Academic literature on the topic 'Multi variate regression'

Abstract In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an $F_2$ intercross mice study and an alcohol dependence study.

AbstractGaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to reformulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, reformulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student-t distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student-t process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real-data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.

We train and compare the performance of two machine learning methods, a multi-variate regression network and a ResNet-50-based neural network, to learn and forecast plant biomass as well as the relative growth rate based onfrom a short sequence of temporal images from plants in aeroponic cultivation. The training dataset consists of images of 57 plants taken from two different angles every hour during a 5-day period. The results show that images taken from a top-down perspective produce better results for the multi-variate regression network, while images taken from the side are better for the ResNet-50 neural network. In addition, using images from both cameras improves the biomass estimates from the ResNet-50 network, but not those from the multivariatemulti-variatemultivariate regression. However, all relative growth rate estimates were improved by using images from both cameras. We found that the best biomass estimates are produced from the multi-variate regression model trained on top camera images using a moving average filter resulting in a root mean square error of 0.0466 g. The best relative growth rate estimates were produced from the ResNet-50 network training on images from both cameras resulting in a root mean square error of 0.1767 g/(g·day).

Abstract. This study presents a sensitivity analysis of multi-variate regressions of recent springtime Antarctic vortex ozone trends using a "big data" ensemble approach. Multi-variate regression methods are widely used for studying the variability and detection of ozone trends. Based on multi-variate regression analysis of total Antarctic springtime vortex ozone it has been suggested that the observed increase of ozone since the late 1990s is statistically significant and can be attributed to decreasing stratospheric halogens (Salby et al., 2011, 2012; Kuttippurath et al., 2013). We find that, when considering uncertainties that have not been addressed in these studies, this conclusion on ozone recovery is not warranted. An ensemble of regressions is constructed based on the analysis of uncertainties in the applied ozone record as well as of uncertainties in the various applied regressors. The presented combination of ensemble members spans up the uncertainty range with about 35 million different regressions. The poleward heat flux (Eliassen–Palm Flux) and the effective chlorine loading explain, respectively, most of the short-term and long-term variability in different Antarctic springtime total ozone records. The inclusion in the regression of stratospheric volcanic aerosols, solar variability, the Quasi-Biennial Oscillation and the Southern Annular Mode is shown to increase rather than to decrease the overall uncertainty in the attribution of Antarctic springtime ozone because of large uncertainties in their respective records. Calculating the trend significance for the ozone record from the late 1990s onwards solely based on the fit of the effective chlorine loading should be avoided, as this does not take fit residuals into account and thereby results in too narrow uncertainty intervals. When taking fit residuals into account, we find that less than 30% of the regressions in the full ensemble result in a statistically significant positive springtime ozone trend over Antarctica from the late 1990s to either 2010 or 2012. Analysis of choices and uncertainties in time series show that, depending on choices in time series and parameters, the fraction of statistically significant trends in parts of the ensemble can range from negligible to more than 90%. However, we were unable to detect a robust statistically significant positive trend in Antarctic springtime vortex ozone in the ensemble.

The ability to identify factors that influence serious injuries and fatalities would help construction firms triage hazardous situations and direct their resources towards more effective interventions. Therefore, this study used odds ratio analysis and logistic regression modeling on historical accident data to investigate the contributing factors impacting occupational accidents among small electrical contracting enterprises. After conducting a thorough content analysis to ensure the reliability of reports, the authors adopted a purposeful variable selection approach to determine the most significant factors that can explain the fatality rates in different scenarios. Thereafter, this study performed an odds ratio analysis among significant factors to determine which factors increase the likelihood of fatality. For example, it was found that having a fatal accident is 4.4 times more likely when the source is a “vehicle” than when it is a “tool, instrument, or equipment”. After validating the consistency of the model, 105 accident scenarios were developed and assessed using the model. The findings revealed which severe accident scenarios happen commonly to people in this trade, with nine scenarios having fatality rates of 50% or more. The highest fatality rates occurred in “fencing, installing lights, signs, etc.” tasks in “alteration and rehabilitation” projects where the source of injury was “parts and materials”. The proposed analysis/modeling approach can be applied among all specialty contracting companies to identify and prioritize more hazardous situations within specific trades. The proposed model-development process also contributes to the body of knowledge around accident analysis by providing a framework for analyzing accident reports through a multivariate logistic regression model.

Abstract. The usual approach for flood damage assessment consists of stage-damage functions which relate the relative or absolute damage for a certain class of objects to the inundation depth. Other characteristics of the flooding situation and of the flooded object are rarely taken into account, although flood damage is influenced by a variety of factors. We apply a group of data-mining techniques, known as tree-structured models, to flood damage assessment. A very comprehensive data set of more than 1000 records of direct building damage of private households in Germany is used. Each record contains details about a large variety of potential damage-influencing characteristics, such as hydrological and hydraulic aspects of the flooding situation, early warning and emergency measures undertaken, state of precaution of the household, building characteristics and socio-economic status of the household. Regression trees and bagging decision trees are used to select the more important damage-influencing variables and to derive multi-variate flood damage models. It is shown that these models outperform existing models, and that tree-structured models are a promising alternative to traditional damage models.

Statistical models are helping palaeontologists to elucidate the history of biodiversity. Sampling standardization has been extensively applied to remedy the effects of uneven sampling in large datasets of fossil invertebrates. However, many vertebrate datasets are smaller, and the issue of uneven sampling has commonly been ignored, or approached using pairwise comparisons with a numerical proxy for sampling effort. Although most authors find a strong correlation between palaeodiversity and sampling proxies, weak correlation is recorded in some datasets. This has led several authors to conclude that uneven sampling does not influence our view of vertebrate macroevolution. We demonstrate that multi-variate regression models incorporating a model of underlying biological diversification, as well as a sampling proxy, fit observed sauropodomorph dinosaur palaeodiversity best. This bivariate model is a better fit than separate univariate models, and illustrates that observed palaeodiversity is a composite pattern, representing a biological signal overprinted by variation in sampling effort. Multi-variate models and other approaches that consider sampling as an essential component of palaeodiversity are central to gaining a more complete understanding of deep time vertebrate diversification.

The study examined the impact of training and development on job performance in the Banking sector in Uganda among the selected four banks of Equity Bank, Bank of Africa, Barclays Bank Uganda and Centenary Bank and specifically looked at the relationship between training needs identification, training methods, monitoring, evaluation of training and job performance in the banking sector in Uganda. The study used correlation research design to address the relationship between variables. The study involved managers, heads of departments at each bank and employees. Data was collected using questionnaires to facilitate quantitative approaches in the study. Data was analyzed at three levels that is; univerariate, bi-variate and multi-variate. Univeriate analysis fetched descriptive statistics in form frequencies and percentages while bivariate analysis obtained correlations between variables. At multivariate level a logistic regression model was used to ascertain the magnitude of effect of each independent variable on the dependent variable. Study findings at a bi-variate level revealed a positive and significant relationship between the independent variables (identify training needs, identify training objectives, training content, on the job training technique, off the job training technique, skills application and Knowledge application) and the dependent variable (job performance). At the multi-variate level, it was revealed that all independent variables except knowledge application in the training and evaluation process explain 69% of job performance in the model. It was concluded that identification of training objectives, identification of training objectives and skills application have a positive significant effect on job performance in the banking sector in Uganda. It was therefore recommended that there is need to need to streamline the needs assessment process before the training process, endeavor to clearly define training objectives and have a strict monitoring and evaluation process on trainees.

Particle size, scatter, and multi-collinearity are long-standing problems encountered in diffuse reflectance spectrometry. Multiplicative combinations of these effects are the major factor inhibiting the interpretation of near-infrared diffuse reflectance spectra. Sample particle size accounts for the majority of the variance, while variance due to chemical composition is small. Procedures are presented whereby physical and chemical variance can be separated. Mathematical transformations—standard normal variate (SNV) and de-trending (DT)—applicable to individual NIR diffuse reflectance spectra are presented. The standard normal variate approach effectively removes the multiplicative interferences of scatter and particle size. De-trending accounts for the variation in baseline shift and curvilinearity, generally found in the reflectance spectra of powdered or densely packed samples, with the use of a second-degree polynomial regression. NIR diffuse reflectance spectra transposed by these methods are free from multi-collinearity and are not confused by the complexity of shape encountered with the use of derivative spectroscopy.