Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Petroleum contamination impact on macrobenthic communities under the influence of an oil refinery: Integrating chemical and biological multivariate data

Petroleum contamination impact on macrobenthic communities in the northeast portion of Todos os Santos Bay was assessed combining in multivariate analyses, chemical parameters such as aliphatic and polycyclic aromatic hydrocarbon indices and concentration ratios with benthic ecological parameters. Sediment samples were taken in August 2000 with a 0.05 m(2) van Veen grab at 28 sampling locations. The predominance of n-alkanes with more than 24 carbons, together with CPI values close to one, and the fact that most of the stations showed UCM/resolved aliphatic hydrocarbons ratios (UCM:R) higher than two, indicated a high degree of anthropogenic contribution, the presence of terrestrial plant detritus, petroleum products and evidence of chronic oil pollution. The indices used to determine the origin of PAH indicated the occurrence of a petrogenic contribution. A pyrolytic contribution constituted mainly by fossil fuel combustion derived PAH was also observed. The results of the stepwise multiple regression analysis performed with chemical data and benthic ecological descriptors demonstrated that not only total PAH concentrations but also specific concentration ratios or indices such as >= C24:< C24, An/178 and Fl/Fl + Py, are determining the structure of benthic communities within the study area. According to the BIO-ENV results petroleum related variables seemed to have a main influence on macrofauna community structure. The PCA ordination performed with the chemical data resulted in the formation of three groups of stations. The decrease in macrofauna density, number of species and diversity from groups III to I seemed to be related to the occurrence of high aliphatic hydrocarbon and PAH concentrations associated with fine sediments. Our results showed that macrobenthic communities in the northeast portion of Todos os Santos Bay are subjected to the impact of chronic oil pollution as was reflected by the reduction in the number of species and diversity. These results emphasise the importance to combine in multivariate approaches not only total hydrocarbon concentrations but also indices, isomer pair ratios and specific compound concentrations with biological data to improve the assessment of anthropogenic impact on marine ecosystems. (c) 2008 Elsevier Ltd. All rights reserved.

Detecting an abnormality in a recovery boiler using dynamic multivariate data analysis with parallel coordinate plots

Data visualization techniques are powerful in the handling and analysis of multivariate systems. One such technique known as parallel coordinates was used to support the diagnosis of an event, detected by a neural network-based monitoring system, in a boiler at a Brazilian Kraft pulp mill. Its attractiveness is the possibility of the visualization of several variables simultaneously. The diagnostic procedure was carried out step-by-step going through exploratory, explanatory, confirmatory, and communicative goals. This tool allowed the visualization of the boiler dynamics in an easier way, compared to commonly used univariate trend plots. In addition it facilitated analysis of other aspects, namely relationships among process variables, distinct modes of operation and discrepant data. The whole analysis revealed firstly that the period involving the detected event was associated with a transition between two distinct normal modes of operation, and secondly the presence of unusual changes in process variables at this time.

Multivariate analyses of UV-Vis absorption spectral data from cachaca wood extracts: a model to classify aged Brazilian cachacas according to the wood species used

Multivariate analyses of UV-Vis spectral data from cachaca wood extracts provide a simple and robust model to classify aged Brazilian cachacas according to the wood species used in the maturation barrels. The model is based on inspection of 93 extracts of oak and different Brazilian wood species by a non-aged cachaca used as an extraction solvent. Application of PCA (Principal Components Analysis) and HCA (Hierarchical Cluster Analysis) leads to identification of 6 clusters of cachaca wood extracts (amburana, amendoim, balsamo, castanheira, jatoba, and oak). LDA (Linear Discriminant Analysis) affords classification of 10 different wood species used in the cachaca extracts (amburana, amendoim, balsamo, cabreuva-parda, canela-sassafras, castanheira, jatoba, jequitiba-rosa, louro-canela, and oak) with an accuracy ranging from 80% (amendoim and castanheira) to 100% (balsamo and jequitiba-rosa). The methodology provides a low-cost alternative to methods based on liquid chromatography and mass spectrometry to classify cachacas aged in barrels that are composed of different wood species.

Liquid-liquid equilibria in binary solutions formed by [Pyridinium-Derived][F4B] ionic liquids and alkanols:new experimental data and validation of a multiparametric model for correlating LLE data

[EN]Experimental solubility data are presented for a set of binary systems composed of ionic liquids (IL) derived from pyridium, with the tetrafluoroborate anion, and normal alcohols ranging from ethanol to decanol, in the temperature interval of 275 420 K, at atmospheric pressure. For each case, the miscibility curve and the upper critical solubility temperature (UCST) values are presented. The effects of the ILs on the behavior of solutions with alkanols are analyzed, paying special attention to the pyridine derivatives, and considering a series of structural characteristics of the compounds involved.

Multiproperty modeling for a set of binary systems. Evaluation of a model to correlate simultaneously several mixing properties of methyl ethanoate+alkanes and new experimental data

[EN] This work makes a theoretical–experimental contribution to the study of ester and alkane solutions. Experimental data of isobaric vapor–liquid equilibria (VLE) are presented at 101.3 kPa for binary systems of methyl ethanoate with six alkanes (from C5 to C10), and of volumes and mixing enthalpies, vE and hE.

A Faster Circular Binary Segmentation Algorithm for the Analysis of Array CGH Data

Motivation: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number (Olshen {\it et~al}, 2004). The algorithm tests for change-points using a maximal $t$-statistic with a permutation reference distribution to obtain the corresponding $p$-value. The number of computations required for the maximal test statistic is $O(N^2),$ where $N$ is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster. algorithm. Results: We present a hybrid approach to obtain the $p$-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analysis of array CGH data from a breast cancer cell line to show the impact of the new approaches on the analysis of real data. Availability: An R (R Development Core Team, 2006) version of the CBS algorithm has been implemented in the ``DNAcopy'' package of the Bioconductor project (Gentleman {\it et~al}, 2004). The proposed hybrid method for the $p$-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.

A Method for Visualizing Multivariate Time Series Data

Visualization and exploratory analysis is an important part of any data analysis and is made more challenging when the data are voluminous and high-dimensional. One such example is environmental monitoring data, which are often collected over time and at multiple locations, resulting in a geographically indexed multivariate time series. Financial data, although not necessarily containing a geographic component, present another source of high-volume multivariate time series data. We present the mvtsplot function which provides a method for visualizing multivariate time series data. We outline the basic design concepts and provide some examples of its usage by applying it to a database of ambient air pollution measurements in the United States and to a hypothetical portfolio of stocks.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.