alr approach for replacing values below the detection limit

All of the imputation techniques usually applied for replacing values below thedetection limit in compositional data sets have adverse effects on the variability. In thiswork we propose a modification of the EM algorithm that is applied using the additivelog-ratio transformation. This new strategy is applied to a compositional data set and theresults are compared with the usual imputation techniques

Simple and fast methods based on solid-phase extraction coupled to liquid chromatography with UV detection for the monitoring of caffeine in natural and waste waters as marker of anthropogenic impact

Two concentration methods for fast and routine determination of caffeine (using HPLC-UV detection) in surface, and wastewater are evaluated. Both methods are based on solid-phase extraction (SPE) concentration with octadecyl silica sorbents. A common “offline” SPE procedure shows that quantitative recovery of caffeine is obtained with 2 mL of an elution mixture solvent methanol-water containing at least 60% methanol. The method detection limit is 0.1 μg L−1 when percolating 1 L samples through the cartridge. The development of an “online” SPE method based on a mini-SPE column, containing 100 mg of the same sorbent, directly connected to the HPLC system allows the method detection limit to be decreased to 10 ng L−1 with a sample volume of 100 mL. The “offline” SPE method is applied to the analysis of caffeine in wastewater samples, whereas the “on-line” method is used for analysis in natural waters from streams receiving significant water intakes from local wastewater treatment plants

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basicfunctionality has seen some conceptual improvement, containing now some facilitiesto work with and represent ilr bases built from balances, and an elaborated subsys-tem for dealing with several kinds of irregular data: (rounded or structural) zeroes,incomplete observations and outliers. The general approach to these irregularities isbased on subcompositions: for an irregular datum, one can distinguish a “regular” sub-composition (where all parts are actually observed and the datum behaves typically)and a “problematic” subcomposition (with those unobserved, zero or rounded parts, orelse where the datum shows an erratic or atypical behaviour). Systematic classificationschemes are proposed for both outliers and missing values (including zeros) focusing onthe nature of irregularities in the datum subcomposition(s).To compute statistics with values missing at random and structural zeros, a projectionapproach is implemented: a given datum contributes to the estimation of the desiredparameters only on the subcompositon where it was observed. For data sets withvalues below the detection limit, two different approaches are provided: the well-knownimputation technique, and also the projection approach.To compute statistics in the presence of outliers, robust statistics are adapted to thecharacteristics of compositional data, based on the minimum covariance determinantapproach. The outlier classification is based on four different models of outlier occur-rence and Monte-Carlo-based tests for their characterization. Furthermore the packageprovides special plots helping to understand the nature of outliers in the dataset.Keywords: coda-dendrogram, lost values, MAR, missing data, MCD estimator,robustness, rounded zeros

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

A fully validated method for the determination of arsenic species in rice and infant cereal products

A full validation of inorganic arsenic (iAs), methylarsonic acid (MA), and dimethyl arsinic acid (DMA) in several types of rice and rice-based infant cereals is reported. The analytical method was developed and validated in two laboratories. The extraction of the As species was performed using nitric acid 0.2 % and hydrogen peroxide 1 %, and the coupled system liquid chromatography-inductively coupled plasma-mass spectrometry (LCICP-MS) was used for speciation measurements. Detection limit (DL), quantification limit, linearity, precision, trueness, accuracy, selectivity, as well as expanded uncertainty for iAs, MA, and DMA were established. The certified reference materials (CRMs) (NMIJ 7503a, NCS ZC73008, NIST SRM 1568a) were used to check the accuracy. The method was shown to be satisfactory in two proficiency tests (PTs). The broad applicability of the method is shown from the results of analysis of 29 samples including several types of rice, rice products, and infant cereal products. Total As ranged from 40.1 to 323.7 μg As kg1. From the speciation results, iAs was predominant, and DMA was detected in some samples while MA was not detected in any sample.

High-pressure processing and antimicrobial biodegradable packaging to control Listeria monocytogenes during storage of cooked ham

The efficiency of combining high-pressure processing (HPP) and active packaging technologies to control Listeria monocytogenes growth during the shelf life of artificially inoculated cooked ham was assessed. Three lots of cooked ham were prepared: control, packaging with alginate films, and packaging with antimicrobial alginate films containing enterocins. After packaging, half of the samples were pressurized. Sliced cooked ham stored at 6 °C experienced a quick growth of L. monocytogenes. Both antimicrobial packaging and pressurization delayed the growth of the pathogen. However, at 6 °C the combination of antimicrobial packaging and HPP was necessary to achieve a reduction of inoculated levels without recovery during 60 days of storage. Further storage at 6 °C of pressurized antimicrobial packed cooked ham resulted in L. monocytogenes levels below the detection limit (day 90). On the other hand, storage at 1 °C controlled the growth of the pathogen until day 39 in non-pressurized ham, while antimicrobial packaging and storage at 1 °C exerted a bacteriostatic effect for 60 days. All HPP lots stored at 1 °C led to counts <100 CFU/g at day 60. Similar results were observed when combining both technologies. After a cold chain break no growth of L. monocytogenes was observed in pressurized ham packed with antimicrobial films, showing the efficiency of combining both technologies.

The Coordinated Radio and Infrared Survey for High-mass Star Formation. II. Source Catalog

The CORNISH project is the highest resolution radio continuum survey of the Galactic plane to date. It is the 5 GHz radio continuum part of a series of multi-wavelength surveys that focus on the northern GLIMPSE region (10° < l < 65°), observed by the Spitzer satellite in the mid-infrared. Observations with the Very Large Array in B and BnA configurations have yielded a 1.''5 resolution Stokes I map with a root mean square noise level better than 0.4 mJy beam 1. Here we describe the data-processing methods and data characteristics, and present a new, uniform catalog of compact radio emission. This includes an implementation of automatic deconvolution that provides much more reliable imaging than standard CLEANing. A rigorous investigation of the noise characteristics and reliability of source detection has been carried out. We show that the survey is optimized to detect emission on size scales up to 14'' and for unresolved sources the catalog is more than 90% complete at a flux density of 3.9 mJy. We have detected 3062 sources above a 7σ detection limit and present their ensemble properties. The catalog is highly reliable away from regions containing poorly sampled extended emission, which comprise less than 2% of the survey area. Imaging problems have been mitigated by down-weighting the shortest spacings and potential artifacts flagged via a rigorous manual inspection with reference to the Spitzer infrared data. We present images of the most common source types found: H II regions, planetary nebulae, and radio galaxies. The CORNISH data and catalog are available online at http://cornish.leeds.ac.uk.