Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

Estatística aplicada à química: dez dúvidas comuns

Ten common doubts of chemistry students and professionals about their statistical applications are discussed. The use of the N-1 denominator instead of N is described for the standard deviation. The statistical meaning of the denominators of the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV) are given for researchers using multivariate calibration methods. The reason why scientists and engineers use the average instead of the median is explained. Several problematic aspects about regression and correlation are treated. The popular use of triplicate experiments in teaching and research laboratories is seen to have its origin in statistical confidence intervals. Nonparametric statistics and bootstrapping methods round out the discussion.

Novel Regression Methods For Spectral Data

Singular Value Decomposition (SVD), Principal Component Analysis (PCA) and Multiple Linear Regression (MLR) are some of the mathematical pre- liminaries that are discussed prior to explaining PLS and PCR models. Both PLS and PCR are applied to real spectral data and their di erences and similarities are discussed in this thesis. The challenge lies in establishing the optimum number of components to be included in either of the models but this has been overcome by using various diagnostic tools suggested in this thesis. Correspondence analysis (CA) and PLS were applied to ecological data. The idea of CA was to correlate the macrophytes species and lakes. The di erences between PLS model for ecological data and PLS for spectral data are noted and explained in this thesis. i

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Wheat Yield Loss in a Two Species Competition with Emex australis and Emex spinosa

Emex australis and E. spinosa are significant weed species in wheat and other crops. Information on the extent of competition of the Emex species will be helpful to access yield losses in wheat. Field experiments were conducted to quantify the interference of tested weed densities each as single or mixture of both at 1:1 on their growth and yield, wheat yield components and wheat grain yield losses in two consecutive years. Dry weight of both weed species increased from 3-6 g m-2 with every additional plant of weed, whereas seed number and weight per plant decreased with increasing density of either weed. Both weed species caused considerable decrease in yield components like spike bearing tillers, number of grains per spike, 1000-grain weight of wheat with increasing density population of the weeds. Based on non-linear hyperbolic regression model equation, maximum yield loss at asymptotic weed density was estimated to be 44 and 62% with E. australis, 56 and 70% with E. spinosa and 63 and 72% with mixture of both species at 1:1 during both year of study, respectively. It was concluded that E. spinosa has more competition effects on wheat crop as compared to E. australis.

Osinkosuhteen, osinkotuoton ja omavaraisuusasteen sijoitusstrateginen hyödynnettävyys Suomen osakemarkkinoilla

Tutkielman tavoitteena on selvittää osinkosuhteen, osinkotuoton ja omavaraisuusasteen vaikutus osakkeesta saatavaan kokonaistuottoon Suomenosakemarkkinoilla vuosina 2002–2013. Muuttujien kausaliteettisuhde kokonaistuottoon selvitetään regressioanalyysilla. Portfolioanalyysin avulla tutkitaan valittujen tunnuslukujen toimivuutta sijoitusstrategiana. Tutkimuksessa muodostetaan myös osinkosuhteen ja osinkotuoton yhdistelmänä tunnusluku, jolla pyritään maksimoimaan sijoittajan saama tuotto. Empiiriset tulokset osoittivat, että sijoittaja pystyy saavuttamaan ylituottoja hyödyntämällä edellä mainittuja tunnuslukuja osakevalinnassa. Osinkotuoton ja osakkeen kokonaistuoton välillä havaittiin positiivinen lineaarinen korrelaatio. Portfolioanalyysin perusteella sekä omavaraisuusasteen että osinkosuhteen osalta vaikutus sijoittajan saamaan riskisuhteutettuun kokonaistuottoon on ei-lineaarinen. Valittuja tunnuslukuja ja menetelmiä hyödyntäen sijoittaja saa parhaimman riskisuhteutetun tuoton valitsemalla sijoitussalkkuunsa osakkeita, joiden osinkosuhteen arvo sijoittuu toiseksi ylimpään kvartiiliin sekä osakkeita, joiden osinkotuotto on korkea ja omavaraisuusaste on samanaikaisesti alhainen.

Atherosclerosis in aged mice over-expressing the reverse cholesterol transport genes

We determined whether over-expression of one of the three genes involved in reverse cholesterol transport, apolipoprotein (apo) AI, lecithin-cholesterol acyl transferase (LCAT) and cholesteryl ester transfer protein (CETP), or of their combinations influenced the development of diet-induced atherosclerosis. Eight genotypic groups of mice were studied (AI, LCAT, CETP, LCAT/AI, CETP/AI, LCAT/CETP, LCAT/AI/CETP, and non-transgenic) after four months on an atherogenic diet. The extent of atherosclerosis was assessed by morphometric analysis of lipid-stained areas in the aortic roots. The relative influence (R²) of genotype, sex, total cholesterol, and its main sub-fraction levels on atherosclerotic lesion size was determined by multiple linear regression analysis. Whereas apo AI (R² = 0.22, P < 0.001) and CETP (R² = 0.13, P < 0.01) expression reduced lesion size, the LCAT (R² = 0.16, P < 0.005) and LCAT/AI (R² = 0.13, P < 0.003) genotypes had the opposite effect. Logistic regression analysis revealed that the risk of developing atherosclerotic lesions greater than the 50th percentile was 4.3-fold lower for the apo AI transgenic mice than for non-transgenic mice, and was 3.0-fold lower for male than for female mice. These results show that apo AI overexpression decreased the risk of developing large atherosclerotic lesions but was not sufficient to reduce the atherogenic effect of LCAT when both transgenes were co-expressed. On the other hand, CETP expression was sufficient to eliminate the deleterious effect of LCAT and LCAT/AI overexpression. Therefore, increasing each step of the reverse cholesterol transport per se does not necessarily imply protection against atherosclerosis while CETP expression can change specific athero genic scenarios.

Association between the -174 G/C promoter polymorphism of the interleukin-6 gene and cardiovascular disease risk factors in Brazilian older women

In worldwide studies, interleukin-6 (IL-6) is implicated in age-related disturbances. The aim of the present report was to determine the possible association of IL-6 -174 C/G promoter polymorphism with the cytokine profile as well as with the presence of selected cardiovascular risk features. This was a cross-sectional study on Brazilian women aged 60 years or older. A sample of 193 subjects was investigated for impaired glucose regulation, diabetes, hypertension, and dyslipidemia. Genotyping was done by direct sequencing of PCR products. IL-6 and C-reactive protein were quantified by high-sensitivity assays. General linear regression models or the Student t-test were used to compare continuous variables among genotypes, followed by adjustments for confounding variables. The chi-square test was used to compare categorical variables. The genotypes were consistent with Hardy-Weinberg equilibrium proportions. In a recessive model, mean waist-to-hip ratio, serum glycated hemoglobin and serum glucose were markedly lower in C homozygotes (P = 0.001, 0.028, and 0.047, respectively). In a dominant hypothesis, G homozygotes displayed a trend towards higher levels of circulating IL-6 (P = 0.092). Non-parametric analysis revealed that impaired fasting glucose and hypertension were findings approximately 2-fold more frequent among G homozygous subjects (P = 0.042 and 0.043, respectively). Taken together, our results show that the IL-6 -174 G-allele is implicated in a greater cardiovascular risk. To our knowledge, this is the first investigation of IL-6 promoter variants and age-related disturbances in the Brazilian elderly population.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Trans fatty acid intake is associated with insulin sensitivity but independently of inflammation

High saturated and trans fatty acid intake, the typical dietary pattern of Western populations, favors a proinflammatory status that contributes to generating insulin resistance (IR). We examined whether the consumption of these fatty acids was associated with IR and inflammatory markers. In this cross-sectional study, 127 non-diabetic individuals were allocated to a group without IR and 56 to another with IR, defined as homeostasis model assessment-IR (HOMA-IR) >2.71. Diet was assessed using 24-h food recalls. Multiple linear regression was employed to test independent associations with HOMA-IR. The IR group presented worse anthropometric, biochemical and inflammatory profiles. Energy intake was correlated with abdominal circumference and inversely with adiponectin concentrations (r = -0.227, P = 0.002), while saturated fat intake correlated with inflammatory markers and trans fat with HOMA-IR (r = 0.160, P = 0.030). Abdominal circumference was associated with HOMA-IR (r = 0.430, P < 0.001). In multiple analysis, HOMA-IR remained associated with trans fat intake (β = 1.416, P = 0.039) and body mass index (β = 0.390, P < 0.001), and was also inversely associated with adiponectin (β = -1.637, P = 0.004). Inclusion of other nutrients (saturated fat and added sugar) or other inflammatory markers (IL-6 and CRP) into the models did not modify these associations. Our study supports that trans fat intake impairs insulin sensitivity. The hypothesis that its effect could depend on transcription factors, resulting in expression of proinflammatory genes, was not corroborated. We speculate that trans fat interferes predominantly with insulin signaling via intracellular kinases, which alter insulin receptor substrates.

Investigation of the composition of linear alkylbenzenes with emphasis on the identification and quantitation of some trace compounds using GS/MS system in both electron impact and chemical ionization modes

Linear alkylbenzenes, LAB, formed by the Alel3 or HF catalyzed alkylation of benzene are common raw materials for surfactant manufacture. Normally they are sulphonated using S03 or oleum to give the corresponding linear alkylbenzene sulphonates In >95 % yield. As concern has grown about the environmental impact of surfactants,' questions have been raised about the trace levels of unreacted raw materials, linear alkylbenzenes and minor impurities present in them. With the advent of modem analytical instruments and techniques, namely GCIMS, the opportunity has arisen to identify the exact nature of these impurities and to determine the actual levels of them present in the commercial linear ,alkylbenzenes. The object of the proposed study was to separate, identify and quantify major and minor components (1-10%) in commercial linear alkylbenzenes. The focus of this study was on the structure elucidation and determination of impurities and on the qualitative determination of them in all analyzed linear alkylbenzene samples. A gas chromatography/mass spectrometry, (GCIMS) study was performed o~ five samples from the same manufacturer (different production dates) and then it was followed by the analyses of ten commercial linear alkylbenzenes from four different suppliers. All the major components, namely linear alkylbenzene isomers, followed the same elution pattern with the 2-phenyl isomer eluting last. The individual isomers were identified by interpretation of their electron impact and chemical ionization mass spectra. The percent isomer distribution was found to be different from sample to sample. Average molecular weights were calculated using two methods, GC and GCIMS, and compared with the results reported on the Certificate of Analyses (C.O.A.) provided by the manufacturers of commercial linear alkylbenzenes. The GC results in most cases agreed with the reported values, whereas GC/MS results were significantly lower, between 0.41 and 3.29 amu. The minor components, impurities such as branched alkylbenzenes and dialkyltetralins eluted according to their molecular weights. Their fragmentation patterns were studied using electron impact ionization mode and their molecular weight ions confirmed by a 'soft ionization technique', chemical ionization. The level of impurities present i~ the analyzed commercial linear alkylbenzenes was expressed as the percent of the total sample weight, as well as, in mg/g. The percent of impurities was observed to vary between 4.5 % and 16.8 % with the highest being in sample "I". Quantitation (mg/g) of impurities such as branched alkylbenzenes and dialkyltetralins was done using cis/trans-l,4,6,7-tetramethyltetralin as an internal standard. Samples were analyzed using .GC/MS system operating under full scan and single ion monitoring data acquisition modes. The latter data acquisition mode, which offers higher sensitivity, was used to analyze all samples under investigation for presence of linear dialkyltetralins. Dialkyltetralins were reported quantitatively, whereas branched alkylbenzenes were reported semi-qualitatively. The GC/MS method that was developed during the course of this study allowed identification of some other trace impurities present in commercial LABs. Compounds such as non-linear dialkyltetralins, dialkylindanes, diphenylalkanes and alkylnaphthalenes were identified but their detailed structure elucidation and the quantitation was beyond the scope of this study. However, further investigation of these compounds will be the subject of a future study.

The relationship between socioeconomic status, schools and bone health among adolescent females in Southern Ontario

We studied the association between socioeconomic status (SES), school attended and bone health measured by bone speed of sound (SOS) among adolescent females in Canada. 412 participants from six randomly selected schools in Southern Ontario were examined. Bone SOS was measured by quantitative ultrasound. Participant’s school and aggregate area-based census-derived (AABCD) SES were evaluated as predictors. Mean participant age was 15.7 (SD 1.0) years. Average median family income was $68,162 (SD $19,366). Median family income was non-linearly associated with bone SOS and restricted cubic splines described the relationship. Univariate regression, accounting for clustering of participants in schools, revealed a significant non-linear association between AABCD-median family income and non-dominant tibial SOS (LRT p = 0.031). Multivariable regression revealed school to have a significant impact (LRT p = 0.0001). High schools had a strong influence on the bone health of female students and this effect overrode the effect of SES.

The Mediating Role of Perceived Scholastic Competence in the Relationship Between Motor Coordination and Academic Performance

Children with developmental coordination disorder (DCD) are often referred to as clumsy because of their compromised motor coordination. Clumsiness and slow movement performances while scripting in children with DCD often result in poor academic performance and a diminished sense of scholastic competence. This study purported to examine the mediating role of perceived scholastic competence in the relationship between motor coordination and academic performance in children in grade six. Children receive a great deal of comparative information on their academic performances, which influence a student's sense of scholastic competence and self-efficacy. The amount of perceived academic self-efficacy has significant impact on academic performance, their willingness to complete academic tasks, and their self-motivation to improve where necessary. Independent t-tests reveal a significant difference (p < .001) between DCD and non-DCD groups when compared against their overall grade six average with the DCD group performing significantly lower. Independent t-tests found no significant difference between DCD and non-DCD groups for perceived scholastic competence. However, multiple linear regression analysis revealed a significant mediating role of 15% by perceived scholastic competence when examining the relationship between motor coordination and academic performance. While children with probable DCD may not rate their perceived scholastic competence as less than their healthy peers, there is a significant mediating effect on their academic performance.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.