Hierarchical Nonlinear Model Research Articles

Service product codesign with digital platform operators based on hierarchical interactive optimization

This paper proposes a novel approach to address the evolving landscape of service product design, particularly in collaboration with digital platform operators. By formulating a nonlinear hierarchical interactive optimization model (HIO) based on bilevel programming (BLP), the paper tackles the complexities of joint decision-making between service providers and digital platforms. At the upper level, the model optimizes digital platform selection, product attribute configuration, and pricing to maximize provider profit, while the lower level determines platform participation in codesign to maximize their own profits. Furthermore, a codesign incentive mechanism, encompassing revenue-sharing proportions and platform promotion efforts, is designed to incentivize collaboration.Applied to the tourism industry, the HIO model is solved using a nested genetic algorithm (NGA), allowing for sensitivity analyses on platform contribution and promotion efforts. Results indicate that increased platform participation in codesign may raise configuration complexity and costs for the service agency, potentially impacting profitability. Additionally, higher platform promotion efforts can drive profit growth for both parties, supporting long-term development. Ultimately, the HIO model demonstrates superior performance compared to traditional two-stage method (TSM), underscoring its applicability and effectiveness in addressing codesign challenges between service agencies and digital platforms.

Micromechanical analysis of fiber-reinforced ceramic matrix composites by a geometrically nonlinear hierarchical quadrature element model

The stress fields of fiber-reinforced ceramic matrix composites (CMCs) under longitudinal tension are predicted using a non-linear hierarchical quadrature element method (HQEM) in this work. The HQEM combines the differential quadrature method (DQM) with the hierarchical finite element method (HFEM), which is a typical p-version finite element method (FEM). High-order interpolation functions of the HQEM allow accurate evaluation of stress distribution. Fiber, matrix, and interfaces of the CMCs are modeled as linear elastic materials that may have large displacements. The nonlinear HQEM estimation of CMCs stress distributions are validated by comparing with analytical results obtained using classical BHE shear-lag model. Stress distribution in three characteristic stages in the damage evolution process, namely, interface perfectly bonded, interface debonding, and fiber failure are investigated. It is shown that when fiber failure happens, geometric non-linearity must be considered to avoid excessive stress concentration. Furthermore, the stress distribution within three-dimensional cylindrical CMCs cell is studied, which sheds light on the future exploration of three-dimensional CMCs analyses.

Aortic stenosis rapid progression is associated with premature cardiac damage independently of baseline severity

Abstract Background Aortic stenosis (AS) is one of the major valvular heart diseases in developed countries. Degenerative fibrocalcific AS is a progressive disease of the valve and, ultimately, the myocardium. AS is a potentially fatal disease characterized not only by a narrowing of the aortic orifice but also by gradual cardiac damage (CD) that may extend beyond the left ventricle (LV). However, the presence and extent of extra-aortic cardiac damage did not reflect the baseline hemodynamic severity of AS in retrospective studies. Purpose This study aims to determine the rate of AS progression and its impact on cardiac damage and survival. Methods We retrospectively identified 914 patients (age 76 ± 8 years, 52% female, median follow-up time 6.8 years) with AS who had undergone > 1 echocardiogram. Bayesian hierarchical nonlinear models were used to predict aortic peak velocity as a function of time and estimate individual AS acceleration rates. Then, patients were clustered into rapid (RP) and slow progressors (SP) using machine learning algorithms. Results APV was best modeled by a logistic function of time. 483 patients were clustered as RP (53 %) and 431 as SP (47 %), with acceleration rate coefficients estimated at 0.14 ± 0.02 years-1 and 0.09 ± 0.02 years-1, respectively (p < 0.01). No association between progression rate and clinical variables was found. Compared with SP, RP had significantly higher 5-year incidences of LV damage, combined left atrium and mitral valve damage and combined tricuspid valve damage and pulmonary hypertension (all p ≤ 0.01). No statistically significant differences were seen for right ventricle damage between RP and SP, as the number of events was low. After multivariate adjustment for age, gender, comorbidities and baseline AS severity, RP remained an independent predictor for all extra-aortic cardiac damages except for the RV dysfunction. Importantly, baseline AS severity was not predictive of AS-related CD. RP was associated with higher mortality (HR 1.28, p = 0.02), persisting after adjustment for demographics, comorbidities, AS severity, and time-dependent aortic valve replacement (AVR) (HR = 1.36, p < 0.01). Conclusions RP may impair cardiac adaption to rapidly changing loading conditions, which induces premature cardiac damage that may not be reversible in the late stages of AS, when guideline-triggered interventions are currently delivered.

Modeling the growth of Pacific white shrimp (Litopenaeus vannamei) using the new Bayesian hierarchical approach based on correcting bias caused by incomplete or limited data

The revenue, costs, and profit of an aquaculture farm are based on the weight of animal protein sold. Thus, there is a relationship between the economic and zootechnical indexes to the growth model of animals in a production system. The growth modeling of cultivated organisms can be used as a production management tool, allowing estimates of anticipated size at harvest, waste outputs, as well as nutrient and feed requirements, helping in decision-making in the face of Aquaculture 4.0. It is important to emphasize that recent research has indicated the possible underestimation of parameters in nonlinear growth models due to the characteristic of incomplete or limited data in aquaculture. Therefore, the objective of this research was to model the growth of Pacific white shrimp (Litopenaeus vannamei) in an industrial-scale shrimp farm in northeastern Brazil. Based on the Bayesian methodology for correcting this bias, six nonlinear hierarchical growth models were evaluated in this research (Morgan-Mercer-Flodin, Michaelis–Menten, Weibull, von Bertalanffy, Gompertz, and logistic growth equation) and fitted to real data from a shrimp farm in northeastern Brazil. The model was validated based on the predictive capacity (accuracy) to forecasting shrimp growth at different hierarchical levels. Finally, for one of the main expected results, a sensitivity analysis was performed to compare different treatments according to the new approach. The Weibull growth equation stands out as the best among all those studied (WAIC = 2661.3, LOO-IC = 2705.2). Although it presented a poor fit for the hierarchical population level, good predictions were realized at the pond level and at the production cycle level. The dataset was split into fit and homologation subsets for a model validation analysis which showed an accuracy of 95.76% and 85.71% at the pond and production cycle levels respectively. The proposed method detected subtle differences between production cycles, which would be imperceptible if analyzed using the zootechnical indices usually practiced in shrimp farms. The new approach can contribute to improving products, processes, and decision-making in aquaculture management.

Migration or not? Impact of individual and urban factors on migrant workers' willingness of household registration transfer

PurposeThe purpose of this paper is to explore the factors that influence migrant workers' household registration transfer willingness at both individual and urban levels and to provide empirical evidence on adjusting the household registration system to accommodate economic development and migrant workers' imbalances.Design/methodology/approachThis paper adopts a hierarchical nonlinear model and examines individual and urban influencing factors of migrant workers' household registration transfer willingness, based on the data from China Migrants Dynamic Survey (CMDS) and the Urban Statistical Yearbooks.FindingsThis paper shows that: (1) multi-factors, such as age, education, marital status, household demographics, industry and migrant workers' contract coverage, have significant effects on migrant workers' household registration transfer willingness; (2) The urban public service equalization indicators, such as regional economic, educational resources, medical care and ecological quality, have significant effects on migrant workers' willingness to transfer household registration; (3) The heterogeneity of migrant workers' willingness to transfer household registration is significant in central, eastern and western China.Research limitations/implicationsThe authors provide a fresh perspective on population migration research in China and other countries worldwide based on the pull–push migration theory, which incorporates both individual and macro (urban) factors, enabling a comprehensive examination of the factors influencing household registration transfer willingness. This hierarchical ideology and approach (hierarchical nonlinear model) could be extended to investigate the influencing factors of various other human intentions and behaviors.Originality/valueMicro approaches (individual perspective) have dominated existing studies examining the factors influencing migrant workers' household registration transfer willingness. The authors combine individual and urban perspectives and adopt a more comprehensive hierarchical nonlinear model to extend the empirical evidence and provide theoretical explanations for the above issues.

A bidirectional link between metabolic syndrome and elevation in alanine aminotransferase in elderly female: a longitudinal community study.

Pre-obesity, as a significant risk factor for the progression of metabolic syndrome (MS), has become a prevalent public health threat globally. In this three-year longitudinal study of pre-obese women at baseline, the goal was to clarify the female-specific bidirectional relationship between the risk of MS and blood alanine aminotransferase. In this manuscript, the MS score was determined using the following equation: MS score = 2*waist/height + fasting glucose/5.6 + TG/1.7 + SBP/130-HDL/1.02 for men and 1.28 for women, which is highly related to the risk of MS. With 2,338 participants, a hierarchical nonlinear model with random effects was utilized to analyze the temporal trends of serum characteristics from 2017 to 2019. A bivariate cross-lagged panel model (CLPM) was employed to estimate the structural relations of frequently measured variables at three different time points to determine the directionality of the relationship between the risk of MS and serum characteristics. MassARRAY Analyzer 4 platforms were used to evaluate and genotype candidate SNPs. In this study, the MS score only rose with age in females; it was positively correlated with serum alanine aminotransferase (ALT) in females; the CLPM revealed that the MS score in 2017 predicted ALT in 2018 (β = 0.066, p < 0.001); and ALT in 2018 predicted an MS score in 2019 (β = 0.037, p < 0.050); both relationships were seen in females. Additionally, the MS score in elderly females with NAFLD was related to the rs295 in the lipoprotein lipase (LPL) gene (p = 0.042). Our work showed that there may be female-specific causal correlations between elevated ALT and risk of MS and that the polymorphism rs295 in LPL may serve as a marker for the prognosis of MS. The genetic roles of rs295 in the LPL gene in the onset of MS and the development of ALT in the elderly Chinese Han population are thus provided by this, offering one potential mechanism.

Nonlinear Hierarchical MPC With Application to Aircraft Fuel Thermal Management Systems

A nonlinear hierarchical model predictive control (MPC) framework is proposed and applied to maximize the thermal endurance of aircraft. Effectively controlling the fuel temperatures in a nonlinear multitimescale aircraft fuel thermal management system (FTMS) requires controllers capable of long-term planning and fast update rates. In this article, a two-level hierarchical MPC controller is formulated using successive linearization (SL) that directly accounts for the multitimescale and nonlinear system dynamics to achieve accurate predictive capabilities and computational efficiency. Detailed simulation results show that the proposed hierarchical structure can increase aircraft thermal endurance by at least 21% compared to a centralized approach while significantly reducing the computational cost. The results also show that SL provides a valuable framework for efficiently accounting for nonlinear system dynamics within both levels of the hierarchical MPC formulation.

Consumers’ choice of private label considering reference price and moderating effect

Retailers frequently place private labels (PLs) next to the top-moving sales national brands (NBs) and utilize comparative pricing that is related to the national brands. There is thus always an external reference price between the private labels and the national brands. In this study, two categories of products were selected, and a hierarchical non-linear model used to study the impact of external reference prices on consumers’ choice of private labels. In addition, the effects of package size and average disposable income (ADI) were introduced into the analysis for the relationship between external reference price and consumers’ choice of private label. The findings show an inverted U-shaped curve between consumers’ choice of private labels and the external reference price discrepancy. Consumers in areas with high ADI are more likely to buy private labels. Package size and ADI have different direct and moderating effects on two categories of products. This study contributes to reference dependence theory and category management.

Fault Rate Estimation of Electric Energy Meter Based on WDPOD-NHBM

To solve the problems of the small amount of sample information in the original failure rate data of smart energy meters and the difficulty of mining under typical environmental stress, a smart energy meter failure rate prediction and reliability evaluation model based on double precision combined with nonlinear hierarchical Bayes is proposed. First, the KNN algorithm is used to test the outliers in the original data, and a double-precision outlier detection algorithm is further established to assign the weight to outliers. Then, a nonlinear hierarchical Bayesian model is built based on Weibull distribution, and couples the failure rate data of smart energy meters with various typical environmental stresses. Through multi-dimensional analysis of the data distribution rule, the most prior distribution is selected. Finally, the Markov Chain Monte Carlo method is used to sample and solve the posterior condition distribution of the model parameters. The posterior parameters and confidence interval estimation are obtained, and the reliability of the smart energy meters is calculated as 95%. The experimental results show that the method can accurately predict the trend of the failure rate of smart energy meters over time in a typical environment.

The gender-specific bidirectional relations between chronic diseases and total bilirubin/urea in the elderly population: A 3-year longitudinal study.

Aging is accompanied by changes in physiology over time, which remains the largest risk of chronic diseases. The aim of this study was to explore the gender-specific bidirectional relations between the risk of chronic diseases and serum traits in a 3-year longitudinal study. A hierarchical non-linear model with random effects was used to assess the temporal patterns of anthropometric and serum traits from 2017 to 2019 among 2,338 participants. To assess the directional effect between the risk of chronic diseases and serum traits, a bivariate cross-lagged panel model (CLPM) was used to estimate the structural relations of repeatedly measured variables at three different time points. Candidate SNPs were analyzed and genotyped in MassARRAY Analyzer 4 platforms. In this study, metabolic syndrome (MS) score increased with aging in females, whereas the fatty liver disease (FLD) index decreased with aging in males; the MS score was negatively correlated with TB in females, and FLD index was positively related to urea in males; CLPM showed that the MS score predicted total bilirubin (TB) in females, and urea predicted the FLD index in males. Additionally, rs2292354 in G protein-coupled receptor kinase interactor 2 (GIT2) was associated with the MS score and TB in aged females. Our study suggests the potential gender-specific causal associations between development in MS and increase in TB level in females, and rise in urea level and improved FLD index in males. The SNP rs2292354 we investigated might be a biomarker for predicting MS in the elderly Chinese Han population.

Accommodating site variation in neuroimaging data using normative and hierarchical Bayesian models

The potential of normative modeling to make individualized predictions from neuroimaging data has enabled inferences that go beyond the case-control approach. However, site effects are often confounded with variables of interest in a complex manner and can bias estimates of normative models, which has impeded the application of normative models to large multi-site neuroimaging data sets. In this study, we suggest accommodating for these site effects by including them as random effects in a hierarchical Bayesian model. We compared the performance of a linear and a non-linear hierarchical Bayesian model in modeling the effect of age on cortical thickness. We used data of 570 healthy individuals from the ABIDE (autism brain imaging data exchange) data set in our experiments. In addition, we used data from individuals with autism to test whether our models are able to retain clinically useful information while removing site effects. We compared the proposed single stage hierarchical Bayesian method to several harmonization techniques commonly used to deal with additive and multiplicative site effects using a two stage regression, including regressing out site and harmonizing for site with ComBat, both with and without explicitly preserving variance caused by age and sex as biological variation of interest, and with a non-linear version of ComBat. In addition, we made predictions from raw data, in which site has not been accommodated for. The proposed hierarchical Bayesian method showed the best predictive performance according to multiple metrics. Beyond that, the resulting z-scores showed little to no residual site effects, yet still retained clinically useful information. In contrast, performance was particularly poor for the regression model and the ComBat model in which age and sex were not explicitly modeled. In all two stage harmonization models, predictions were poorly scaled, suffering from a loss of more than 90% of the original variance. Our results show the value of hierarchical Bayesian regression methods for accommodating site variation in neuroimaging data, which provides an alternative to harmonization techniques. While the approach we propose may have broad utility, our approach is particularly well suited to normative modeling where the primary interest is in accurate modeling of inter-subject variation and statistical quantification of deviations from a reference model.

Hierarchical model predictive vibration control for high‐rise structures using semi‐active tuned liquid column damper

Vibration control for high-rise structures has become more important as buildings become more lightweight. Tuned liquid column dampers are an established approach for this problem, as they do not consume high amounts of energy while achieving high damping forces. The natural frequency of tuned liquid column dampers (TLCDs) can be changed semi-actively by modifying their column geometry. As shown by previous studies, this approach increases the control performance of the damper and allows a larger application field. However, this modification simultaneously provokes strong nonlinearities, which need to be addressed for controller design. In this contribution a model-based controller for such TLCDs is proposed, which explicitly accounts for the nonlinear dynamics of the coupled system consisting of a multi-storey structure with a semi-active TLCD. To account for various system dynamics of the structure, a hierarchical nonlinear model predictive controller (NMPC) in combination with a multi-start strategy is formulated. In addition, an extrapolation algorithm is developed to determine an approximation of the future trajectory of the structure's induced excitation load. The excitation trajectory is then incorporated in the NMPC framework. For validation, a frequency response analysis and a case study are conducted on a 20-storey benchmark structure, which is equipped with a semi-active TLCD. The study is carried out in simulation, and the results are compared with passive vibration control. With the proposed hierarchical control, a significant improvement is shown in the reduction of structural vibrations over the relevant spectrum of excitation frequencies up to a mean of 50%.

A hierarchical Bayesian approach to dynamic ordinary differential equations modeling for repeated measures data on wheat growth

Experimental data collected on growth and development of plants over a growing season are typically analyzed using a linear mixed model, analogous to a hierarchical linear model in a Bayesian setting. Alternative modeling approaches for repeated measures data involve non-linear models such as logistic regression and ecophysiological dynamic models based on a system of ordinary differential equations (ODE). Yet, current implementations of ODE models are mostly deterministic in nature, which negates recognition of uncertainty in the data generation process and thus impairs inference and prediction. The primary objective of this study was to demonstrate the use of a dynamic ODE model within a Bayesian framework to make stochastic inference on system-level parameters. A secondary objective was to compare the predictive performance of an ODE model relative to methodologies more commonly used for repeated measures data from designed experiments, namely hierarchical linear models and hierarchical non-linear models. Using a hierarchical Bayesian implementation, we fit all three types of models to data on leaf area index (LAI) and biomass from a winter wheat dataset. In the context of this application, none of the modeling approaches clearly outperformed any other in terms of goodness of fit or prediction accuracy as indicated by similar posterior median values for root mean squared error (RMSE), Willmott’s agreement index (d), and Nash-Sutcliffe efficiency (NSE). The prediction statistics for the ODE, linear, and non-linear models respectively, were: RMSEp of 1.38, 1.14, and 1.19; dp of 0.91, 0.93, and 0.93; and NSEp of 0.69, 0.78, and 0.76 for LAI and RMSEp of 274.08, 253.04, and 207.63; dp of 0.95, 0.95, and 0.97; and NSEp of 0.82, 0.84, and 0.89 for biomass. The dynamic ODE model enabled biologically meaningful system-level inferences relevant to the research questions that were not possible when using the hierarchical linear or non-linear modeling approaches.

Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference

Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to scalable and accurate inference. First, I derive a new mean-field variational algorithm for estimating binomial logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose “marginally augmented variational Bayes” (MAVB) that further improves the initial approximation through a step of Bayesian post-processing. I prove that MAVB provides a guaranteed improvement in the approximation quality at low computational cost and induces dependencies that were assumed away by the initial factorization assumptions. I apply these techniques to a study of voter behavior using a high-dimensional application of the popular approach of multilevel regression and post-stratification (MRP). Existing estimation took hours whereas the algorithms proposed run in minutes. The posterior means are well-recovered even under strong factorization assumptions. Applying MAVB further improves the approximation by partially correcting the under-estimated variance. The proposed methodology is implemented in an open source software package.

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.

Diagnostic performance of elastography on liver fibrosis in antiviral treatment-naive chronic hepatitis B patients: a meta-analysis.

BackgroundThis study aimed to assess the performance of transient elastography (TE), two-dimensional shear wave elastography (2D-SWE), and magnetic resonance elastography (MRE) for staging significant fibrosis and cirrhosis in untreated chronic hepatitis B (CHB) patients.MethodsPubmed, Embase, Web of Science, and Cochrane Library were searched for terms involving CHB, TE, 2D-SWE, and MRE. Other etiologies of chronic liver disease, previous treatment in patients, or articles not published in SCI journals were excluded. Hierarchical non-linear models were used to evaluate the diagnostic accuracy of TE, 2D-SWE, and MRE. Heterogeneity was explored via analysis of threshold effect and meta-regression.ResultsTwenty-eight articles with a total of 4,540 untreated CHB patients were included. The summary areas under the receiver-operating characteristic curves (AUROCs) using TE, 2D-SWE, and MRE for predicting significant fibrosis (SF) were 0.84, 0.89, and 0.99, respectively. The AUROC values of TE, 2D-SWE, and MRE for staging cirrhosis were 0.9, 0.94, and 0.99, respectively. Based on the meta-analysis of studies with head-to-head comparison, 2D-SWE is superior to TE (0.92 vs 0.85, P < 0.01) in staging significant fibrosis.ConclusionTE, 2D-SWE, and MRE express acceptable diagnostic accuracies in staging significant fibrosis and cirrhosis in untreated CHB patients. 2D-SWE outperforms TE in detecting significant fibrosis in treatment-naive people with hepatitis B virus.

Stability of a class of nonlinear hierarchical size-structured population model.

This paper investigates the existence of positive equilibrium as well as the stability of positive equilibrium and zero equilibrium in a nonlinear size-structured hierarchical population model. Under the condition that larger individuals are more competitive advantages than smaller ones, a non-zero fixed point theorem is used to show that there is at lest one positive equilibrium in the system. Moreover, we obtain the stability results of positive equilibrium and zero equilibrium by deriving characteristic equations and establishing Liapunov function. Finally, some numerical experiments are presented.

Hierarchical nonlinear model predictive control of offshore hybrid power systems

This paper presents an approach for controlling ofshore hybrid power systems consisting of gas turbines, offshore wind, and batteries for satisfying an exogenous power demand. A hierarchical controller is developed comprising a high-level economic nonlinear model predictive controller that distributes the power demand according to some economic objective, a low-level nonlinear tracking model predictive controller that actuates on the hybrid power system, and a nonlinear moving horizon estimator to estimate the system state. Simulation results and concluding remarks reveal the advantage of such a hierarchical approach for a simple simulation study.

Hierarchical nonlinear model predictive control with multi-time-scale for wastewater treatment process

Different time scales are inevitable for the controlled variables of wastewater treatment process (WWTP), which may degrade the operation performance or even destroy the stability of the closed-loop system. In this paper, a hierarchical nonlinear model predictive control (HNMPC) strategy is developed to deal with the different time scales of controlled variables to improve the operation performance of WWTP. The main merits of HNMPC are three-fold. First, a hierarchical control structure is developed to obtain reasonable control laws. Then, the controlled variables with different time scales can be tracked by different level controllers. Second, a gradient method is developed to solve the hierarchical optimization problem of HNMPC to reduce the computational cost. Then, the fast response of HNMPC can be achieved to improve the operation performance. Third, the stability of HNMPC is proved in theory. Then, the corresponding stability conditions are given to guide the practical application. Finally, the testing results on the benchmark simulation model verify that the proposed HNMPC can achieve suitable operation performance in terms of control accuracy.

Testing a multilevel opportunity theory of crime (place in neighborhood theory)

This research aims to empirically test a newly developed “place in neighborhood (PIN)” theory, proposed by Wilcox and Tillyer recently. Using secondary data, the authors generate measures of crime and opportunity factors in street blocks nested in neighborhood clusters in Chicago. Hierarchical non-linear models are used to assess the impact of factors in street block level, neighborhood level, and their cross-level interactions on residential burglary. The results show that all four street block level variables are associated with levels of burglary, and two of three neighborhood level variables (social control and delinquency rate) are significantly associated with lower and higher levels of residential burglary, respectively. Five of the twelve cross-level interaction terms are significantly associated with residential burglary rates. Two of the main effects and one of the cross-level interaction terms show unexpected opposite directions. The findings lend partial support to PIN theory.