computer graphics have been combined in a coherent new system of tools for the biometric analysis of landmarks , or labelled points, along with the biological images in which they are seen. Multivariate analyses of samples for all the usual scientific purposes - description of mean shapes, of shape variation, and of the covariation of shape with size, group, or other causes or effects - may be carried out very effectively in the tangent space to David Kendall's shape space at the Procrustes average shape. For biometric interpretation of such analyses, we need a basis for the tangent space that is Procrustes-orthonormal, and we need graphics for visualizing mean shape differences and other segments and vectors there; both of these needs are managed by the thin-plate spline. The spline also links the biometrics of landmarks to deformation analysis of curves in the images from which the landmarks originally arose. This article reviews the principal tools of this synthesis in a typical study design involving landmarks and edge information from a microfossil.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75091/1/j.1365-3121.1995.tb00535.x.pd

An EWMA control chart for the multivariate coefficient of variation

This is the peer reviewed version of the following article: Giner-Bosch, V, Tran, KP, Castagliola, P, Khoo, MBC. An EWMA control chart for the multivariate coefficient of variation. Qual Reliab Engng Int. 2019; 35: 1515-1541, which has been published in final form at https://doi.org/10.1002/qre.2459. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] Monitoring the multivariate coefficient of variation over time is a natural choice when the focus is on stabilising the relative variability of a multivariate process, as is the case in a significant number of real situations in engineering, health sciences, and finance, to name but a few areas. However, not many tools are available to practitioners with this aim. This paper introduces a new control chart to monitor the multivariate coefficient of variation through an exponentially weighted moving average (EWMA) scheme. Concrete methodologies to calculate the limits and evaluate the performance of the chart proposed and determine the optimal values of the chart's parameters are derived based on a theoretical study of the statistic being monitored. Computational experiments reveal that our proposal clearly outperforms existing alternatives, in terms of the average run length to detect an out-of-control state. A numerical example is included to show the efficiency of our chart when operating in practice.Generalitat Valenciana, Grant/Award Number: BEST/2017/033 and GV/2016/004; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2013-45381-PGiner-Bosch, V.; Tran, KP.; Castagliola, P.; Khoo, MBC. (2019). An EWMA control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International. 35(6):1515-1541. https://doi.org/10.1002/qre.2459S15151541356Kang, C. W., Lee, M. S., Seong, Y. J., & Hawkins, D. M. (2007). A Control Chart for the Coefficient of Variation. Journal of Quality Technology, 39(2), 151-158. doi:10.1080/00224065.2007.11917682Amdouni, A., Castagliola, P., Taleb, H., & Celano, G. (2015). Monitoring the coefficient of variation using a variable sample size control chart in short production runs. The International Journal of Advanced Manufacturing Technology, 81(1-4), 1-14. doi:10.1007/s00170-015-7084-4Amdouni, A., Castagliola, P., Taleb, H., & Celano, G. (2017). A variable sampling interval Shewhart control chart for monitoring the coefficient of variation in short production runs. International Journal of Production Research, 55(19), 5521-5536. doi:10.1080/00207543.2017.1285076Yeong, W. C., Khoo, M. B. C., Tham, L. K., Teoh, W. L., & Rahim, M. A. (2017). Monitoring the Coefficient of Variation Using a Variable Sampling Interval EWMA Chart. Journal of Quality Technology, 49(4), 380-401. doi:10.1080/00224065.2017.11918004Teoh, W. L., Khoo, M. B. C., Castagliola, P., Yeong, W. C., & Teh, S. Y. (2017). Run-sum control charts for monitoring the coefficient of variation. European Journal of Operational Research, 257(1), 144-158. doi:10.1016/j.ejor.2016.08.067Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/jpm.1994.409501Van Valen, L. (1974). Multivariate structural statistics in natural history. Journal of Theoretical Biology, 45(1), 235-247. doi:10.1016/0022-5193(74)90053-8Albert, A., & Zhang, L. (2010). A novel definition of the multivariate coefficient of variation. Biometrical Journal, 52(5), 667-675. doi:10.1002/bimj.201000030Aerts, S., Haesbroeck, G., & Ruwet, C. (2015). Multivariate coefficients of variation: Comparison and influence functions. Journal of Multivariate Analysis, 142, 183-198. doi:10.1016/j.jmva.2015.08.006Bennett, B. M. (1977). On multivariate coefficients of variation. Statistische Hefte, 18(2), 123-128. doi:10.1007/bf02932744Underhill, L. G. (1990). The coefficient of variation biplot. Journal of Classification, 7(2), 241-256. doi:10.1007/bf01908718Boik, R. J., & Shirvani, A. (2009). Principal components on coefficient of variation matrices. Statistical Methodology, 6(1), 21-46. doi:10.1016/j.stamet.2008.02.006MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3(3), 403-414. doi:10.1016/0967-0661(95)00014-lBersimis, S., Psarakis, S., & Panaretos, J. (2007). Multivariate statistical process control charts: an overview. Quality and Reliability Engineering International, 23(5), 517-543. doi:10.1002/qre.829Yeong, W. C., Khoo, M. B. C., Teoh, W. L., & Castagliola, P. (2015). A Control Chart for the Multivariate Coefficient of Variation. Quality and Reliability Engineering International, 32(3), 1213-1225. doi:10.1002/qre.1828Lim, A. J. X., Khoo, M. B. C., Teoh, W. L., & Haq, A. (2017). Run sum chart for monitoring multivariate coefficient of variation. Computers & Industrial Engineering, 109, 84-95. doi:10.1016/j.cie.2017.04.023Roberts, S. W. (1966). A Comparison of Some Control Chart Procedures. Technometrics, 8(3), 411-430. doi:10.1080/00401706.1966.10490374Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 1(3), 239-250. doi:10.1080/00401706.1959.10489860Lucas, J. M., & Saccucci, M. S. (1990). Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics, 32(1), 1-12. doi:10.1080/00401706.1990.10484583Wijsman, R. A. (1957). Random Orthogonal Transformations and their use in Some Classical Distribution Problems in Multivariate Analysis. The Annals of Mathematical Statistics, 28(2), 415-423. doi:10.1214/aoms/1177706969The general sampling distribution of the multiple correlation coefficient. (1928). Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 121(788), 654-673. doi:10.1098/rspa.1928.0224Paolella, M. S. (2007). Intermediate Probability. doi:10.1002/9780470035061WalckC.Handbook on statistical distributions for experimentalists. Tech. Rep. SUFPFY/96‐01 Stockholm   Particle Physics Group Fysikum University of Stockholm;2007. http://inspirehep.net/record/1389910BROOK, D., & EVANS, D. A. (1972). An approach to the probability distribution of cusum run length. Biometrika, 59(3), 539-549. doi:10.1093/biomet/59.3.539Castagliola, P., Celano, G., & Psarakis, S. (2011). Monitoring the Coefficient of Variation Using EWMA Charts. Journal of Quality Technology, 43(3), 249-265. doi:10.1080/00224065.2011.11917861Vining, G. (2009). Technical Advice: Phase I and Phase II Control Charts. 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Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Analysis of Ratios in Multivariate Morphometry

The analysis of ratios of body measurements is deeply ingrained in the taxonomic literature. Whether for plants or animals, certain ratios are commonly indicated in identification keys, diagnoses, and descriptions. They often provide the only means for separation of cryptic species that mostly lack distinguishing qualitative characters. Additionally, they provide an obvious way to study differences in body proportions, as ratios reflect geometric shape differences. However, when it comes to multivariate analysis of body measurements, for instance, with linear discriminant analysis (LDA) or principal component analysis (PCA), interpretation using body ratios is difficult. Both techniques are commonly applied for separating similar taxa or for exploring the structure of variation, respectively, and require standardized raw or log-transformed variables as input. Here, we develop statistical procedures for the analysis of body ratios in a consistent multivariate statistical framework. In particular, we present algorithms adapted to LDA and PCA that allow the interpretation of numerical results in terms of body proportions. We first introduce a method called the “LDA ratio extractor,” which reveals the best ratios for separation of two or more groups with the help of discriminant analysis. We also provide measures for deciding how much of the total differences between individuals or groups of individuals is due to size and how much is due to shape. The second method, a graphical tool called the “PCA ratio spectrum,” aims at the interpretation of principal components in terms of body ratios. Based on a similar idea, the “allometry ratio spectrum” is developed which can be used for studying the allometric behavior of ratios. Because size can be defined in different ways, we discuss several concepts of size. Central to this discussion is Jolicoeur's multivariate generalization of the allometry equation, a concept that was derived only with a heuristic argument. Here we present a statistical derivation of the allometric size vector using the method of least squares. The application of the above methods is extensively demonstrated using published data sets from parasitic wasps and rock crabs

The Origin and Initial Rise of Pelagic Cephalopods in the Ordovician

BACKGROUND: During the Ordovician the global diversity increased dramatically at family, genus and species levels. Partially the diversification is explained by an increased nutrient, and phytoplankton availability in the open water. Cephalopods are among the top predators of today's open oceans. Their Ordovician occurrences, diversity evolution and abundance pattern potentially provides information on the evolution of the pelagic food chain. METHODOLOGY/PRINCIPAL FINDINGS: We reconstructed the cephalopod departure from originally exclusively neritic habitats into the pelagic zone by the compilation of occurrence data in offshore paleoenvironments from the Paleobiology Database, and from own data, by evidence of the functional morphology, and the taphonomy of selected cephalopod faunas. The occurrence data show, that cephalopod associations in offshore depositional settings and black shales are characterized by a specific composition, often dominated by orthocerids and lituitids. The siphuncle and conch form of these cephalopods indicate a dominant lifestyle as pelagic, vertical migrants. The frequency distribution of conch sizes and the pattern of epibionts indicate an autochthonous origin of the majority of orthocerid and lituitid shells. The consistent concentration of these cephalopods in deep subtidal sediments, starting from the middle Tremadocian indicates the occupation of the pelagic zone early in the Early Ordovician and a subsequent diversification which peaked during the Darriwilian. CONCLUSIONS/SIGNIFICANCE: The exploitation of the pelagic realm started synchronously in several independent invertebrate clades during the latest Cambrian to Middle Ordovician. The initial rise and diversification of pelagic cephalopods during the Early and Middle Ordovician indicates the establishment of a pelagic food chain sustainable enough for the development of a diverse fauna of large predators. The earliest pelagic cephalopods were slowly swimming vertical migrants. The appearance and early diversification of pelagic cephalopods is interpreted as a consequence of the increased food availability in the open water since the latest Cambrian

Caloric beverage consumption patterns in Mexican children

<p>Abstract</p> <p>Background</p> <p>Mexico has seen a very steep increase in child obesity level. Little is known about caloric beverage intake in this country as well as all other countries outside a few high income countries. This study examines overall patterns and trends in all caloric beverages from two nationally representative surveys from Mexico.</p> <p>Methods</p> <p>The two nationally representative dietary intake surveys (1999 and 2006) from Mexico are used to study caloric beverage intake in 17, 215 children. The volume (ml) and caloric energy (kcal) contributed by all beverages consumed by the sample subjects were measured. Results are weighted to be nationally representative.</p> <p>Results</p> <p>The trends from the dietary intake surveys showed very large increases in caloric beverages among pre-school and school children. The contribution of whole milk and sugar-sweetened juices was an important finding. Mexican pre-school children consumed 27.8% of their energy from caloric beverages in 2006 and school children consumed 20.7% of their energy from caloric beverages during the same time. The three major categories of beverage intake are whole milk, fruit juice with various sugar and water combinations and carbonated and noncarbonated sugared-beverages.</p> <p>Conclusion</p> <p>The Mexican government, greatly concerned about obesity, has identified the large increase in caloric beverages from whole milk, juices and soft drinks as a key target and is initiating major changes to address this problem. They have already used the data to shift 20 million persons in their welfare and feeding programs from whole to 1.5% fat milk and in a year will shift to nonfat milk. They are using these data to revise school beverage policies and national regulations and taxation policies related to an array of less healthful caloric beverages.</p

South Atlantic paleobathymetry since early Cretaceous

We present early Cretaceous to present paleobathymetric reconstructions and quantitative uncertainty estimates for the South Atlantic, offering a strong basis for studies of paleocirculation, paleoclimate and paleobiogeography. Circulation in an initially salty and anoxic ocean, restricted by the topography of the Falkland Plateau, Rio Grande Ridge and Walvis Rise, favoured deposition of thick evaporites in shallow water of the Brazilian-Angolan margins. This ceased as sea oor spreading propagated northwards, opening an equatorial gateway to shallow and intermediate circulation. This gateway, together with subsiding volcano-tectonic barriers would have played a key role in Late Cretaceous climate changes. Later deepening and widening of the South Atlantic, together with gateway opening at Drake Passage would lead, by mid-Miocene (∼15 Ma) to the establishment of modern-style thermohaline circulation

Modulation of social interactions by immune stimulation in honey bee, Apis mellifera, workers

International audienceBACKGROUND:Immune response pathways have been relatively well-conserved across animal species, with similar systems in both mammals and invertebrates. Interestingly, honey bees have substantially reduced numbers of genes associated with immune function compared with solitary insect species. However, social species such as honey bees provide an excellent environment for pathogen or parasite transmission with controlled environmental conditions in the hive, high population densities, and frequent interactions. This suggests that honey bees may have developed complementary mechanisms, such as behavioral modifications, to deal with disease.RESULTS:Here, we demonstrate that activation of the immune system in honey bees (using bacterial lipopolysaccharides as a non-replicative pathogen) alters the social responses of healthy nestmates toward the treated individuals. Furthermore, treated individuals expressed significant differences in overall cuticular hydrocarbon profiles compared with controls. Finally, coating healthy individuals with extracts containing cuticular hydrocarbons of immunostimulated individuals significantly increased the agonistic responses of nestmates.CONCLUSION:Since cuticular hydrocarbons play a critical role in nestmate recognition and other social interactions in a wide variety of insect species, modulation of such chemical profiles by the activation of the immune system could play a crucial role in the social regulation of pathogen dissemination within the colony