Linear Covariance Research Articles

Effects of measurement errors on semicircle control chart

In recent years, the impacts of measurement errors on the performance of various control charts have been well evaluated. The existing semicircle (SC) control chart has been proposed based on the assumption that there are no measurement errors. In this paper, we investigated the effect of measurement errors using the linear covariate error model with constant variance and linearly increasing variance on the performance of the SC chart. We used simulation to evaluate the performance of the SC chart, in terms of average run length (ARL), standard deviation of the run length (SDRL), median run length (MDRL), and expected average run length (EARL) metrics. The results obtained indicate that measurement errors negatively affect the performance of the SC chart and taking multiple measurements on each item or/and increasing the slope coefficient of the covariate error model can effectively reduce the adverse impact of errors on the chart’s performance. Finally, an illustrative real life example is provided to demonstrate the undesired impact of measurement errors on the detection capability of the SC chart.

Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe)

We propose a new method for the simultaneous selection and estimation of multivariate sparse additive models with correlated errors. Our method called Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe) simultaneously selects among null, linear, and smooth non-linear effects for each predictor while incorporating joint estimation of the sparse residual structure among responses, with the motivation that accounting for inter-response correlation structure can lead to improved accuracy in variable selection and estimation efficiency. CoMPAdRe is constructed in a computationally efficient way that allows the selection and estimation of linear and non-linear covariates to be conducted in parallel across responses. Compared to single-response approaches that marginally select linear and non-linear covariate effects, we demonstrate in simulation studies that the joint multivariate modeling leads to gains in both estimation efficiency and selection accuracy, of greater magnitude in settings where signal is moderate relative to the level of noise. We apply our approach to protein-mRNA expression levels from multiple breast cancer pathways obtained from The Cancer Proteome Atlas and characterize both mRNA-protein associations and protein-protein subnetworks for each pathway. We find non-linear mRNA-protein associations for the Core Reactive, EMT, PIK-AKT, and RTK pathways. Supplementary Materials are available online.

Performance evaluation of extended EWMA control chart in the presence of measurement error

In any manufacturing or service industry, substantial effort is made to keep a process under control. However, factors such as measurement error are bound to create distortions. Many researchers have studied the effect of measurement error on various types of control charts including the EWMA control chart. In this paper, we study the effect of measurement error on the competency of the extended EWMA control chart. We examine the performance of the chart in the case of a shift in mean taking into account the model with linear covariates. The consequence of making multiple measurements on each sampled unit is also investigated. Last but not the least, we examine the case of linearly increasing variance. Through a simulation study, we demonstrate that the performance of the chart for detecting a shift in the mean is substantially reduced in the presence of measurement error. The important finding, however, is that, in spite of the existence of measurement error, the EEWMA control chart performs better than the EWMA control chart. A practical example is provided to elucidate this finding.

217 Effect of within-litter competition on lamb survivability

Abstract The objective of this study was to evaluate the influence of lamb and littermate competition on lamb survivability to weaning. Litter sex composition and litter birth weight variation were the primary considerations for influencing competition. Records from maternal dual-purpose (Polypay, Rambouillet, and Targhee) and terminal breeds [Suffolk and Paternal Composite (PC; 3/8 Columbia, 3/8 Suffolk, 1/4 Texel)] were used, with 18,654 single and 56,324 twin records from all breeds and 11,082 triplet records from the 3 maternal breeds. Records were reported from 1980 to 2023, except for the PC, which began inter se mating in 2009. Lamb survivability to 90 d was analyzed using a Bayesian logistic regression model with the logit link function. Lamb survivability was assumed binomially distributed and influenced by age of dam, birth year, lamb sex, and sex of littermates as fixed effects. The relationship among littermates was also accounted for. Least squares means were transformed from the log odds scale to the probability scale. Birth weight was assumed normally distributed and influenced by the same fixed effects as lamb survival and was analyzed using a linear mixed model. Lamb survivability was also analyzed using the same model described above but including mean litter weight and individual birth weight deviation as linear covariates. Accounting for mean litter birth weight and individual birth weight deviation removed the birth weight differences between the sexes, leaving only true sex differences between lambs for survivability. For single births, females tended to have greater survivability than males when adjusted for birth weight for all breeds but was only significant (P < 0.05) for Rambouillet and Targhee. For maternal breeds, females in twin litters had significantly greater survivability (P < 0.05) than their male counterparts when adjusted for birth weight; differences in terminal breeds were not significant (Table 1). Males in twin litters had heavier birth weights than females (P < 0.05) for all breeds. Triplet born females for all litter-sex combinations had significantly higher survival than males (P < 0.05) for Polypay when adjusted for birth weight. Females in female-female-male (FFM) litters had 76.4% survival versus 58.9% for males while females in female-male-male (FMM) litters had 75.9% versus 66.7% for males. When lamb survivability was adjusted for birth weight, Rambouillet females in FFM litters had 72.2% survival compared with 59.9% for males (P < 0.05) and females in FMM litters had 73.0% survival compared with 63.8% for males. Similar significant differences were observed for FFM and FMM Targhee litters. This study suggests lamb performance is influenced by its littermate(s). Changes in postnatal management of mixed-sex litters may benefit overall lamb survival. USDA is an equal opportunity provider and employer.

Functional sufficient dimension reduction through distance covariance

Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has several advantages over existing methods. Unlike current techniques which require restrictive assumptions such as linear conditional mean and constant covariance, our method has mild requirements on the predictor. Additionally, our method does not involve the use of the unbounded inverse of the covariance operator. The link function between the response and predictor can be arbitrary, and our proposed method maintains the advantage of being model-free, without the need to estimate the link function. Furthermore, our method is naturally suited for sparse longitudinal data. We utilize functional principal component analysis with truncation as a regularization mechanism in the development of our method. We provide justification for the validity of our proposed method, and establish statistical consistency of the estimator under certain regularization conditions. To demonstrate the effectiveness of our proposed method, we conduct simulation studies and real data analysis. The results show improved performance compared to existing methods.

Stochastic Trajectory Planning for Autonomous Aerobraking Using Convex Optimization and Covariance Control

Trajectory planning for autonomous aerobraking poses significant technical challenges, primarily due to the complexities associated with ensuring reliable onboard computation, mitigating flying uncertainty, enhancing aerodeceleration efficacy, and guaranteeing sufficient precision. To address this issue, this paper utilizes convex optimization for the first time to synchronously generate an anti-uncertainty trajectory and corresponding closed-loop controller with efficient, robust, and high-precision computational capability. Specifically, a double-loop planning framework is developed. In the inner loop, techniques of covariance control and linear covariance analysis are employed to give rise to a stochastic trajectory planning problem that optimizes the orbiter’s capacity to withstand and overcome deviations during flight. Furthermore, for onboard planning considerations, the problem’s nonlinearity is equivalently reduced by projecting the time-independent variable into the altitude variable. On this basis, a novel state-complete linearization method is introduced to enable the utilization of sequential convex programming with improved convergence. For the outer loop, the orbiter’s motion is decomposed into low-accuracy longitudinal and high-precision dynamics. A differential-correction-based technique is specifically designed to remedy the dynamics in turn. Numerical simulations demonstrate that the proposed method can reduce mission risk by at least 70% while only experiencing an additional cost of velocity impulse amounting to 20%.

Robust trajectory planning for non-cooperative target rendezvous based on closed-loop uncertainty analysis

A robust trajectory planning method for non-cooperative target rendezvous is investigated based on closed-loop uncertainty analysis. The proposed method addresses the issue that uncertainties affect the optimality of objective functions and the reliability of constraints. Considering multiple uncertainties, a stochastic optimal rendezvous model with a robustness performance index and chance constraints is presented with line-of-sight dynamics. The guidance model, angles-only navigation model and control model are derived, and uncertainty propagation equations for closed-loop GN&C system is proposed by using linear covariance analysis. The stochastic optimal rendezvous model is transformed into a robust optimal rendezvous model by using 3-σ of the random variables. The genetic algorithm is used to solve the robust trajectory planning problem, and a series of examples demonstrate that the robust maneuver solution can be significantly better than the solution corresponding to deterministic trajectory optimization problem.

Genotype by environment interaction and stability analysis of three agronomic traits in Kersting's groundnut (Macrotyloma geocarpum) using factor analytic modeling and environmental covariates

AbstractUnderstanding genotype by environment interaction (GEI) represents a challenge in Kersting's groundnut [Macrotyloma geocarpum (Harms) Maréchal and Baudet] breeding for selecting high‐performing and stable lines across environments. Here, we investigated GEI and stability in Kersting's groundnut using factor analytic (FA) based linear mixed models and environmental covariates. A total of 375 accessions were evaluated across 3 years (2017, 2018, and 2019) and two locations (Sékou and Savè) in Benin, generating five environments (E1, E2, E3, E4, and E5). The traits measured included days to 50% flowering (DFF), grain yield (YLD), and 100‐seed weight (HSW). The study generated multi‐environment values for grain yield and its components in Kersting's groundnut. The genetic correlations between pairs of environments ranged from −0.71 to 0.99. The genetic correlations between YLD and HSW indicated positive and moderate to high correlations in all environments. The FA analysis revealed that FA2 structure accounted for 93.9% of the genetic variability in DFF with factor 1 accounting for more than 90% of the environments variations. Two factors explained 87% of the genetic variance in grain yield, and 70% of the environments variability were clustered by factor 1. For HSW, two factors explained 85% of the genetic variance of the environments, and factor 1 accounted for 72.7%. Combining environmental covariates to FA models revealed that precipitation, temperature, and growth cycle duration were highly correlated to the environmental loadings of factor 1. Relative humidity and solar radiation showed moderate to high correlations with factor 2 loadings. Those covariates explained the high GEI among environments clustered by a given factor. Precipitations and temperatures affected the variations in grain yield. Finally, based on latent regression analysis, the accessions AF202, AF221, AF223, AF225, and AF256 were identified as accessions combining best performance for grain yield, early flowering, and 100‐seed weight, showing adaptability across environments and stability to some environments.

Genetic parameters for mesenteric torsion in a pig maternal line

Mesenteric torsion (MT) is a condition characterized by the twisting of intestinal loops, leading to a disruption in blood flow and abdominal distension. Several factors can predispose animals to this condition, which primarily affects healthy, fast-growing pigs and often results in fatal outcomes. Given the absence of studies on the genetic factors associated with this condition, our research aimed to estimate the heritability coefficient for MT and explore the genetic correlations between MT and performance traits in pigs. Our dataset comprised of 43,384 records of pigs from a maternal line from a nucleus farm. These pigs were born between 2010 and 2022 and had recorded information regarding MT status (0 for healthy and 1 for affected animals), weaning weight (WW), as well as pedigree, genotypes, and genomic estimated breeding values (GEBVs) for the following traits: MT status, days to reach 110 kg (D110), feed conversion adjusted to 110 kg (FC110), and backfat thickness adjusted to 110 kg (BT110). In our statistical model, the effects of contemporary group (CG: sex, year, and week of weaning) and the linear covariate WW were considered fixed effects, while the direct additive genetic effect was accounted as random. On average, pigs affected by MT had an age of 104.35 ± 37.75 days, and the condition had an overall herd frequency of 2.46 %. Mesenteric torsion occurred more frequently in female pigs raised in collective pens compared to non-castrated males raised in individual pens. Heritability estimates for MT, using both pedigree (0.13 ± 0.02) and genomic (0.12 ± 0.02) data, were of low magnitude. This suggests that while there is genetic variability associated with MT, a significant portion of this variation is due to environmental variance. The correlation between MT and BT110 GEBVs was of low magnitude (0.05). In contrast, the correlations between GEBVs for MT and both D110 and FC110 were moderate in magnitude (0.22 for both traits). This implies that pigs taking longer to reach 110 kg and those with poorer feed conversion are more likely to develop MT. There is genetic variability for mesenteric torsion in pigs. Selection aimed at improving feed conversion and reducing the age at which pigs reach 110 kg could lead to a decrease in the occurrence of MT within pig populations.

Optimal design of adaptive EWMA monitoring schemes for the coefficient of variation and performance evaluation with measurement errors

The coefficient of variation (CV) usually describes the relative dispersion in production or service processes and has been widely applied in various fields. Monitoring the CV has received great attention in statistical process monitoring. This paper develops two one-sided adaptive EWMA (AEWMA) CV schemes to enhance the existing CV schemes’ monitoring efficiency. This scheme can effectively defect various shift sizes by dynamically adjusting the smoothing parameter of the EWMA based on the residuals. The optimization models of the AEWMA CV are designed based on the Markov chain method from two different perspectives, (i) a pair of changes; (ii) a range of changes. The numerical and graphical comparisons confirm the superiority of the proposed schemes. Moreover, in the data collection process, measurement errors from devices and human operations may arise. To assess the impact of such measurement errors on the monitoring performance, a linear covariate error model is adopted. For illustration and validation, the proposed schemes are implemented to a real industrial example from the sintering process.

Multi-Objective Robust Trajectory Design for Powered Descent and Landing

A robust trajectory optimization approach for guidance algorithm gain and target vector selection for powered descent and landing is developed. A genetic algorithm is used to determine optimized guidance algorithm parameters to minimize the impact of initial condition, environment, navigation, and vehicle property uncertainty on flight performance for a given sensor suite. Vehicle state uncertainties are computed efficiently using linear covariance analysis techniques. When implemented in the guidance algorithm, the optimized gains and target vectors shape a trajectory that has more favorable conditions for a given navigation sensor suite, resulting in improved flight performance. As a demonstration of this method, the optimized guidance parameters are found for a multiphase trajectory from powered descent initiation to touchdown for a robotic lunar landing mission. Single-objective optimization results demonstrate a reduction in uncertainty and an improvement in nominal performance. Multi-objective optimization results showing the tradeoff between terminal position uncertainty and total propellant usage are presented for multiple sensor suite compositions. Further, guidance parameters selected using the developed robust trajectory design approach may enable acceptable flight performance with fewer and/or lower-quality sensors. The resulting Pareto fronts present the optimal trade space early in the mission design process to enable informed decision-making.

The performance of the one-sided truncated exponentially weighted moving average X ¯ control chart in the presence of measurement errors

When the direction of a potential mean shift can be anticipated, the one-sided exponentially weighted moving average (EWMA) X ¯ control chart using the truncation method (namely, the one-sided TEWMA X ¯ chart) is more efficient than those conventional one- and two-sided EWMA X ¯ schemes for process monitoring. Although attractive, there are no studies on designing the one-sided TEWMA X ¯ chart by taking measurement errors into account. In this context, we investigate the effect of measurement errors on the performance of the one-sided TEWMA X ¯ chart based on the linear covariate error model. Additionally, a Markov chain model is established to evaluate the run length properties of the scheme in the presence of measurement errors. Then, an optimal design procedure is developed for searching the optimal design parameters of the scheme. Based on these mentioned studies, several tables and figures are presented to evaluate the detecting performance of the scheme under different parameters of the linear covariate error model, and then a conventional one-sided EWMA X ¯ chart with reflecting boundary is introduced to further study the effect of the presence and absence of measurement errors on control chart comparison studies. Simulation results show that although the detecting performance of the proposed scheme is significantly affected by measurement errors, its performance is still superior to the classic competing chart under the same comparison conditions. Finally, an illustrative example is given to show the implementation of the recommended scheme.

Multivariate pattern analysis: a method and software to reveal, quantify, and visualize predictive association patterns in multicollinear data

BackgroundStrongly multicollinear covariates, such as those typically represented in metabolomics applications, represent a challenge for multivariate regression analysis. These challenges are commonly circumvented by reducing the number of covariates to a subset of linearly independent variables, but this strategy may lead to loss of resolution and thus produce models with poorer interpretative potential. The aim of this work was to implement and illustrate a method, multivariate pattern analysis (MVPA), which can handle multivariate covariates without compromising resolution or model quality.ResultsMVPA has been implemented in an open-source R package of the same name, mvpa. To facilitate the usage and interpretation of complex association patterns, mvpa has also been integrated into an R shiny app, mvpaShiny, which can be accessed on www.mvpashiny.org. MVPA utilizes a general projection algorithm that embraces a diversity of possible models. The method handles multicollinear and even linear dependent covariates. MVPA separates the variance in the data into orthogonal parts within the frame of a single joint model: one part describing the relations between covariates, outcome, and explanatory variables and another part describing the “net” predictive association pattern between outcome and explanatory variables. These patterns are visualized and interpreted in variance plots and plots for pattern analysis and ranking according to variable importance. Adjustment for a linear dependent covariate is performed in three steps. First, partial least squares regression with repeated Monte Carlo resampling is used to determine the number of predictive PLS components for a model relating the covariate to the outcome. Second, postprocessing of this PLS model by target projection provided a single component expressing the predictive association pattern between the outcome and the covariate. Third, the outcome and the explanatory variables were adjusted for the covariate by using the target score in the projection algorithm to obtain “net” data. We illustrate the main features of MVPA by investigating the partial mediation of a linearly dependent metabolomics descriptor on the association pattern between a measure of insulin resistance and lifestyle-related factors.ConclusionsOur method and implementation in R extend the range of possible analyses and visualizations that can be performed for complex multivariate data structures. The R packages are available on github.com/liningtonlab/mvpa and github.com/liningtonlab/mvpaShiny.

Erratum to: Genotype–environment interaction and yield stability analysis of Colombian yellow diploid potato cultivars using mixed linear models and environmental covariates

Erratum to: Genotype–environment interaction and yield stability analysis of Colombian yellow diploid potato cultivars using mixed linear models and environmental covariates

Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers

Determining the predictor variables that have a non-linear effect as well as those that have a linear effect on the response variable is crucial in additive semi-parametric models. This issue has been extensively investigated by many researchers in the area of semi-parametric linear additive models, and various separation methods are proposed by the authors. A popular issue that might affect both estimation and separation results is the existence of outliers among the observations. In order to address this lack of sensitivity towards extreme observations, robust estimating approaches are frequently applied. We propose a robust method for simultaneously identifying the linear and nonlinear components of a semi-parametric linear additive model, even in the presence of outliers in the observations. Additionally, this model is sparse in that it may be used to determine which explanatory variables are ineffective by giving accurate zero estimates for their coefficients. To assess the effectiveness of the proposed method, a comprehensive Monte Carlo simulation study is conducted along with an application to investigate the dataset, which includes Boston property prices dataset.

Reaction-norm animal model analysis of average daily gain heat tolerance in purebred Duroc pigs.

The present study aimed to genetically improve growth performance under high-heat environments by specifically designing a reaction-norm animal model (RNAM) for purebred Duroc pigs in Japan. A total of 54,750 records of average daily gain (ADG) measured for pigs reared at four farms in different prefectures were analyzed. Estimated maximum daily temperatures at the respective farm locations were used to calculate the average cumulative thermal load (TL). The TL values served as an indicator of high-heat environments for pigs. The plausible cumulative period length and threshold temperature for calculating TL were determined to be 8 weeks until just before shipping and 25°C, respectively. Variance components were estimated via RNAM analysis using TL as a linear covariate. The estimated additive genetic variances under both responsive and non-responsive to TL were found to be significant. Moreover, the estimated heritability of ADG ranged from 0.38 to 0.73 for TL values of 0-8. These results suggest that the RNAM developed holds the potential for improving the genetic ability of growth under high-heat environments in pigs.

Performance-based inference of selection on stomatal length and specific leaf area varies with climate-of-origin of the forest tree, Eucalyptus ovata

Understanding how functional traits affect plant performance and fitness is a key step in unravelling the role of natural selection in shaping the evolutionary trajectory of populations. We examined early-age selection acting on leaf traits via their effects on growth performance and fitness, measured in Eucalyptus ovata trees planted in a common-garden field trial embedded in a reforestation planting in Tasmania, Australia. We focused on two important leaf traits - stomatal length and specific leaf area (SLA) - measured two years after planting, and compared interplanted E. ovata groups originating from dry and wet home-site climates, with the trial site having intermediate long-term mean annual rainfall. Two-year height growth was used as the performance attribute, and the time-averaged tree survival over the subsequent six years as the fitness component. There was evidence for performance-based selection on the leaf traits, with the strength and form of selection depending on the trait and climate group being considered. In this sense, selection in the dry group operated mainly on stomatal length where a combination of directional (favouring longer stomata) and stabilizing selection was detected, whereas selection in the wet group acted only on SLA and was purely stabilizing. Estimates of performance-based correlational selection were not statistically significant. For both climate groups, estimates of fitness-based selection gradients provided evidence for significant directional (but not quadratic) selection on height performance, favouring individuals with faster growth, but did not indicate statistical support for direct effects of the leaf traits on tree survival, conditional on measured performance. These results validated qualitative inferences of selection from the performance-based analysis, and suggested that selection on the leaf traits appeared to be mediated by their effects on early-age height performance, which in turn directly influenced later-age survival. We discuss the mechanisms by which the focal traits may have affected height performance, and likely factors contributing to the different patterns of phenotypic selection observed in the two groups experiencing the same environment. We also provide expressions of analytical derivatives that were developed for the estimation of selection gradients based on a logistic regression model relating a binary fitness response to linear and nonlinear covariate terms for the target regressor variables.

Monitoring the process mean under the Bayesian approach with application to hard bake process

This study introduces the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart within the framework of measurement error, examining two separate loss functions: the squared error loss function and the linex loss function. We conduct an analysis of the posterior and posterior predictive distributions utilizing a conjugate prior. In the presence of measurement error (ME), we employ a linear covariate model to assess the control chart's effectiveness. Additionally, we explore the impacts of measurement error by investigating multiple measurements and a method involving linearly increasing variance. We conduct a Monte Carlo simulation study to assess the control chart's performance under ME, examining its run length profile. Subsequently, we offer a specific numerical instance related to the hard-bake process in semiconductor manufacturing, serving to verify the functionality and practical application of the suggested Bayesian AEWMA control chart when confronted with ME.

Spatial Confounding and Spatial+ for Nonlinear Covariate Effects

Regression models for spatially varying data use spatial random effects to reflect spatial correlation structure. Such random effects, however, may interfere with the covariate effect estimates and make them unreliable. This problem, known as spatial confounding, is complex and has only been studied for models with linear covariate effects. However, as illustrated by a forestry example in which we assess the effect of soil, climate, and topography variables on tree health, the covariate effects of interest are in practice often unknown and nonlinear. We consider, for the first time, spatial confounding in spatial models with nonlinear effects implemented in the generalised additive models (GAMs) framework. We show that spatial+, a recently developed method for alleviating confounding in the linear case, can be adapted to this setting. In practice, spatial+ can then be used both as a diagnostic tool for investigating whether covariate effect estimates are affected by spatial confounding and for correcting the estimates for the resulting bias when it is present. Supplementary materials accompanying this paper appear online.

Fatigue and quality of life during neoadjuvant chemotherapy of early breast cancer: a prospective multicenter cohort study

BackgroundFew measurements of fatigue and quality of life have been performed during neoadjuvant chemotherapy of early breast cancer. This study evaluates fatigue and quality of life experienced by early breast cancer patients during neoadjuvant chemotherapy and their association with different clinical parameters.MethodsFifty-four stage I–III patients’ responses to the Multidimensional Fatigue Inventory (MFI) and to the Functional Assessment of Cancer Therapy-Breast (FACT-B) were analyzed by a linear covariance pattern model. Chemotherapy regimen, age, baseline fatigue level, body-mass-index and cancer stage were added to the model to estimate their impact on both outcomes.ResultsAll fatigue dimensions worsened in clinically relevant levels. Physical fatigue worsened the most, mental fatigue the least. For quality of life, physical and functional well-being worsened the most. Only emotional well-being improved during chemotherapy. Physical well-being worsened more during standard than during dose-dense chemotherapy, and more during anthracycline than during taxane cycles. Age, body-mass-index and cancer stage had no impact. The higher the fatigue levels at baseline, the less they worsened during chemotherapy.ConclusionsFurther actions to reduce fatigue and improve quality of life during neoadjuvant chemotherapy of early breast cancer are needed. Focus should be laid on the physical dimension. Future research should also investigate the impact of different chemotherapy sequences and densities on fatigue and quality of life.Study registrationThe study was registered in the German Clinical Trials Register in May 2019 (DRKS00016761).