Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Spatial model of site index based on Y-ray spectrometry and a digital elevation model for two Pinus species in Tuan Toolara State Forest, Queensland, Australia

Site index prediction models are an important aid for forest management and planning activities. This paper introduces a multiple regression model for spatially mapping and comparing site indices for two Pinus species (Pinus elliottii Engelm. and Queensland hybrid, a P. elliottii x Pinus caribaea Morelet hybrid) based on independent variables derived from two major sources: g-ray spectrometry (potassium (K), thorium (Th), and uranium (U)) and a digital elevation model (elevation, slope, curvature, hillshade, flow accumulation, and distance to streams). In addition, interpolated rainfall was tested. Species were coded as a dichotomous dummy variable; interaction effects between species and the g-ray spectrometric and geomorphologic variables were considered. The model explained up to 60% of the variance of site index and the standard error of estimate was 1.9 m. Uranium, elevation, distance to streams, thorium, and flow accumulation significantly correlate to the spatial variation of the site index of both species, and hillshade, curvature, elevation and slope accounted for the extra variability of one species over the other. The predicted site indices varied between 20.0 and 27.3 m for P. elliottii, and between 23.1 and 33.1 m for Queensland hybrid; the advantage of Queensland hybrid over P. elliottii ranged from 1.8 to 6.8 m, with the mean at 4.0 m. This compartment-based prediction and comparison study provides not only an overview of forest productivity of the whole plantation area studied but also a management tool at compartment scale.

Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

Optimization of an ammonia reactor using regression analysis

This paper presents an optimization algorithm for an ammonia reactor based on a regression model relating the yield to several parameters, control inputs and disturbances. This model is derived from the data generated by hybrid simulation of the steady-state equations describing the reactor behaviour. The simplicity of the optimization program along with its ability to take into account constraints on flow variables make it best suited in supervisory control applications.

Large-MIMO Receiver based on Linear Regression of MMSE Residual

Multiple input multiple output (MIMO) systems with large number of antennas have been gaining wide attention as they enable very high throughputs. A major impediment is the complexity at the receiver needed to detect the transmitted data. To this end we propose a new receiver, called LRR (Linear Regression of MMSE Residual), which improves the MMSE receiver by learning a linear regression model for the error of the MMSE receiver. The LRR receiver uses pilot data to estimate the channel, and then uses locally generated training data (not transmitted over the channel), to find the linear regression parameters. The proposed receiver is suitable for applications where the channel remains constant for a long period (slow-fading channels) and performs quite well: at a bit error rate (BER) of 10(-3), the SNR gain over MMSE receiver is about 7 dB for a 16 x 16 system; for a 64 x 64 system the gain is about 8.5 dB. For large coherence time, the complexity order of the LRR receiver is the same as that of the MMSE receiver, and in simulations we find that it needs about 4 times as many floating point operations. We also show that further gain of about 4 dB is obtained by local search around the estimate given by the LRR receiver.

Optimization of degree of sphericity of primary phase during cooling slope casting of A356 Al alloy: Taguchi method and regression analysis

The present work presents the results of experimental investigation of semi-solid rheocasting of A356 Al alloy using a cooling slope. The experiments have been carried out following Taguchi method of parameter design (orthogonal array of L-9 experiments). Four key process variables (slope angle, pouring temperature, wall temperature, and length of travel of the melt) at three different levels have been considered for the present experimentation. Regression analysis and analysis of variance (ANOVA) has also been performed to develop a mathematical model for degree of sphericity evolution of primary alpha-Al phase and to find the significance and percentage contribution of each process variable towards the final outcome of degree of sphericity, respectively. The best processing condition has been identified for optimum degree of sphericity (0.83) as A(3), B-3, C-2, D-1 i.e., slope angle of 60 degrees, pouring temperature of 650 degrees C, wall temperature 60 degrees C, and 500 mm length of travel of the melt, based on mean response and signal to noise ratio (SNR). ANOVA results shows that the length of travel has maximum impact on degree of sphericity evolution. The predicted sphericity obtained from the developed regression model and the values obtained experimentally are found to be in good agreement with each other. The sphericity values obtained from confirmation experiment, performed at 95% confidence level, ensures that the optimum result is correct and also the confirmation experiment values are within permissible limits. (c) 2014 Elsevier Ltd. All rights reserved.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Semisupervised Dimensionality Reduction and Classification Through Virtual Label Regression

Semisupervised dimensionality reduction has been attracting much attention as it not only utilizes both labeled and unlabeled data simultaneously, but also works well in the situation of out-of-sample. This paper proposes an effective approach of semisupervised dimensionality reduction through label propagation and label regression. Different from previous efforts, the new approach propagates the label information from labeled to unlabeled data with a well-designed mechanism of random walks, in which outliers are effectively detected and the obtained virtual labels of unlabeled data can be well encoded in a weighted regression model. These virtual labels are thereafter regressed with a linear model to calculate the projection matrix for dimensionality reduction. By this means, when the manifold or the clustering assumption of data is satisfied, the labels of labeled data can be correctly propagated to the unlabeled data; and thus, the proposed approach utilizes the labeled and the unlabeled data more effectively than previous work. Experimental results are carried out upon several databases, and the advantage of the new approach is well demonstrated.

Weighted and two-stage least squares estimation of semiparametric truncated regression models

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Structured Illumination Microscopy and a Quantitative Image Analysis for the Detection of Positive Margins in a Pre-Clinical Genetically Engineered Mouse Model of Sarcoma.

Intraoperative assessment of surgical margins is critical to ensuring residual tumor does not remain in a patient. Previously, we developed a fluorescence structured illumination microscope (SIM) system with a single-shot field of view (FOV) of 2.1 × 1.6 mm (3.4 mm2) and sub-cellular resolution (4.4 μm). The goal of this study was to test the utility of this technology for the detection of residual disease in a genetically engineered mouse model of sarcoma. Primary soft tissue sarcomas were generated in the hindlimb and after the tumor was surgically removed, the relevant margin was stained with acridine orange (AO), a vital stain that brightly stains cell nuclei and fibrous tissues. The tissues were imaged with the SIM system with the primary goal of visualizing fluorescent features from tumor nuclei. Given the heterogeneity of the background tissue (presence of adipose tissue and muscle), an algorithm known as maximally stable extremal regions (MSER) was optimized and applied to the images to specifically segment nuclear features. A logistic regression model was used to classify a tissue site as positive or negative by calculating area fraction and shape of the segmented features that were present and the resulting receiver operator curve (ROC) was generated by varying the probability threshold. Based on the ROC curves, the model was able to classify tumor and normal tissue with 77% sensitivity and 81% specificity (Youden's index). For an unbiased measure of the model performance, it was applied to a separate validation dataset that resulted in 73% sensitivity and 80% specificity. When this approach was applied to representative whole margins, for a tumor probability threshold of 50%, only 1.2% of all regions from the negative margin exceeded this threshold, while over 14.8% of all regions from the positive margin exceeded this threshold.

Determinants of WTP for Prosecco wine: A latent class regression with attitudinal responses

Purpose – Under investigation is Prosecco wine, a sparkling white wine from North-East Italy.
Information collection on consumer perceptions is particularly relevant when developing market
strategies for wine, especially so when local production and certification of origin play an important
role in the wine market of a given district, as in the case at hand. Investigating and characterizing the
structure of preference heterogeneity become crucial steps in every successful marketing strategy. The
purpose of this paper is to investigate the sources of systematic differences in consumer preferences.
Design/methodology/approach – The paper explores the effect of inclusion of answers to
attitudinal questions in a latent class regression model of stated willingness to pay (WTP) for this
specialty wine. These additional variables were included in the membership equations to investigate
whether they could be of help in the identification of latent classes. The individual specific WTPs from
the sampled respondents were then derived from the best fitting model and examined for consistency.
Findings – The use of answers to attitudinal question in the latent class regression model is found to
improve model fit, thereby helping in the identification of latent classes. The best performing model
obtained makes use of both attitudinal scores and socio-economic covariates identifying five latent
classes. A reasonable pattern of differences in WTP for Prosecco between CDO and TGI types were
derived from this model.
Originality/value – The approach appears informative and promising: attitudes emerge as
important ancillary indicators of taste differences for specialty wines. This might be of interest per se
and of practical use in market segmentation. If future research shows that these variables can be of use
in other contexts, it is quite possible that more attitudinal questions will be routinely incorporated in
structural latent class hedonic models.

Transform both sides model: A parametric approach

A parametric regression model for right-censored data with a log-linear median regression function and a transformation in both response and regression parts, named parametric Transform-Both-Sides (TBS) model, is presented. The TBS model has a parameter that handles data asymmetry while allowing various different distributions for the error, as long as they are unimodal symmetric distributions centered at zero. The discussion is focused on the estimation procedure with five important error distributions (normal, double-exponential, Student's t, Cauchy and logistic) and presents properties, associated functions (that is, survival and hazard functions) and estimation methods based on maximum likelihood and on the Bayesian paradigm. These procedures are implemented in TBSSurvival, an open-source fully documented R package. The use of the package is illustrated and the performance of the model is analyzed using both simulated and real data sets.

An integrated approach for real-time model-based state-of-charge estimation of lithium-ion batteries

Lithium-ion batteries have been widely adopted in electric vehicles (EVs), and accurate state of charge (SOC) estimation is of paramount importance for the EV battery management system. Though a number of methods have been proposed, the SOC estimation for Lithium-ion batteries, such as LiFePo4 battery, however, faces two key challenges: the flat open circuit voltage (OCV) vs SOC relationship for some SOC ranges and the hysteresis effect. To address these problems, an integrated approach for real-time model-based SOC estimation of Lithium-ion batteries is proposed in this paper. Firstly, an auto-regression model is adopted to reproduce the battery terminal behaviour, combined with a non-linear complementary model to capture the hysteresis effect. The model parameters, including linear parameters and non-linear parameters, are optimized off-line using a hybrid optimization method that combines a meta-heuristic method (i.e., the teaching learning based optimization method) and the least square method. Secondly, using the trained model, two real-time model-based SOC estimation methods are presented, one based on the real-time battery OCV regression model achieved through weighted recursive least square method, and the other based on the state estimation using the extended Kalman filter method (EKF). To tackle the problem caused by the flat OCV-vs-SOC segments when the OCV-based SOC estimation method is adopted, a method combining the coulombic counting and the OCV-based method is proposed. Finally, modelling results and SOC estimation results are presented and analysed using the data collected from LiFePo4 battery cell. The results confirmed the effectiveness of the proposed approach, in particular the joint-EKF method.