Covariance Model Research Articles

Mixture regression for longitudinal data based on joint mean–covariance model

In the process of modeling longitudinal data, we focus on the case that the studied population is comprised of different groups of individuals and individuals within the same group share the similar kind of mean progression trajectories, where finite mixture models (FMM) are often used to address this kind of unobserved heterogeneity in terms of mean. Existing methods, such as parametric and semiparametric mixture regression, usually model the mean in each subpopulation with assumption that observations sharing a common trajectory are independent or their covariance structure is pre-specified, but less research considers modeling of covariance structures while accounting for heterogeneity. In this paper, we introduce a joint model which models the mean and covariance structures simultaneously in a finite normal mixture regression, demonstrating how important the within-subject correlation is in clustering longitudinal data. Model parameters are estimated with an iteratively re-weighted least squares EM (IRLS-EM) algorithm. Our estimators are shown to be consistent and asymptotically normal. We can identify different mean trajectories and covariance structures in all clusters. Simulations show that the proposed method performs well and gives more accurate clustering results by introducing covariance modeling. Real data analysis is also used to illustrate the usefulness of the proposed method, and it presents good performance in clustering COVID-19 deaths for European countries in terms of progression trajectory.

The Aging, Community and Health Research Unit Community Partnership Program (ACHRU-CPP) for\xa0older adults with diabetes and multiple chronic conditions: study protocol for a randomized\xa0controlled trial

BackgroundOlder adults (≥65 years) with diabetes and multiple chronic conditions (MCC) (> 2 chronic conditions) experience reduced function and quality of life, increased health service use, and high mortality. Many community-based self-management interventions have been developed for this group, however the evidence for their effectiveness is limited. This paper presents the protocol for a randomized controlled trial (RCT) comparing the effectiveness and implementation of the Aging, Community and Health Research Unit-Community Partnership Program (ACHRU-CPP) to usual care in older adults with diabetes and MCC and their caregivers.MethodsWe will conduct a cross-jurisdictional, multi-site implementation-effectiveness type II hybrid RCT. Eligibility criteria are: ≥65 years, diabetes diagnosis (Type 1 or 2) and at least one other chronic condition, and enrolled in a primary care or diabetes education program. Participants will be randomly assigned to the intervention (ACHRU-CPP) or control arm (1:1 ratio). The intervention arm consists of home/telephone visits, monthly group wellness sessions, multidisciplinary case conferences, and system navigation support. It will be delivered by registered nurses and registered dietitians/nutritionists from participating primary care or diabetes education programs and program coordinators from community-based organizations. The control arm consists of usual care provided by the primary care setting or diabetes education program. The primary outcome is the change from baseline to 6 months in mental functioning. Secondary outcomes will include, for example, the change from baseline to 6 months in physical functioning, diabetes self-management, depressive symptoms, and cost of use of healthcare services. Analysis of covariance (ANCOVA) models will be used to analyze all outcomes, with intention-to-treat analysis using multiple imputation to address missing data. Descriptive and qualitative data from older adults, caregivers and intervention teams will be used to examine intervention implementation, site-specific adaptations, and scalability potential.DiscussionAn interprofessional intervention supporting self-management may be effective in improving health outcomes and client/caregiver experience and reducing service use and costs in this complex population. This pragmatic trial includes a scalability assessment which considers a range of effectiveness and implementation criteria to inform the future scale-up of the ACHRU-CPP.Trial registrationClinical Trials.gov Identifier NCT03664583. Registration date: September 10, 2018.

Uncertainties of GRACE‐Based Terrestrial Water Storage Anomalies for Arbitrary Averaging Regions

AbstractThe application of terrestrial water storage (TWS) data observed with GRACE and GRACE‐FO often requires realistic uncertainties. For gridded TWS data, this requires the knowledge of the covariances, which can be derived from the formal, i.e., formally estimated in the parameter estimation, variance‐covariance matrix provided together with the Stokes coefficients. However, the propagation of monthly variance‐covariance matrices to TWS data is computationally expensive, so we apply a spatial covariance model for TWS data. The covariance model provides non‐homogeneous (location depending), non‐stationary (time depending), and anisotropic (orientation depending) covariances between any two given points. Further, the model accommodates wave‐like behavior of East‐West‐directed covariances, which residuals of GRACE striping errors can cause. The main application of such spatial covariances is the estimation of uncertainties for mean TWS time series for arbitrary regions such as river basins. Alternatively, regional uncertainties can be derived from the above mentioned formal variance‐covariance matrices of the Stokes coefficients. This study compares modeled basin uncertainties for GFZ RL06 and ITSG‐Grace2018 TWS data with the formal basin uncertainties from the ITSG‐Grace 2018 solution. The modeled and formal uncertainties fit both in the spatial and temporal domain. We further evaluate the modeled uncertainties by comparison to empirical uncertainties over arid regions. Here, again the appropriateness of the modeled uncertainties is shown. The results, namely the TWS uncertainties for global river basins, are available via the GravIS portal. Further, we provide a Python toolbox, which allows computing uncertainties and covariance matrices.

Heteroskedastic PCA: Algorithm, optimality, and applications

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis on singular subspaces, which can be of independent interest. The effectiveness of the proposed algorithm is demonstrated in a suite of problems in high-dimensional statistics, including singular value decomposition (SVD) under heteroskedastic noise, Poisson PCA, and SVD for heteroskedastic and incomplete data.

Graph-based prior and forward models for inverse problems on manifolds with boundaries

This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. We also investigate the graph-based approximation of forward models from PDE parameters to observed quantities. In the construction of graph-based prior and forward models, we leverage the ghost point diffusion map algorithm to approximate second-order elliptic operators with classical boundary conditions. Numerical results validate our graph-based approach and demonstrate the need to design prior covariance models that account for boundary conditions.

Analytical process noise covariance modeling for absolute and relative orbits

This paper develops new analytical process noise covariance models for both absolute and relative spacecraft states. Process noise is always present when propagating a spacecraft state due to dynamics modeling deficiencies. Accurately modeling this noise is essential for sequential orbit determination and improves satellite conjunction analysis. A common approach called state noise compensation models process noise as zero-mean Gaussian white noise accelerations. The resulting process noise covariance can be evaluated numerically, which is computationally intensive, or through a widely used analytical model that is restricted to an absolute Cartesian state and small propagation intervals. Moreover, mathematically rigorous, analytical process noise covariance models for relative spacecraft states are not currently available. To address these limitations of the state of the art, new analytical process noise covariance models are developed for state noise compensation for both Cartesian and orbital element absolute state representations by leveraging spacecraft relative dynamics models. Two frameworks are then presented for modeling the process noise covariance of relative spacecraft states by assuming either small or large interspacecraft separation. The presented techniques are validated through numerical simulations.

Microbial mediators of plant community response to long-term N and P fertilization: Evidence of a role of plant responsiveness to mycorrhizal fungi.

Climate changes and anthropogenic nutrient enrichment widely threaten plant diversity and ecosystem functions. Understanding the mechanisms governing plant species turnover across nutrient gradients is crucial to developing successful management and restoration strategies. We tested whether and how soil microbes, particularly arbuscular mycorrhizal fungi (AMF), could mediate plant community response to a 15years long-term N (0, 4, 8, and 16g N m-2 year-1 ) and P (0 and 8g N m-2 year-1 ) enrichment in a grassland system. We found N and P enrichment resulted in plant community diversity decrease and composition change, in which perennial C4 graminoids were dramatically reduced while annuals and perennial forbs increased. Metabarcoding analysis of soil fungal community showed that N and P changed fungal diversity and composition, of which only a cluster of AMF identified by the co-occurrence networks analysis was highly sensitive to P treatments and was negatively correlated with shifts in percentage cover of perennial C4 graminoids. Moreover, by estimating the mycorrhizal responsiveness (MR) of 41 plant species in the field experiment from 264 independent tests, we found that the community weighted mean MR of the plant community was substantially reduced with nutrient enrichment and was positively correlated with C4 graminoids percentage cover. Both analyses of covariance and structural equation modeling indicated that the shift in MR rather than AMF composition change was the primary predictor of the decline in perennial C4 graminoids, suggesting that the energy cost invested by C4 plants on those sensitive AMF might drive the inferior competitive abilities compared with other groups. Our results suggest that shifts in the competitive ability of mycorrhizal responsive plants can drive plant community change to anthropogenic eutrophication, suggesting a functional benefit of mycorrhizal mutualism in ecological restoration following climatic or anthropogenic degradation of soil communities.

Do curious students learn more science in an immersive virtual reality environment? Exploring the impact of advance organizers and epistemic curiosity

Past studies have found mixed results of the impact of immersive virtual reality (IVR) environments on students' learning. In this study, we examined the effect of using concept maps, a kind of advance organizer, on students' learning of science via IVR. In this exploratory and immersive learning environment, we also explored the roles played by learners' epistemic curiosity and other affective factors. Seventy-four sixth-grade students participated in this research and were randomly assigned to the advance organizer group (AO; experimental group) and the non-advance organizer group (NAO; control group). Data collection included survey questionnaires and a science test for assessing students' understanding of plants. We examined the structural relationships among students’ curiosity and affective factors (including presence, control and active learning, positive emotional engagement, and negative emotional engagement), and compared the learning outcomes of the experimental and control groups. We used analysis of covariance (ANCOVA) and partial least squares-structural equation modeling (PLS-SEM) for the data analysis. The results showed that students in the AO group had significantly higher scores for science concepts than those in the NAO group. In both groups, the interest-type curiosity and control and active learning positively predicted emotional engagement. Moreover, in the AO group, positive emotional engagement positively predicted the scientific knowledge of plant concepts. Implications for future research and instructional design are suggested in the study.

The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running

Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert spaces, and graph based models. This article describes how the stochastic partial differential equation approach to generalising Matérn covariance models via Hilbert space projections connects with several of these approaches, with each connection being useful in different situations. In addition to an overview of the main ideas, some important extensions, theory, applications, and other recent developments are discussed. The methods include both Markovian and non-Markovian models, non-Gaussian random fields, non-stationary fields and space–time fields on arbitrary manifolds, and practical computational considerations.

Common UGT1A9 polymorphisms do not have a clinically meaningful impact on the apparent oral clearance of dapagliflozin in type 2 diabetes mellitus.

Dapagliflozin is an inhibitor of human renal sodium‐glucose cotransporter 2 (SGLT2), first approved for the treatment of type 2 diabetes mellitus (T2DM). Dapagliflozin is primarily metabolized by uridine diphosphate glucuronosyltransferase 1A9 (UGT1A9). The effect of UGT1A9 polymorphisms on dapagliflozin apparent oral clearance (CL/F) was studied with dapagliflozin population pharmacokinetic data and UGT1A9 genotype data (I.399C>T, rs2011404, rs6759892, rs7577677, rs4148323, UGT1A9*2 and UGT1A9*3) from a Phase 2 study conducted in subjects with T2DM (n = 187). An analysis of covariance (ANCOVA) model accounting for known covariates influencing dapagliflozin CL/F was applied to these data to quantify the impact of each UGT1A9 polymorphism relative to the wildtype UGT1A9 genotype. The analysis showed that the geometric mean ratios of dapagliflozin CL/F for all of the UGT1A9 polymorphisms studied were within the range of wildtype UGT1A9 CL/F values. Consequently, the polymorphisms of UGT1A9 studied had no clinically meaningful impact on the CL/F of dapagliflozin.

Metabolomics Signatures and Subsequent Maternal Health among Mothers with a Congenital Heart Defect-Affected Pregnancy.

Congenital heart defects (CHDs) are the most prevalent and serious of all birth defects in the United States. However, little is known about the impact of CHD-affected pregnancies on subsequent maternal health. Thus, there is a need to characterize the metabolic alterations associated with CHD-affected pregnancies. Fifty-six plasma samples were identified from post-partum women who participated in the National Birth Defects Prevention Study between 1997 and 2011 and had (1) unaffected control offspring (n = 18), (2) offspring with tetralogy of Fallot (ToF, n = 22), or (3) hypoplastic left heart syndrome (HLHS, n = 16) in this pilot study. Absolute concentrations of 408 metabolites using the AbsoluteIDQ® p400 HR Kit (Biocrates) were evaluated among case and control mothers. Twenty-six samples were randomly selected from above as technical repeats. Analysis of covariance (ANCOVA) and logistic regression models were used to identify significant metabolites after controlling for the maternal age at delivery and body mass index. The receiver operating characteristic (ROC) curve and area-under-the-curve (AUC) are reported to evaluate the performance of significant metabolites. Overall, there were nine significant metabolites (p < 0.05) identified in HLHS case mothers and 30 significant metabolites in ToF case mothers. Statistically significant metabolites were further evaluated using ROC curve analyses with PC (34:1), two sphingolipids SM (31:1), SM (42:2), and PC-O (40:4) elevated in HLHS cases; while LPC (18:2), two triglycerides: TG (44:1), TG (46:2), and LPC (20:3) decreased in ToF; and cholesterol esters CE (22:6) were elevated among ToF case mothers. The metabolites identified in the study may have profound structural and functional implications involved in cellular signaling and suggest the need for postpartum dietary supplementation among women who gave birth to CHD offspring.

Unifying compactly supported and Matérn covariance functions in spatial statistics

The Matérn family of covariance functions has played a central role in spatial statistics for decades, being a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. This paper proposes a family of spatial covariance functions, which stems from a reparameterization of the generalized Wendland family. As for the Matérn case, the proposed family allows for a continuous parameterization of the smoothness of the underlying Gaussian random field, being additionally compactly supported.More importantly, we show that the proposed covariance family generalizes the Matérn model which is attained as a special limit case. This implies that the (reparametrized) Generalized Wendland model is more flexible than the Matérn model with an extra-parameter that allows for switching from compactly to globally supported covariance functions.Our numerical experiments elucidate the speed of convergence of the proposed model to the Matérn model. We also inspect the asymptotic distribution of the maximum likelihood method when estimating the parameters of the proposed covariance models under both increasing and fixed domain asymptotics. The effectiveness of our proposal is illustrated by analyzing a georeferenced dataset of mean temperatures over a region of French, and performing a re-analysis of a large spatial point referenced dataset of yearly total precipitation anomalies.

Multivariate Generalized Linear Models for Twin and Family Data.

Multivariate twin and family studies are one of the most important tools to assess diseases inheritance as well as to study their genetic and environment interrelationship. The multivariate analysis of twin and family data is in general based on structural equation modelling or linear mixed models that essentially decomposes sources of covariation as originally suggested by Fisher. In this paper, we propose a flexible and unified statistical modelling framework for analysing multivariate Gaussian and non-Gaussian twin and family data. The non-normality is taken into account by actually modelling the mean and variance relationship, while the covariance structure is modelled by means of a linear covariance model including the option to model the dispersion components as functions of known covariates in a regression model fashion. The marginal specification of our models allows us to extend classic models and biometric indices such as the bivariate heritability, genetic, environmental and phenotypic correlations to non-Gaussian data. We illustrate the proposed models through simulation studies and six data analyses and provide computational implementation in R through the package mglm4twin.

The impact of partial-oral endocarditis treatment on anxiety and depression in the POET trial

BackgroundThe Partial-Oral versus Intravenous Antibiotic Treatment of Endocarditis Trial (POET) found that partial-oral outpatient treatment was non-inferior to conventional in-hospital intravenous treatment in patients with left-sided infective endocarditis. We examined the impact of treatment strategy on levels of anxiety and depression. MethodsPatients completed the Hospital Anxiety and Depression Scale (HADS) at randomization, at antibiotic completion, and after month 3 and month 6. Changes in anxiety and depression (each subdimension 0–21, high scores indicating worse) were calculated using a repeated measure analysis of covariance model with primary assessment after 6 months. Change in score of 1.7 represented a minimal clinical important difference (MCID). ResultsAmong the 400 patients enrolled in the POET trial, 263 (66%) completed HADS at randomization with reassessment rates of 86–87% at the three subsequent timepoints. Patients in the partial-oral group and the intravenous group had similar improvements after 6 months in levels of anxiety (−1.8 versus −1.6, P = 0.62) and depression (−2.1 versus −1.9, P = 0.63), although patients in the partial-oral group had numerically lower levels of anxiety and depression throughout. An improvement in MCID scores after 6 months was reported by 47% versus 45% (p = 0.80) patients for anxiety and by 51% versus 54% (p = 0.70) for depression. ConclusionPatients with endocarditis receiving partial-oral outpatient treatment reported similar significant improvements in anxiety and depression at 6 months, as compared to conventionally treated, but numerically lower levels throughout. These findings support the usefulness of partial-oral treatment.

A comparison of minimum variance and maximum Sharpe ratio portfolios for mainstream investors

PurposeMotivated by the recent theoretical rehabilitation of mean-variance analysis, the authors revisit the question of whether minimum variance (MinVar) or maximum Sharpe ratio (MaxSR) investment weights are preferable in practical portfolio formation.Design/methodology/approachThe authors answer this question with a focus on mainstream investors which can be modeled by a preference for simple portfolio optimization techniques, a tendency to cling to past asset characteristics and a strong interest in index products. Specifically, in a rolling-window approach, the study compares the out-of-sample performance of MinVar and MaxSR portfolios in two asset universes covering multiple asset classes (via investable indices and their subindices) and for two popular input estimation methods (full covariance and single-index model).FindingsThe authors find that, regardless of the setting, there is no statistically significant difference between MinVar and MaxSR portfolio performance. Thus, the choice of approach does not matter for mainstream investors. In addition, the analysis reveals that, contrary to previous research, using a single-index model does not necessarily improve out-of-sample Sharpe ratios.Originality/valueThe study is the first to provide an in-depth comparison of MinVar and MaxSR returns which considers (1) multiple asset classes, (2) a single-index model and (3) state-of-the-art bootstrap performance tests.

An Iterative Lq-norm Based Optimization Algorithm for Generalized SPICE

A novel approach of the direction of arrival (DOA) estimation is proposed to improve the sparse iterative covariance-based estimator (SPICE) for the formulation, which chooses different norm constraints of signal and noise in the data covariance model. For a given norm, the problem of DOA estimation is solved by differentiating the objective function with respect to signal and noise parameters separately, without considering some model constraints. The iterative formulas of signal and noise components are derived for both single-snapshot and multiple-snapshot cases. Inspired by the derivation of the approach, a weighted version of generalized SPICE (WEQ-SPICE), is also considered from the gradient approach for the same estimation problem. The performances of the new optimization algorithm and the weighted version are both preferable to the generalized SPICE method. Especially in the case of the low signal-to-noise (SNR) ratio, the weighted version can effectively find the correct support of signals. The results of Monte Carlo simulations show the efficiency and advantages.

A generalized information criterion for high-dimensional PCA rank selection

Principal component analysis (PCA) is a commonly used statistical tool for dimension reduction. An important issue in PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. Among information-based criteria, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are the two most common ones. Both use the number of free parameters for assessing model complexity, which requires the validity of the simple spiked covariance model. As a result, AIC and BIC may suffer from the problem of model misspecification when the tail eigenvalues do not follow the simple spiked model assumption. To alleviate this difficulty, we adopt the idea of the generalized information criterion (GIC) to propose a model complexity measure for PCA rank selection. The proposed model complexity takes into account the sizes of eigenvalues and, hence, is more robust to model misspecification. Asymptotic properties of our GIC are established under the high-dimensional setting, where \(n\rightarrow \infty \) and \(p/n\rightarrow c >0\). Our asymptotic results show that GIC is better than AIC in excluding noise eigenvalues, and is more sensitive than BIC in detecting signal eigenvalues. Numerical studies and a real data example are presented.

Bias for Treatment Effect by Measurement Error in Pretest in ANCOVA Analysis.

This paper investigated consequences of measurement error in the pretest on the estimate of the treatment effect in a pretest-posttest design with the analysis of covariance (ANCOVA) model, focusing on both the direction and magnitude of its bias. Some prior studies have examined the magnitude of the bias due to measurement error and suggested ways to correct it. However, none of them clarified how the direction of bias is affected by measurement error. This study analytically derived a formula for the asymptotic bias for the treatment effect. The derived formula is a function of the reliability of the pretest, the standardized population group mean difference for the pretest, and the correlation between pretest and posttest true scores. It revealed a concerning consequence of ignoring measurement errors in pretest scores: treatment effects could be overestimated or underestimated, and positive treatment effects can be estimated as negative effects in certain conditions. A simulation study was also conducted to verify the derived bias formula.

Swarm Intelligence-based Hierarchical Clustering for Identification of ncRNA using Covariance Search Model

Covariance Model (CM) has been quite effective in finding potential members of existing families of non-coding Ribonucleic Acid (ncRNA) identification and has provided ex-cellent accuracy in genome sequence database. However, it has significant drawbacks with family-specific search. An existing Hierarchical Agglomerative Clustering (HAC) technique merged overlapping sequences which is known as combined CM (CCM). However, the structural information will be discarded, and the sequence features of each family will be significantly diluted as the number of original structures increases. Additionally, it can only find members of the existing families and is not useful in finding potential members of novel ncRNA families. Furthermore, it is also important to construct generic sequence models which can be used to recognize new potential members of novel ncRNA families and define unknown ncRNA sequence as the potential members for known families. To achieve these objectives, this study proposes to implement Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) to ensure the CCMs have the best quality for every level of dendrogram hierarchy. This study will also apply distance matrix as the criteria to measure the compatibility between two CMs. The proposed techniques will be using five gene families with fifty sequences from each family from Rfam database which will be divided into training and testing dataset to test CMs combination method. The proposed techniques will be compared to the existing HAC in terms of identification accuracy, sum of bit-scores, and processing time, where each of these performance measurements will be statistically validated.

Kronecker-structured covariance models for multiway data

Many applications produce multiway data of exceedingly high dimension. Modeling such multi-way data is important in multichannel signal and video processing where sensors produce multi-indexed data, e.g. over spatial, frequency, and temporal dimensions. We will address the challenges of covariance representation of multiway data and review some of the progress in statistical modeling of multiway covariance over the past two decades, focusing on tensor-valued covariance models and their inference. We will illustrate through a space weather application: predicting the evolution of solar active regions over time.