Field #3 of the Palomar-Groningen Survey II. Near-infrared photometry of semiregular variables

Near-infrared photometry (JHKL'M) was obtained for 78 semiregular variables (SRVs) in field #3 of the Palomar-Groningen survey (PG3, l=0, b=-10). Together with a sample of Miras in this field a comparison is made with a sample of field SRVs and Miras. The PG3 SRVs form a sequence (period-luminosity & period-colour) with the PG3 Miras, in which the SRVs are the short period extension to the Miras. The field and PG3 Miras follow the same P/(J--K)o relation, while this is not the case for the field and PG3 SRVs. Both the PG3 SRVs and Miras follow the SgrI period-luminosity relation adopted from Glass et al. (1995, MNRAS 273, 383). They are likely pulsating in the fundamental mode and have metallicities spanning the range from intermediate to approximately solar.Comment: 14 pages LaTeX (2 tables, 8 figures), to appear in A&A 338 (1998); minor modifications in tex

Orthogonal regression for three-part compositional data via linear model with type-II constraints

Orthogonal regression is a proper tool for fitting two-dimensional data points when errors occur in both the variables. This type of modelling technique is also called the total least squares (TLS) in the statistical literature. In its simplest form it attempts to fit a line that explains the set of n two-dimensional data points in such a way that the sum of squared distances from data points to the estimated line is minimal. Orthogonal regression is invariant under the orthogonal rotation of coordinates and thus it is convenient for regression analysis of three-part compositional data, performed after isometric logratio transformation

Cox regression survival analysis with compositional covariates: application to modelling mortality risk from 24-h physical activity patterns

Survival analysis is commonly conducted in medical and public health research to assess the association of an exposure or intervention with a hard end outcome such as mortality. The Cox (proportional hazards) regression model is probably the most popular statistical tool used in this context. However, when the exposure includes compositional covariables (that is, variables representing a relative makeup such as a nutritional or physical activity behaviour composition), some basic assumptions of the Cox regression model and associated significance tests are violated. Compositional variables involve an intrinsic interplay between one another which precludes results and conclusions based on considering them in isolation as is ordinarily done. In this work, we introduce a formulation of the Cox regression model in terms of log-ratio coordinates which suitably deals with the constraints of compositional covariates, facilitates the use of common statistical inference methods, and allows for scientifically meaningful interpretations. We illustrate its practical application to a public health problem: the estimation of the mortality hazard associated with the composition of daily activity behaviour (physical activity, sitting time and sleep) using data from the U.S. National Health and Nutrition Examination Survey (NHANES)

Robust compositional data analysis

Many practical data sets contain outliers or other forms of data inhomogeneities. Robust statistics offers concepts how to deal with these situations where the data do not follow strict model assumptions. These concepts are designed for the usual Euclidean space, and they can be easily applied to compositional data if they are represented in this space as well. It turns out that the isometric logratio (ilr) transformation is best suitable in the context of robust estimation. Depending on the method applied, an interpretation of result is usually done in a back-transformed space

Interpretation of orthonormal coordinates in case of three-part compositions applied to orthogonal regression for compositional data.

Orthonormal coordinates are very important tool for compositional data processing using standard statistical methods. Namely, in order to express a D-part composition in the Euclidean real space we use isometric log-ratio (ilr) transformation, which is an isometric mapping from the sample space of compositions, the simplex S D with the Aitchison geometry, to the (D −1)-dimensional Euclidean real space RD−1 . The ilr transformation results in coordinates of an orthonormal basis on the simplex. Advantages coming from this transformation, like the mentioned isometry between S D and RD−1 , are closely related with the problem of interpreting orthonormal coordinates, constructed by sequential binary partition. Their interpretation can be approached as balances between groups of parts of a composition as well as by expressing their covariance structure by log-ratios of parts of the analyzed composition, i.e. in terms of ratios. Note that if we want to achieve interpretation of results of statistical analysis directly on the simplex (in terms of the original compositional parts), the backtransformation is required

Analysis of compositional data using robust methods. The R-package robCompositons

The free and open-source programming language and software environment R (R Development Core Team, 2010) is currently both, the most widely used and most popular software for statistics and data analysis. In addition, R becomes quite popular as a (programming) language, ranked currently (February 2011) on place 25 at the TIOBE Programming Community Index (e.g., Matlab: 29, SAS: 30, see http://www.tiobe.com). The basic R environment can be downloaded from the comprehensive R archive network (http://cran.rproject.org). R is enhanceable via packages which consist of code and structured standard documentation including code application examples and possible further documents (so called vignettes) showing further applications of the packages. Two contributed packages for compositional data analysis comes with R, version 2.12.1.: the package compositions (van den Boogaart et al., 2010) and the package robCompositions (Templ et al., 2011). Package compositions provides functions for the consistent analysis of compositional data and positive numbers in the way proposed originally by John Aitchison (see van den Boogaart et al., 2010). In addition to the basic functionality and estimation procedures in package compositions, package robCompositions provides tools for a (classical) and robust multivariate statistical analysis of compositional data together with corresponding graphical tools. In addition, several data sets are provided as well as useful utility functions

Classical and robust imputation of missing values for compositional data using balances

Classical and Robust Imputation of Missing Values for Compositional Data using Balance

Simplicial principal component analysis for density functions in Bayes spaces

Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria