All‐subsets regression under effect heredity restrictions for experimental designs with complex aliasing

We consider an all‐subsets regression method for models under effect heredity restrictions for experimental designs with complex aliasing, whose number of potential main effects and two‐factor interactions exceed the number of runs. In this paper, we present an algorithm that systematically attempts to fit all such models. We illustrate the algorithm with two published experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

Graphical diagnostics for regression model determinations with consideration of the bias/variance trade-off

Estimates of model parameters (regression coefficients forming the regression vector) for a multivariate linear model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a multivariate linear model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on model bias and do not include variance or model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in model parameters as determined by plots of regression diagnostics using bias, variance, and/or model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper model parameters without cross-validation is possible. This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality.     

Visualizable and interpretable regression models with good prediction power

Many methods can fit models with a higher prediction accuracy, on average, than the least squares linear regression technique. But the models, including linear regression, are typically impossible to interpret or visualize. We describe a tree-structured method that fits a simple but nontrivial model to each partition of the variable space. This ensures that each piece of the fitted regression function can be visualized with a graph or a contour plot. For maximum interpretability, our models are constructed with negligible variable selection bias and the tree structures are much more compact than piecewise-constant regression trees. We demonstrate, by means of a large empirical study involving 27 methods, that the average prediction accuracy of our models is almost as high as that of the most accurate “black-box” methods from the statistics and machine learning literature.     

Kernel estimation of the regression function with random sampling times

Summary LetZ = (X, Y)= {Z(t)} _t∈ℛ be a stationary continuous-time process taking values in ℛ. By means of the corresponding discrete-time process {X(t _i ),Y(t _i )} _i=1 ⁿ , sampled at random instants {t _i }, a nonparametric kernel estimator of the regression function,m(x)=E(Y|X=x), is studied. Under mixing dependence conditions, the Mean Integrated Square Error (MISE) is derived and asymptotic normality is proven. In addition, we compare our results with those obtained under a classical approach for evenly-spaced observations. Finally, similar issues arising in the recursive case are considered. This work was awarded the Ramiro Melendreras price, offered to young researchers by the Spanish Statistical Society.     

Variance plus bias optimal response surface designs with qualitative factors applied to stem choice modeling

This paper explores the issue of model misspecification, or bias, in the context of response surface design problems involving quantitative and qualitative factors. New designs are proposed specifically to address bias and compared with five types of alternatives ranging from types of composite to D‐optimal designs using four criteria including D‐efficiency and measured accuracy on test problems. Findings include that certain designs from the literature are expected to cause prediction errors that practitioners would likely find unacceptable. A case study relating to the selection of science, technology, engineering, or mathematics majors by college students confirms that the expected substantial improvements in prediction accuracy using the proposed designs can be realized in relevant situations. Copyright © 2011 John Wiley & Sons, Ltd.     

Separation in D‐optimal experimental designs for the logistic regression model

The D‐optimality criterion is often used in computer‐generated experimental designs when the response of interest is binary, such as when the attribute of interest can be categorized as pass or fail. The majority of methods in the generation of D‐optimal designs focus on logistic regression as the base model for relating a set of experimental factors with the binary response. Despite the advances in computational algorithms for calculating D‐optimal designs for the logistic regression model, very few have acknowledged the problem of separation, a phenomenon where the responses are perfectly separable by a hyperplane in the design space. Separation causes one or more parameters of the logistic regression model to be inestimable via maximum likelihood estimation. The objective of this paper is to investigate the tendency of computer‐generated, nonsequential D‐optimal designs to yield separation in small‐sample experimental data. Sets of local D‐optimal and Bayesian D‐optimal designs with different run (sample) sizes are generated for several “ground truth” logistic regression models. A Monte Carlo simulation methodology is then used to estimate the probability of separation for each design. Results of the simulation study confirm that separation occurs frequently in small‐sample data and that separation is more likely to occur when the ground truth model has interaction and quadratic terms. Finally, the paper illustrates that different designs with identical run sizes created from the same model can have significantly different chances of encountering separation.     

Modified robust continuum regression by net analyte signal to improve prediction performance for data with outliers

Contaminated data exist in diverse situations, even in high quality surveys and experiments. If classical statistic models are blindly applied to data containing outliers, the results can be misleading at best. In this paper, a modified robust continuum regression (mRCR) method is proposed to improve prediction performance for data with outliers. The mRCR method constructs projection pursuit directions by using projection matrix for computing the net analyte signal (NAS) of the target analyte. This paper examines applications to the determination of glucose concentration by near-infrared (NIR) spectrometry, including aqueous solution with glucose experiment, plasma experiment in vitro, oral glucose tolerance test (OGTT) in vivo, to illustrate the advantages of mRCR for various kinds of outliers depending on the way of contamination. The results indicate that the mRCR method is entirely robust with respect to any type of outlying observations, and it yields smaller prediction errors for normal samples than other calibration methods.     

Influence of duct bias on deposition rate of DLC film in T-shape filtered arc deposition

Diamond-like carbon (DLC) films were deposited by a T-shape filtered arc deposition (T-FAD) apparatus, applying bias voltage to the plasma transportation duct which filters the macrodroplet emitted from the cathode, in order to obtain a higher deposition rate. Ion current, deposition rate, discharge voltage, duct current, and anode current were measured as a function of duct bias. The anode current decreased and the duct current increased when a positive bias was applied to the duct. This fact indicates that the T-shape duct acted as another anode of the vacuum arc discharge. It was found that the maximum deposition rate as well as the ion current was obtained at about 15 V of duct bias. Improvement in plasma transportation to the process chamber through the duct was considered from the viewpoint of the characteristics of duct current against bias voltage. The value of the optimum duct bias was the same as the intersection point of the characteristics of duct current against bias voltage.     

Pedestrian injury analysis with consideration of the selectivity bias in linked police-hospital data

Evaluation of crash-related injuries by medical specialists in hospitals is believed to be more exact than rather a cursory evaluation made at the crash scene. Safety analysts sometimes reach for hospital data and use them in combination with the police crash data. One issue that needs to be addressed is the, so-called, selectivity (or selection) bias possible when data used in analysis are not coming from random sampling. If not properly addressed, this issue can lead to a considerable bias in both the model coefficient estimates and the model predictions. This paper investigates pedestrian injury severity factors using linked police-hospital data.A bivariate ordered probit model with sample selection is used to check for the presence of the selectivity bias and to account for it in the MAIS estimates on the Maximum Abbreviated Injury Scale (MAIS). The presence of the sample selection issue has been confirmed. The selectivity bias is considerable in predictions of low injury levels.The pedestrian injury analysis identified and estimated several severity factors, including pedestrian, road, and vehicle characteristics. Male and older pedestrians were found to be particularly exposed to severe injuries. Rural roads and high-speed urban roads appear to be more dangerous for pedestrians, particularly when crossing such roads. Crossing a road between intersections was found to be particularly dangerous behavior. The size and weight of the vehicle involved in a pedestrian crash were also found to have an effect on the pedestrian injury level. The relevant safety countermeasures that may improve pedestrian safety have been proposed.     

Examining the nonparametric effect of drivers’ age in rear-end accidents through an additive logistic regression model

This study seeks to inspect the nonparametric characteristics connecting the age of the driver to the relative risk of being an at-fault vehicle, in order to discover a more precise and smooth pattern of age impact, which has commonly been neglected in past studies. Records of drivers in two-vehicle rear-end collisions are selected from the general estimates system (GES) 2011 dataset. These extracted observations in fact constitute inherently matched driver pairs under certain matching variables including weather conditions, pavement conditions and road geometry design characteristics that are shared by pairs of drivers in rear-end accidents. The introduced data structure is able to guarantee that the variance of the response variable will not depend on the matching variables and hence provides a high power of statistical modeling. The estimation results exhibit a smooth cubic spline function for examining the nonlinear relationship between the age of the driver and the log odds of being at fault in a rear-end accident. The results are presented with respect to the main effect of age, the interaction effect between age and sex, and the effects of age under different scenarios of pre-crash actions by the leading vehicle. Compared to the conventional specification in which age is categorized into several predefined groups, the proposed method is more flexible and able to produce quantitatively explicit results. First, it confirms the U-shaped pattern of the age effect, and further shows that the risks of young and old drivers change rapidly with age. Second, the interaction effects between age and sex show that female and male drivers behave differently in rear-end accidents. Third, it is found that the pattern of age impact varies according to the type of pre-crash actions exhibited by the leading vehicle.     

Removing mesh bias in mixed-mode cohesive fracture simulation with stress recovery and domain integral

To remove mesh bias and provide an accurate crack path representation in mixed-mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode-I and mixed-mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower-quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed-mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.     

Photocatalytic decomposition of 2-chlorophenol in aqueous solution by UV/TiO2 process with applied external bias voltage

The decomposition of 2-chlorophenol by UV/TiO2 process with the application of external bias voltage was examined in this study. Experiments were conducted in a batch reactor using TiO2-coated titanium sheet as anode and platinum sheet as cathode. The anode photocatalysis of 2-chlorophenol was totally inhibited for experiments conducted with the application of external anodic bias voltage lower than the flat band potential of TiO2. The decomposition rate of 2-chlorophenol was then increased with increasing external anodic bias voltage applied up to 0.0 V (versus SCE). The application of external bias voltage higher than 1.0 V did not markedly promote the photocatalysis of 2-chlorophenol possibly because the photocurrent induced was constant. Experimental results indicated that the decomposition of 2-chlorophenol was more effective for experiments conducted in acidic solutions due to the lower flat band potential of TiO2 and the higher photocurrent induced. The presence of electron scavengers in aqueous solution, such as oxygen molecules, may increase the decomposition rate of 2-chlorophenol. However, the effect of dissolved oxygen was diminished for experiments conducted with applied external bias voltage. The photocatalytic decomposition rate of 2-chlorophenol was enhanced linearly with the increasing UV light intensity when the external bias voltage was applied.     

Positive exchange bias in epitaxial permalloy/MgO integrated with Si (1 0 0)

In magnetic random access memory (MRAM) devices, soft magnetic thin film elements such as permalloy (Py) are used as unit cells of information. The epitaxial integration of these elements with the technologically important substrate Si (1 0 0) and a thorough understanding of their magnetic properties are critical for CMOS-based magnetic devices. We report on the epitaxial growth of Ni_82.5Fe_17.5 (permalloy, Py) on Si (1 0 0) using a TiN/MgO buffer layer. Initial stages of growth are characterized by the formation of discrete islands that gradually merge into a continuous film as deposition times are extended. Interestingly, we find that the magnetic features of Py films in early stages of island coalescence are distinctly different from the films formed initially (discrete islands) and after extended deposition times (narrow distribution of equiaxed granular films). Isothermal in-plane and out-of-plane magnetic measurements performed on these transitional films show highly anisotropic magnetic behavior with an easy magnetization axis lying in the plane of the film. Importantly, when this sample is zero-field cooled, a positive exchange bias and vertical loop shift are observed, unusual for a soft ferromagnet like Py. Repeated field cycling and hysteresis loops up to the fields of 7T produced reproducible hysteresis loops indicating the existence of strongly pinned spin configurations. Classical interface related exchange bias models cannot explain the observed magnetic features of the transitional Py films. We believe that the anomalous magnetic behavior of such Py films may be explained by considering the highly irregular morphology that develops at intermediate growth times that are possibly also undergoing a transition from Bloch to Neel domain wall structures as a function of Py island size. This study broadens the current understanding of magnetic properties of Py thin layers for technological applications in magneto-electronic devices, integrated with Si (1 0 0).     

Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application

In some statistical process control applications, there are some correlated quality characteristics which can be modeled as linear functions of some explanatory variables. We refer to this structure as multivariate multiple linear regression profiles. When the correlation structure between quality characteristics is ignored and profiles are monitored separately then misleading results could be expected. Hence, developing methods to account for this multivariate structure is required. In this paper, we specifically focus on phase I monitoring of multivariate multiple linear regression profiles and develop four methods for this purpose. The performance of the developed methods is compared through simulation studies in terms of probability of a signal. In addition, a diagnostic scheme to find the out‐of‐control samples is developed. Finally, the application of the proposed methods is illustrated using a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center. Copyright © 2009 John Wiley & Sons, Ltd.     

Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis

It is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases unable to fully describe the particle size distribution of comminution products. In order to overcome this shortcoming, piecewise regression analysis was used to predict the size distributions derived, after grinding for various periods four mono-sized fractions of quartz and marble in a laboratory ball mill. The single line was divided into two straight lines, which indicate the presence of two domains of particle sizes and therefore the involvement of two distinct breakage mechanisms. The obtained GGS model parameters were used to determine the evolution of particle size distribution as a function of the energy input.

In addition, the existing relationships between energy input and particle size distribution were improved, by taking into account the effects of the feed size and material type. The new relationships obtained can be used for a more accurate estimation of the required energy for breakage.     

Adaptive weighted least square support vector machine regression integrated with outlier detection and its application in QSAR

In order to eliminate the influence of unavoidable outliers in training sample on a model's performance, a novel least square support vector machine regression, which combines outlier detection approach and adaptive weight value for the training sample, is proposed and named as adaptive weighted least square support vector machine regression (AWLS-SVM). Firstly, the effective robust 3σ principle is used to detect marked outliers for the training sample. Secondly, based on the training sample without marked outliers, least square support vector machine regression is employed to develop the model and the fitting error of each sample data is obtained. Thirdly, according to the fitting error of each sample data, the initial weight is calculated. The bigger the fitting error of sample data is, the smaller the weight value of the sample data. Thus, the potential outliers, which are not detected by the robust 3σ principle and have bigger fitting errors, have smaller weight values to reduce the influence of the potential outliers on the performance of model. Then, LS-SVM is applied for the weighted sample to develop the model again. Finally, via the proposed weight value iterative method, the weight values of the training sample are converged, and the model with good predicting performance is obtained. To illustrate the performance of AWLS-SVM, simulation experiment is designed to produce the training sample with marked outlier and some non-marked outliers. AWLS-SVM, AWLS-SVM without the robust 3σ principle, LS-SVM with the robust 3σ principle, LS-SVM, and radial basis function network are applied to develop the model based on the designed sample. The results show that the influence of marked and un-marked outliers on the model's performance is eliminated by AWLS-SVM, and that the predicting performance of AWLS-SVM is the best. Furthermore, the AWLS-SVM method was applied to develop the quantitative structure–activity relationships (QSAR) model of HIV-1 protease inhibitors, and the satisfactory result was obtained.     

Improvement in the bias stability of zinc oxide thin-film transistors using Si3N4 insulator with SiO2 interlayer

The performance of ZnO thin film transistors (TFT) subjected to SiO₂ interlayer treatments on Si₃N₄ insulators was investigated. In the case of a SiO₂ interlayer of 10 nm on Si₃N₄ insulator, a drastic improvement in device performance was obtained. ZnO TFT with this interlayer showed reduced trap density between the Si₃N₄ and ZnO channel, bringing remarkable improvement in bias stability characteristics. These devices show good performance and exhibit a high field-effect mobility of 6.41 cm²/Vs, an on/off current ratio of 10⁸, and a subthreshold swing of 1.46 V/decade. Also, the turn-on voltage shifted from − 2 V to − 6 V with negligible changes in the subthreshold swing and field effect mobility after total stress time.