Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

This paper is part of a special issue of Applied Geochemistry focusing on reliable applications of compositional multivariate statistical methods. This study outlines the application of compositional data analysis (CoDa) to calibration of geochemical data and multivariate statistical modelling of geochemistry and grain-size data from a set of Holocene sedimentary cores from the Ganges-Brahmaputra (G-B) delta. Over the last two decades, understanding near-continuous records of sedimentary sequences has required the use of core-scanning X-ray fluorescence (XRF) spectrometry, for both terrestrial and marine sedimentary sequences. Initial XRF data are generally unusable in ‘raw-format’, requiring data processing in order to remove instrument bias, as well as informed sequence interpretation. The applicability of these conventional calibration equations to core-scanning XRF data are further limited by the constraints posed by unknown measurement geometry and specimen homogeneity, as well as matrix effects. Log-ratio based calibration schemes have been developed and applied to clastic sedimentary sequences focusing mainly on energy dispersive-XRF (ED-XRF) core-scanning. This study has applied high resolution core-scanning XRF to Holocene sedimentary sequences from the tidal-dominated Indian Sundarbans, (Ganges-Brahmaputra delta plain). The Log-Ratio Calibration Equation (LRCE) was applied to a sub-set of core-scan and conventional ED-XRF data to quantify elemental composition. This provides a robust calibration scheme using reduced major axis regression of log-ratio transformed geochemical data. Through partial least squares (PLS) modelling of geochemical and grain-size data, it is possible to derive robust proxy information for the Sundarbans depositional environment. The application of these techniques to Holocene sedimentary data offers an improved methodological framework for unravelling Holocene sedimentation patterns.

Multivariate statistical modeling of an anode backing furnace - Modélisation statistique multivariée du four à cuisson des anodes utilisées dans la fabrication d'aluminium primaire

La stratégie actuelle de contrôle de la qualité de l’anode est inadéquate pour détecter les anodes défectueuses avant qu’elles ne soient installées dans les cuves d’électrolyse. Des travaux antérieurs ont porté sur la modélisation du procédé de fabrication des anodes afin de prédire leurs propriétés directement après la cuisson en utilisant des méthodes statistiques multivariées. La stratégie de carottage des anodes utilisée à l’usine partenaire fait en sorte que ce modèle ne peut être utilisé que pour prédire les propriétés des anodes cuites aux positions les plus chaudes et les plus froides du four à cuire. Le travail actuel propose une stratégie pour considérer l’histoire thermique des anodes cuites à n’importe quelle position et permettre de prédire leurs propriétés. Il est montré qu’en combinant des variables binaires pour définir l’alvéole et la position de cuisson avec les données routinières mesurées sur le four à cuire, les profils de température des anodes cuites à différentes positions peuvent être prédits. Également, ces données ont été incluses dans le modèle pour la prédiction des propriétés des anodes. Les résultats de prédiction ont été validés en effectuant du carottage supplémentaire et les performances du modèle sont concluantes pour la densité apparente et réelle, la force de compression, la réactivité à l’air et le Lc et ce peu importe la position de cuisson.

Measuring, Modeling, and Forecasting Volatility and Correlations from High-Frequency Data

This dissertation contains four essays that all share a common purpose: developing new methodologies to exploit the potential of high-frequency data for the measurement, modeling and forecasting of financial assets volatility and correlations. The first two chapters provide useful tools for univariate applications while the last two chapters develop multivariate methodologies. In chapter 1, we introduce a new class of univariate volatility models named FloGARCH models. FloGARCH models provide a parsimonious joint model for low frequency returns and realized measures, and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the models in a realistic numerical study and on the basis of a data set composed of 65 equities. Using more than 10 years of high-frequency transactions, we document significant statistical gains related to the FloGARCH models in terms of in-sample fit, out-of-sample fit and forecasting accuracy compared to classical and Realized GARCH models. In chapter 2, using 12 years of high-frequency transactions for 55 U.S. stocks, we argue that combining low-frequency exogenous economic indicators with high-frequency financial data improves the ability of conditionally heteroskedastic models to forecast the volatility of returns, their full multi-step ahead conditional distribution and the multi-period Value-at-Risk. Using a refined version of the Realized LGARCH model allowing for time-varying intercept and implemented with realized kernels, we document that nominal corporate profits and term spreads have strong long-run predictive ability and generate accurate risk measures forecasts over long-horizon. The results are based on several loss functions and tests, including the Model Confidence Set. Chapter 3 is a joint work with David Veredas. We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances on the basis of noisy and asynchronous prices. Along these lines, a minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics. Chapter 4 is co-authored with Niels S. Hansen, Asger Lunde and Kasper V. Olesen, all affiliated with CREATES at Aarhus University. We propose to use the Realized Beta GARCH model to exploit the potential of high-frequency data in commodity markets. The model produces high quality forecasts of pairwise correlations between commodities which can be used to construct a composite covariance matrix. We evaluate the quality of this matrix in a portfolio context and compare it to models used in the industry. We demonstrate significant economic gains in a realistic setting including short selling constraints and transaction costs.

Crowdfunding for entrepreneurship: an exploratory multivariate analysis concerning kickstarter and indiegogo platforms

The general purpose of this work is to describe and analyse the financing phenomenon of crowdfunding and to investigate the relations among crowdfunders, project creators and crowdfunding websites. More specifically, it also intends to describe the profile differences between major crowdfunding platforms, such as Kickstarter and Indiegogo. The findings are supported by literature, gathered from different scientific research papers. In the empirical part, data about Kickstarter and Indiegogo was collected from their websites and also complemented with further data from other statistical websites. For finding out specific information, such as satisfaction of entrepreneurs from both platforms, a satisfaction survey was applied among 200 entrepreneurs from different countries. To identify the profile of users of the Kickstarter and of the Indiegogo platforms, a multivariate analysis was performed, using a Hierarchical Clusters Analysis for each platform under study. Descriptive analysis was used for exploring information about popularity of platforms, average cost and the most popular area of projects, profile of users and future opportunities of platforms. To assess differences between groups, association between variables, and answering to the research hypothesis, an inferential analysis it was applied. The results showed that the Kickstarter and Indiegogo are one of the most popular crowdfunding platforms. Both of them have thousands of users and they are generally satisfied. Each of them uses individual approach for crowdfunders. Despite this, they both could benefit from further improving their services. Furthermore, according the results it was possible to observe that there is a direct and positive relationship between the money needed for the projects and the money collected from the investors for the projects, per platform.

Correlations among behavior, performance and environment in broiler breeders using multivariate analysis

Animal welfare issues have received much attention not only to supply farmed animal requirements, but also to ethical and cultural public concerns. Daily collected information, as well as the systematic follow-up of production stages, produces important statistical data for production assessment and control, as well as for improvement possibilities. In this scenario, this research study analyzed behavioral, production, and environmental data using Main Component Multivariable Analysis, which correlated observed behaviors, recorded using video cameras and electronic identification, with performance parameters of female broiler breeders. The aim was to start building a system to support decision-making in broiler breeder housing, based on bird behavioral parameters. Birds were housed in an environmental chamber, with three pens with different controlled environments. Bird sensitivity to environmental conditions were indicated by their behaviors, stressing the importance of behavioral observations for modern poultry management. A strong association between performance parameters and the behavior at the nest, suggesting that this behavior may be used to predict productivity. The behaviors of ruffling feathers, opening wings, preening, and at the drinker were negatively correlated with environmental temperature, suggesting that the increase of in the frequency of these behaviors indicate improvement of thermal welfare.

Volatility Spillover and Multivariate Volatility Impulse Response Analysis of GFC News Events

This paper applies two measures to assess spillovers across markets: the Diebold Yilmaz (2012) Spillover Index and the Hafner and Herwartz (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility estimates taken from the Oxford Man RV library, running from the beginning of 2000 to October 2016, for the S&P500 and the FTSE, plus ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index, from 3 January 2005 to 31 January 2015. Both data sets capture both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The key difference between the measures is that the spillover index captures an average of spillovers over a period, whilst volatility impulse responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. The VIRF provide information about the impact of independent shocks on volatility. In the latter analysis, we explore the impact of three different shocks, the onset of the GFC, which we date as 9 August 2007 (GFC1). It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, (GFC2). The third shock is 9 May 2010. Our modelling includes leverage and asymmetric effects undertaken in the context of a multivariate GARCH model, which are then analysed using both BEKK and diagonal BEKK (DBEKK) models. A key result is that the impact of negative shocks is larger, in terms of the effects on variances and covariances, but shorter in duration, in this case a difference between three and six months.

Sociodemographic factors influencing adherence to antenatal iron supplementation recommendations among pregnant women in Malawi: Analysis of data from the 2010 Malawi Demographic and Health Survey

Background and Aim: Maternal morbidity and mortality statistics remain unacceptably high in Malawi. Prominent among the risk factors in the country is anaemia in pregnancy, which generally results from nutritional inadequacy (particularly iron deficiency) and malaria, among other factors. This warrants concerted efforts to increase iron intake among reproductive-age women. This study, among women in Malawi, examined factors determining intake of supplemental iron for at least 90 days during pregnancy. Methods: A weighted sample of 10,750 women (46.7%), from the 23,020 respondents of the 2010 Malawi Demographic and Health Survey (MDHS), were utilized for the study. Univariate, bivariate, and regression techniques were employed. While univariate analysis revealed the percent distributions of all variables, bivariate analysis was used to examine the relationships between individual independent variables and adherence to iron supplementation. Chi-square tests of independence were conducted for categorical variables, with the significance level set at P < 0.05. Two binary logistic regression models were used to evaluate the net effect of independent variables on iron supplementation adherence. Results: Thirty-seven percent of the women adhered to the iron supplementation recommendations during pregnancy. Multivariate analysis indicated that younger age, urban residence, higher education, higher wealth status, and attending antenatal care during the first trimester were significantly associated with increased odds of taking iron supplementation for 90 days or more during pregnancy (P < 0.01). Conclusions: The results indicate low adherence to the World Health Organization’s iron supplementation recommendations among pregnant women in Malawi, and this contributes to negative health outcomes for both mothers and children. Focusing on education interventions that target populations with low rates of iron supplement intake, including campaigns to increase the number of women who attend antenatal care clinics in the first trimester, are recommended to increase adherence to iron supplementation recommendations.

A simple approach to integrate the ecotoxicological and chemical data for the establishment of environmental risk levels

O presente trabalho utilizou métodos multivariados e matemáticos para integrar dados químicos e ecotoxicológicos obtidos para o Sistema Estuarino de Santos e para a região próxima à zona de lançamento do emissário submarino de Santos, com a finalidade de estabelecer com maior exatidão os riscos ambientais, e assim identificar áreas prioritárias e orientar programas de controle e políticas públicas. Para ambos os conjuntos de dados, as violações de valores numéricos de qualidade de sedimento tenderam a estar associadas com a ocorrência de toxicidade. Para o estuário, essa tendência foi corroborada pelas correlações entre a toxicidade e as concentrações de HPAs e Cu, enquanto para a região do emissário, pela correlação entre toxicidade e conteúdo de mercúrio no sedimento. Valores normalizados em relação às medias foram calculados para cada amostra, permitindo classificá-las de acordo com a toxicidade e a contaminação. As análises de agrupamento confirmaram os resultados das classificações. Para os dados de sistema estuarino, houve a separação das amostras em três categorias: as estações SSV-2, SSV-3 e SSV-4 encontram-se sob maior risco, seguidas da estação SSV-6. As estações SSV-1 e SSV-5 demonstraram melhores condições. Já em relação ao emissário, as amostras 1 e 2 apresentaram melhores condições, enquanto a estação 5 pareceu apresentar um maior risco, seguida das estações 3 e 4 que tiveram apenas alguns indícios de alteração.

Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.

The efficiency of multivariate macroeconomic forecasts

We examine the efficiency of multivariate macroeconomic forecasts by estimating a vector autoregressive model on the forecast revisions of four variables (GDP, inflation, unemployment and wages). Using a data set of professional forecasts for the G7 countries, we find evidence of cross‐series revision dynamics. Specifically, forecasts revisions are conditionally correlated to the lagged forecast revisions of other macroeconomic variables, and the sign of the correlation is as predicted by conventional economic theory. This indicates that forecasters are slow to incorporate news across variables. We show that this finding can be explained by forecast underreaction.

Structural brain connectivity and cognitive ability differences: A multivariate distance matrix regression analysis

Neuroimaging research involves analyses of huge amounts of biological data that might or might not be related with cognition. This relationship is usually approached using univariate methods, and, therefore, correction methods are mandatory for reducing false positives. Nevertheless, the probability of false negatives is also increased. Multivariate frameworks have been proposed for helping to alleviate this balance. Here we apply multivariate distance matrix regression for the simultaneous analysis of biological and cognitive data, namely, structural connections among 82 brain regions and several latent factors estimating cognitive performance. We tested whether cognitive differences predict distances among individuals regarding their connectivity pattern. Beginning with 3,321 connections among regions, the 36 edges better predicted by the individuals' cognitive scores were selected. Cognitive scores were related to connectivity distances in both the full (3,321) and reduced (36) connectivity patterns. The selected edges connect regions distributed across the entire brain and the network defined by these edges supports high-order cognitive processes such as (a) (fluid) executive control, (b) (crystallized) recognition, learning, and language processing, and (c) visuospatial processing. This multivariate study suggests that one widespread, but limited number, of regions in the human brain, supports high-level cognitive ability differences. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

Using multivariate sequential patterns to improve survival prediction in intensive care burn unit

Resuscitation and stabilization are key issues in Intensive Care Burn Units and early survival predictions help to decide the best clinical action during these phases. Current survival scores of burns focus on clinical variables such as age or the body surface area. However, the evolution of other parameters (e.g. diuresis or fluid balance) during the first days is also valuable knowledge. In this work we suggest a methodology and we propose a Temporal Data Mining algorithm to estimate the survival condition from the patient’s evolution. Experiments conducted on 480 patients show the improvement of survival prediction.