Imputation of Mixed Data With Multilevel Singular Value Decomposition

Statistical analysis of large datasets offers new opportunities to better understand underlying processes. Yet, data accumulation often implies relaxing acquisition procedures or compounding diverse sources. As a consequence, datasets often contain mixed data, that is, both quantitative and qualitative, and many missing values. Furthermore, aggregated data present a natural multilevel structure, where individuals or samples are nested within different sites, such as countries or hospitals. Imputation of multilevel data has therefore drawn some attention recently, but current solutions are not designed to handle mixed data, and suffer from important drawbacks, such as their computational cost. In this article, we propose a single imputation method for multilevel data, which can be used to complete either quantitative, categorical, or mixed data. The method is based on multilevel singular value decomposition (SVD), which consists in decomposing the variability of the data into two components, the between and within groups variability, and performing an SVD on both parts. We show on a simulation study that in comparison to competitors, the method has the advantages of handling datasets of various size, and being computationally faster. Furthermore, it is the first so far to handle mixed data. We apply the method to impute a medical dataset resulting from the aggregation of several hospitals datasets. This application falls in the framework of a larger project on Trauma patients. To overcome obstacles associated to the aggregation of medical data, we turn to distributed computation. The method is implemented in the R package missMDA. Supplementary materials for this article are available online.     

Volumetric properties and enthalpies of solution of alcohols CkH2k+1OH (k = 1, 2, 6) in 1-methyl-3-alkylimidazolium bis(trifluoromethylsulfonyl)imide {[C1CnIm][NTf2] n = 2, 4, 6, 8, 10} ionic liquids

We present a study on the effect of the alkyl chain length of the imidazolium ring in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids, [C₁C_nIm][NTf₂] (n = 2 to 10), on the mixing properties of (ionic liquid + alcohol) mixtures (enthalpy and volume). We have measured small excess molar volumes with highly asymmetric curves as a function of mole fraction composition (S-shape) with more negative values in the alcohol-rich regions. The excess molar volumes increase with the increase of the alkyl-chain length of the imidazolium cation of the ionic liquid. The values of the partial molar excess enthalpy and the enthalpy of mixing are positive and, for the case of methanol, do not vary monotonously with the length of the alkyl side-chain of the cation on the ionic liquid – increasing from n = 2 to 6 and then decreasing from n = 8. This non-monotonous variation is explained by a more favourable interaction of methanol with the cation head group of the ionic liquid for alkyl chains longer than eight carbon atoms. It is also observed that the mixing is less favourable for the smaller alcohols, the enthalpy of mixing decreasing to less positive values as the alkyl chain of the alcohol increases. Based on the data from this work and on the knowledge of the vapour pressure of {[C₁C_nIm][NTf₂] + alcohol} binary mixtures at T = 298 K reported in the literature, the excess Gibbs free energy, excess enthalpy and excess entropy could be then calculated and it was observed that these mixtures behave like the ones constituted by a non-associating and a non-polar component, with its solution behaviour being determined by the enthalpy.     

Monitoring of water quality in South Paris district by clustering and SIMCA classification

With the aim of obtaining a monitoring tool to assess the quality of water, a multivariate statistical procedure based on cluster analysis (CA) coupled with soft independent modelling class analogy (SIMCA) algorithm, providing an effective classification method, is proposed. The experimental data set, carried out throughout the year 2004, was composed of analytical parameters from 68 water sources in a vast southwest area of Paris. Nine variables carrying the most useful information were selected and investigated (nitrate, sulphate, chloride, turbidity, conductivity, hardness, alkalinity, coliforms and Escherichia coli). Principal component analysis provided considerable data reduction, gathering in the first two principal components the majority of information representing about 92.2% of the total variance. CA grouped samples belonging to different sites, distinctly correlating them with chemical variables, and a classification model was built by SIMCA. This model was optimised and validated and then applied to a new data matrix, consisting of the parameters measured during the year 2005 from the same objects, providing a fast and accurate classification of all the samples. The most of the examined sources appeared unchanged during the 2-year period, but five sources resulted distributed in different classes, due to statistical significant changes of some characteristic analytical parameters.     

Confidence Areas for Fixed-Effects PCA

Principal component analysis (PCA) is often used to visualize data when the rows and the columns are both of interest. In such a setting, there is a lack of inferential methods on the PCA output. We study the asymptotic variance of a fixed-effects model for PCA, and propose several approaches to assessing the variability of PCA estimates: a method based on a parametric bootstrap, a new cell-wise jackknife, as well as a computationally cheaper approximation to the jackknife. We visualize the confidence regions by Procrustes rotation. Using a simulation study, we compare the proposed methods and highlight the strengths and drawbacks of each method as we vary the number of rows, the number of columns, and the strength of the relationships between variables.     

2,2′:6′,2″‐Terpyridines Functionalized with Thienyl Substituents: Synthesis and Applications

This review deals with the synthesis and applications of 2,2′:6′,2″‐terpyridines which are functionalized with thiophene ring, directly linked to the terpyridine core or via a spacer. Two main methodologies were used, ring closure of diketo‐derivatives and cross coupling reactions. The obtained compounds find applications in various fields especially in material sciences such as solar cells or macromolecular sciences.     

Two-dimensional molecular imprinting approach to produce optical biosensor recognition elements

This article describes a new two-step methodology for preparing thiol monolayers having artificial recognition sites for dansylated amino acids on gold optical biosensor surfaces. Nepsilon-Dansyl-L-lysine (DK) was used as the template molecule to form molecularly imprinted monolayers (MIMs). Impact factors that were studied were the concentration of DK in step one (template deposition) and the time and method for thiol monolayer formation in step two (backfilling). Compared to a prior method that used the simultaneous adsorption of the template and thiol from solution, this new approach provides the flexibility to imprint template molecules that have low binding energies on gold. Control over the surface density of imprinting sites can be achieved by this approach, and rebinding studies done using surface plasmon resonance spectroscopy confirmed that the MIMs prepared against DK showed selectivity for that template over didansyl-L-lysine.     

An unusual dimerization of primary unsaturated alcohols catalyzed by RuHCl(CO)(PPh3)3

When primary unsaturated alcohols were treated with a catalytic amount of RuHCl(CO)(PPh3)3 in benzene under reflux, dimerization reactions took place to give alpha-hydroxymethyl ketones as major product.