Nonlinear Effects Models Research Articles

Forecasting realized volatility with spillover effects: Perspectives from graph neural networks

We present a novel nonparametric methodology for modeling and forecasting multivariate realized volatilities using customized graph neural networks to incorporate spillover effects across stocks. The proposed model offers the benefits of incorporating spillover effects from multi-hop neighbors, capturing nonlinear relationships, and flexible training with different loss functions. The empirical findings suggest that incorporating spillover effects from multi-hop neighbors alone does not yield a clear advantage in terms of predictive accuracy. Furthermore, modeling nonlinear spillover effects enhances the forecasting accuracy of realized volatilities, particularly for short-term horizons of up to one week. More importantly, our results consistently indicate that training with the quasi-likelihood loss leads to substantial improvements in model performance compared to the commonly used mean squared error, primarily due to its superior handling of heteroskedasticity. A comprehensive series of empirical evaluations in alternative settings confirm the robustness of our results.

History of Incarceration and Dental Care Use Among Older Adults in the United States

IntroductionDental care is a critical component of healthy aging; however, emerging evidence suggests that having been previously incarcerated is a risk factor for not using dental care services. This study investigates the relationship between prior incarceration and dental care among older adults and assesses whether wealth and dental insurance explain this relationship. MethodsData are from the Health and Retirement Study, a nationally representative sample of community-dwelling older adults in the United States, collected in 2012 and 2014. Multivariable logistic regression is used to assess the relationship between a history of incarceration and dental care. Mediation analyses were conducted using the Karlson-Holm-Breen method of indirect effects in non-linear models. Statistical analyses were conducted from February to April 2024. ResultsAdjusting for potential confounding variables, a respondent's prior incarceration is associated with a 25% lower odds of dental care use (adjusted odds ratio [aOR] = .748, 95% CI = .624, .896). The relationship between incarceration and dental care use is fully mediated—over 90% is explained by—wealth and having dental care insurance. Prior incarceration decreased the likelihood of dental care only among non-Hispanic White respondents. ConclusionsThe findings offer new evidence that prior incarceration is a risk factor for lacking the ability to utilize dental care among older adults and suggest that broader consequences of incarceration for wealth accumulation and access to dental insurance underpin this relationship. These results suggest the urgent need to expand access to affordable dental care services for older adults with a history of incarceration.

Modeling non-linear effects with neural networks in Relational Event Models

Dynamic networks offer an insight of how relational systems evolve. However, modeling these networks efficiently remains a challenge, primarily due to computational constraints, especially as the number of observed events grows. This paper addresses this issue by introducing the Deep Relational Event Additive Model (DREAM) as a solution to the computational challenges presented by modeling non-linear effects in Relational Event Models (REMs). DREAM relies on Neural Additive Models to model non-linear effects, allowing each effect to be captured by an independent neural network. By strategically trading computational complexity for improved memory management and leveraging the computational capabilities of graphic processor units (GPUs), DREAM efficiently captures complex non-linear relationships within data. This approach demonstrates the capability of DREAM in modeling dynamic networks and scaling to larger networks. Comparisons with traditional REM approaches showcase DREAM superior computational efficiency. The model potential is further demonstrated by an examination of the patent citation network, which contains nearly 8 million nodes and 100 million events.

The fractional soliton solutions of dynamical system arising in plasma physics: The comparative analysis

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions.

Abstract 17485: Risk of Heart Failure Hospitalizations With Exposure to Colder Temperature and Regional Variations Among Older Adults in the United States

Introduction: Extreme cold was associated with excess heart failure (HF) deaths in ecological studies. The relationship between colder temperatures and HF hospitalizations is not well understood. Hypothesis: Lower minimum temperatures (T min ) increase the risk of HF hospitalization among older adults and the impact varies by climate regions. Methods: A time-stratified case-crossover study among adults aged ≥66 hospitalized for HF was conducted using a 20% sample of Medicare data (2008-2019, Nov-Feb). Daily T min from the Parameter-elevation Relationships on Independent Slopes model were linked to Medicare data by zip code of residence. We used bidirectional sampling to select up to 5 controls. We used conditional logistic regression with a restricted cubic spline to model non-linear effects between T min and HF hospitalization in all patients and regional subgroups. Results: Among 529,879 cases (mean age 79, 61% female, 86% white), the risk of HF hospitalization peaked at 4 °F (OR 1.29 [CI 1.28-1.30]) and plateaued over colder T min relative to the median T min (31.5°F). Above 31.5 °F, the risk was reduced by 18% for every 10 °F (Figure 1). This inverse relationship between T min and HF hospitalizations during the winter were most prominent in colder regions (Figure 2). Conclusions: T min ≤4 °F increased the risk of HF hospitalizations by upwards of 29% compared to the national median T min . The plateau at more extreme T min may be due to avoidance of outdoor exposure. A similar behavioral response may occur in warmer regions, whereas some degree of cold exposure is inevitable in colder regions. HF patients should be aware of the risks from exposure to colder temperatures during winter months.

Fast angles-only relative navigation using polynomial dynamics

A fast and efficient method for initial relative orbit determination from bearing-angle measurements is introduced. The range ambiguity problem for angles-only relative navigation is addressed by modeling nonlinear effects with a novel second-order mapping from relative orbit elements (ROE) to relative position coordinates. This model is used to form a system of polynomial constraint equations linking the line-of-sight measurements to the ROE. An efficient method for solving this system is developed around the insight that the ROE scale with the ratio of the inter-spacecraft separation to the orbit radius and are therefore small for most applications of interest. The method uses a truncated expansion of the quadratic formula to recursively eliminate unknowns, reduce the dimension of the system, and ultimately acquire an approximate solution. Strategies for improving robustness, efficiency, and accuracy are developed and the method is applied to general second-order systems as well as to a broad range of intial relative orbit determination scenarios. Modifications to the constraint equations and a solution algorithm are introduced to address the challenge of bias in the bearing-angle measurements.

Predicting motions of deepwater platform based on the inverse reconstruction of environmental loads

In hybrid model testing technique, model tests are primarily used to verify numerical models which is used to predict the responses of full-depth systems. However, hybrid model testing method based on potential flow theory highly rely on the accuracy of mathematical model, facing challenges in accurately predicting full-depth responses with viscous effects, such as flow-induced motion. To solve the problem, a method for predicting motions of full-depth system is proposed based on the inverse reconstruction of the environmental loads from the truncated model test, considering viscous and nonlinear effects on platform. To validate the method, a series of model tests were conducted for a semi-submersible platform in head seas using both truncated and full-depth mooring systems to validate the method. The environmental loads could be extracted accurately via the inverse reconstruction method under different environmental conditions, including 100-year-return-period wave-only, current-only, coupled wave, wind, and current conditions. The results of time history, statistics, and power distribution show that the proposed method has better performance than conventional method of hybrid model test in situations where viscous effects are obvious.

How well can VMEC predict the initial saturation of external kink modes in near circular tokamaks and l = 2 stellarators?

The equilibrium code, VMEC, is used to study external kinks in low β tokamaks and l = 2 stellarators. The applicability of the code when modeling nonlinear MHD effects is explored in an attempt to understand and predict how the initial saturation of the MHD mode depends on the external rotational transform. It is shown that helicity preserving, free boundary VMEC computations do not converge to a single perturbed solution with increasing spectral resolution. Additional constraints are applied to narrow down the numerical resolution parameters appropriate for physical scans. The dependence of the modeled (4, 1) kink mode on the external rotational transform and field periodicity is then studied. While saturated states can be identified which decrease in amplitude with increasing external rotational transform, alternative bifurcated states are found, which contradict this trend. As a result, it was not possible to use VMEC alone to identify the physical dependency of the nonlinear mode amplitude on the magnetic geometry. Nevertheless, the accuracy of VMEC solutions is demonstrated by showing that the expected toroidal mode coupling is captured in the magnetic energy spectrum for stellarator cases. Comparing with the initial value code, JOREK, the predicted redistribution of poloidal magnetic energy from the vacuum to plasma region in VMEC is shown to be physical. This work is a first step toward using VMEC to study MHD modes in stellarator geometry.

Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

Introduction to the special issue: Nonlinear effects and dynamics in close relationships

Relationship processes often involve fluctuating, variable, or tumultuous dynamics. Yet, close relationship models have traditionally focused on linear processes. The purpose of this Journal of Social and Personal Relationships special issue is to provide examples of how modeling nonlinear effects and dynamics can: (I) test nonlinear theoretical assumptions, (II) reconcile inconsistencies and reveal novel effects, (III) detect dynamic shifts in core relationship constructs, and (IV) capture temporal and spatial synchrony between partners within dyads. By showcasing a variety of nonlinear applications, we hope to encourage close relationship scholars to utilize similar nonlinear methods in order to advance relationship science by discovering common and important, but currently under-examined, relationship processes.

DeepNull models non-linear covariate effects to improve phenotypic prediction and association power

Genome-wide association studies (GWASs) examine the association between genotype and phenotype while adjusting for a set of covariates. Although the covariates may have non-linear or interactive effects, due to the challenge of specifying the model, GWAS often neglect such terms. Here we introduce DeepNull, a method that identifies and adjusts for non-linear and interactive covariate effects using a deep neural network. In analyses of simulated and real data, we demonstrate that DeepNull maintains tight control of the type I error while increasing statistical power by up to 20% in the presence of non-linear and interactive effects. Moreover, in the absence of such effects, DeepNull incurs no loss of power. When applied to 10 phenotypes from the UK Biobank (n = 370K), DeepNull discovered more hits (+6%) and loci (+7%), on average, than conventional association analyses, many of which are biologically plausible or have previously been reported. Finally, DeepNull improves upon linear modeling for phenotypic prediction (+23% on average).

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument (DESI) and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed in Ref. [1] is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory~(LPT) up to third order for dark matter in real space and compare it with $N$-body simulations. We find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

Deep neural networks for genomic prediction do not estimate marker effects.

Genomic prediction is a promising technology for advancing both plant and animal breeding, with many different prediction models evaluated in the literature. It has been suggested that the ability of powerful nonlinear models, such as deep neural networks, to capture complex epistatic effects between markers offers advantages for genomic prediction. However, these methods tend not to outperform classical linear methods, leaving it an open question why this capacity to model nonlinear effects does not seem to result in better predictive capability. In this work, we propose the theory that, because of a previously described principle called shortcut learning, deep neural networks tend to base their predictions on overall genetic relatedness rather than on the effects of particular markers such as epistatic effects. Using several datasets of crop plants [lentil (Lens culinaris Medik.), wheat (Triticum aestivum L.), and Brassica carinata A. Braun], we demonstrate the network's indifference to the values of the markers by showing that the same network, provided with only the locations of matches between markers for two individuals, is able to perform prediction to the same level of accuracy.

Partially linear single-index generalized mean residual life models.

Mean residual life (MRL) function defines the remaining life expectancy of a subject who has survived to a time point and is an important alternative to the hazard function for characterizing the distribution of a time-to-event variable. Existing MRL models primarily focus on studying the association between risk factors and disease risks using linear model specifications in multiplicative or additive scale. When risk factors have complex correlation structures, nonlinear effects, or interactions, the prefixed linearity assumption may be insufficient to capture the relationship. Single-index modeling framework offers flexibility in reducing dimensionality and modeling nonlinear effects. In this article, we propose a class of partially linear single-index generalized MRL models, the regression component of which consists of both a semiparametric single-index part and a linear regression part. Regression spline technique is employed to approximate the nonparametric single-index function, and parameters are estimated using an iterative algorithm. Double-robust estimators are also proposed to protect against the misspecification of censoring distribution or MRL models. A further contribution of this article is a nonparametric test proposed to formally evaluate the linearity of the single-index function. Asymptotic properties of the estimators are established, and the finite-sample performance is evaluated through extensive numerical simulations. The proposed models and inference approaches are demonstrated by a New York University Langone Health (NYULH) COVID-19 dataset.

Quadratic relations of BMI with depression and brain volume in children: Analysis of data from the ABCD study

BackgroundWeight-related health conditions and depression peak during adolescence and show relations with brain structure. Understanding how these conditions relate to each other prior to adolescence may guide research on the co-development of unhealthy weight conditions (both underweight and overweight) and depression, with a potential brain-based link. This study examines the cross-sectional relations between body mass index (BMI), depressive symptoms, and brain volume (total and regional) to determine whether BMI has a linear or quadratic relation with depressive symptoms and brain volume and how depressive symptoms and brain volume are related. MethodsCross-sectional study using structural magnetic resonance imaging, height and weight to calculate BMI z-scores, and Child Behavior Checklist withdrawn depression scores. Data were from the Adolescent Brain Cognitive Development Study, collected at 21 sites across the United States from 11,875 9- and 10-year-old children recruited as a national sample. Mixed models were used to examine the linear and quadratic effects of BMI z-score on both brain volume (total and regional) and withdrawn depression scores, as well as the relations between brain volume and depression scores. Intracranial volume, age, sex, race, site, and family were included in the models as covariates. ResultsOverall, BMI z-scores showed a quadratic relation with brain volumes and depressive symptoms. When including intracranial volume as a covariate, regional volumes investigated did not follow the same global pattern of effects except for right hippocampus and left lateral orbitofrontal cortex. Total brain volume was negatively related to depressive symptoms. ConclusionsLinks between depressive symptoms and low or high weight could improve our understanding of brain structural differences in depression. These findings also emphasize the importance of including the full spectrum of BMI from underweight to overweight and testing for nonlinear effects in models.

Random Survival Forests Analysis of Intraoperative Complications as Predictors of Descemet Stripping Automated Endothelial Keratoplasty Graft Failure in the Cornea Preservation Time Study

A new analytic method can evaluate factors of interest associated with graft failure after Descemet stripping automated endothelial keratoplasty (DSAEK) or more generally in any ophthalmic surgical setting with a time-to-event outcome. To reanalyze types of intraoperative complications associated with DSAEK graft failure in the Cornea Preservation Time Study using random survival forests. This cohort study, initially conceived in April 2019, used a prediction model to conduct a post hoc secondary analysis of data collected in a multicenter, double-masked, randomized clinical trial. Forty US clinical sites with 70 surgeons participated, with donor corneas provided by 23 US eye banks. The study included 1090 participants, representing 1330 eyes, undergoing DSAEK for Fuchs dystrophy (1255 eyes [94.4%]) or pseudophakic or aphakic corneal edema (75 eyes [5.6%]). Enrollment occurred between April 16, 2012, and February 20, 2014, and follow-up ended June 5, 2017. Statistical analysis was performed from July 10, 2019, to May 29, 2020. Descemet stripping automated endothelial keratoplasty with random assignment of a donor cornea with preservation time of 7 days or less or 8 to 14 days. Ranked variable importance for intraoperative complications among 50 donor, recipient, and eye bank variables and restricted mean survival time through 47 months (1434 days) after DSAEK were examined. Random survival forests, a nonparametric method (with less restrictive model assumptions) that is far more flexible in its ability to model nonlinear effects and interactions, was used to analyze the data. This study included 1090 participants (663 women [60.8%]; median age, 70 years [range, 42-90 years]), representing 1330 eyes. Random survival forests ranked a DSAEK intraoperative complication as the third most predictive factor of graft failure, after surgeon and eye bank, in the final model with 5 predictors. In the first 47 months after DSAEK, the estimated mean difference in restricted mean survival time for grafts that experienced a DSAEK intraoperative complication vs those that did not was -227 days (99% CI, -352 to -70 days) based on the final RSF model. These findings, while post hoc, support the hypothesis that random survival forests allow for an improved analytic approach for identifying factors predictive of graft failure and for obtaining adjusted graft survival estimates. Random survival forests offer the opportunity to guide the development of future population-based cohort ophthalmic surgical studies, establishing definitive factors for procedural success.

Approximate Bayesian inference for multivariate point pattern analysis in disease mapping.

We present a novel approach for analysing multivariate case-control georeferenced data in a Bayesian disease mapping context using stochastic partial differential equations (SPDEs) and the integrated nested Laplace approximation (INLA) for model fitting. In particular, we propose smooth terms based on SPDE models to estimate the underlying spatial variation as well as risk associated to pollution sources. Log-Gaussian Cox processes are used to estimate the intensity of the cases and controls, to account for risk factors and include a term to measure spatial residual variation. Each intensity is modelled on a baseline spatial effect (estimated from both controls and cases), a disease-specific spatial term and the effects of some covariates. By fitting these models, the residual spatial terms can be easily compared to detect high-risk areas not explained by the covariates. Three different types of effects to model exposure to pollution sources are considered on the distance to the source: a fixed effect, a smooth term to model non-linear effects by means of a discrete random walk of order one and a Gaussian process in one dimension with a Matérn covariance function. Spatial terms are modelled using a Gaussian process in two dimensions with a Matérn covariance function and are approximated using an approach based on solving an SPDE through INLA. Finally, this new framework is applied to a dataset of three different types of cancer and a set of controls from Alcalá de Henares (Madrid, Spain). Covariates available include the distance to several polluting industries and socioeconomic indicators. Our findings point to a possible risk increase due to the proximity to some of these industries.

Three-dimensional nonlinear finite element model to estimate backflow during flow-controlled infusions into the brain.

Convection-enhanced delivery is a technique to bypass the blood-brain barrier and deliver therapeutic drugs into the brain tissue. However, animal investigations and preliminary clinical trials have reported reduced efficacy to transport the infused drug in specific zones, attributed mainly to backflow, in which an annular gap is formed outside the catheter and the fluid preferentially flows toward the surface of the brain rather than through the tissue in front of the cannula tip. In this study, a three-dimensional human brain finite element model of backflow was developed to study the influence of anatomical structures during flow-controlled infusions. Predictions of backflow length were compared under the influence of ventricular pressure and the distance between the cannula and the ventricles. Simulations with zero relative ventricle pressure displayed similar backflow length predictions for larger cannula-ventricle distances. In addition, infusions near the ventricles revealed smaller backflow length and the liquid was observed to escape to the longitudinal fissure and ventricular cavities. Simulations with larger cannula-ventricle distances and nonzero relative ventricular pressure showed an increase of fluid flow through the tissue and away from the ventricles. These results reveal the importance of considering both the subject-specific anatomical details and the nonlinear effects in models focused on analyzing current and potential treatment options associated with convection-enhanced delivery optimization for future clinical trials.

Step Out of Line: Modeling Nonlinear Effects and Dynamics in Close-Relationships Research

Despite widespread acknowledgment that close relationships frequently involve tumultuous and dynamic experiences, most models in relationship psychology focus on linear relationship processes. Modeling nonlinear patterns can, however, be an important way to assess and better understand the complexities inherent in close relationships. In this article, I draw on one of the most widely studied theories in relationship science—attachment theory—to illustrate how modeling nonlinear effects between variables (i.e., curvilinear effects) and nonlinear dynamics across time (i.e., within-person variation and within-dyad flexibility) can reconcile inconsistencies in the literature, reveal unique relationship experiences, and broaden our understanding of complex relationship processes.

Non-linear mixed models in the study of growth of naturalized chickens

ABSTRACT This study was conducted to examine the inclusion of random effects in non-linear models, identify the most suitable models, and describe the growth of naturalized chickens. Live-weight records of 166 birds of the Grauna Dourada, Nordestina, and Teresina ecotypes were estimated. The asymptotic weight (A), integration constant, related to animal initial weight (B), and the maturing rate (k) parameters of the non-linear Gompertz, Logistic, and von Bertalanffy models were estimated and adjusted using the Gauss-Newton method. Residual variance decreased [...]