Functions Of Regression Coefficients Research Articles

Locally sparse and robust partial least squares in scalar-on-function regression

We present a novel approach for estimating a scalar-on-function regression model, leveraging a functional partial least squares methodology. Our proposed method involves computing the functional partial least squares components through sparse partial robust M regression, facilitating robust and locally sparse estimations of the regression coefficient function. This strategy delivers a robust decomposition for the functional predictor and regression coefficient functions. After the decomposition, model parameters are estimated using a weighted loss function, incorporating robustness through iterative reweighting of the partial least squares components. The robust decomposition feature of our proposed method enables the robust estimation of model parameters in the scalar-on-function regression model, ensuring reliable predictions in the presence of outliers and leverage points. Moreover, it accurately identifies zero and nonzero sub-regions where the slope function is estimated, even in the presence of outliers and leverage points. We assess our proposed method’s estimation and predictive performance through a series of Monte Carlo experiments and an empirical dataset—that is, data collected in relation to oriented strand board. Compared to existing methods our proposed method performs favorably. Notably, our robust procedure exhibits superior performance in the presence of outliers while maintaining competitiveness in their absence. Our method has been implemented in the robsfplsr package in .

Quantile Regression for Longitudinal Functional Data with Application to Feed Intake of Lactating Sows

AbstractThis article focuses on the study of lactating sows, where the main interest is the influence of temperature, measured throughout the day, on the lower quantiles of the daily feed intake. We outline a model framework and estimation methodology for quantile regression in scenarios with longitudinal data and functional covariates. The quantile regression model uses a time-varying regression coefficient function to quantify the association between covariates and the quantile level of interest, and it includes subject-specific intercepts to incorporate within-subject dependence. Estimation relies on spline representations of the unknown coefficient functions and can be carried out with existing software. We introduce bootstrap procedures for bias adjustment and computation of standard errors. Analysis of the lactation data indicates, among others, that the influence of temperature increases during the lactation period.Supplementary materials accompanying this paper appear on-line.

Dynamic modeling for multivariate functional and longitudinal data

Dynamic interactions among several stochastic processes are common in many scientific fields. It is crucial to model these interactions to understand the dynamic relationship of the corresponding multivariate processes with their derivatives and to improve predictions. In reality, full observations of the multivariate processes are not feasible as measurements can only be taken at discrete locations or time points, and often only sparingly and intermittently in longitudinal studies. This results in multivariate longitudinal data that are measured at different times for different subjects. We propose a time-dynamic model to handle multivariate longitudinal data by modeling the derivatives of multivariate processes using the values of these processes. Starting with a linear concurrent model, we develop methods to estimate the regression coefficient functions, which can accommodate irregularly measured longitudinal data that are possibly contaminated with noise. Our approach can also be applied to settings when the observational times are the same for all subjects. We establish the convergence rates of our estimators with phase transitions and further illustrate our model through a simulation study and a real data application.

FTO variation and early frontostriatal brain development in children.

Common obesity-associated genetic variants at the fat mass and obesity-associated (FTO) locus have been associated with appetitive behaviors and altered structure and function of frontostriatal brain regions. The authors aimed to investigate the influence of FTO variation on frontostriatal appetite circuits in early life. Data were drawn from RESONANCE, a longitudinal study of early brain development. Growth trajectories of nucleus accumbens and frontal lobe volumes, as well as total gray matter and white matter volume, by risk allele (AA) carrier status on FTO single-nucleotide polymorphism rs9939609 were examined in 228 children (102 female, 126 male) using magnetic resonance imaging assessments obtained from infancy through middle childhood. The authors fit functional concurrent regression models with brain volume outcomes over age as functional responses, and FTO genotype, sex, BMI z score, and maternal education were included as predictors. Bootstrap pointwise 95% CI for regression coefficient functions in the functional concurrent regression models showed that the AA group versus the group with no risk allele (TT) had greater nucleus accumbens volume (adjusted for total brain volume) in the interval of 750 to 2250 days (2-6 years). These findings suggest that common genetic risk for obesity is associated with differences in early development of brain reward circuitry and argue for investigating dynamic relationships among genotype, brain, behavior, and weight throughout development.

Sparse estimation of historical functional linear models with a nested group bridge approach

AbstractThe conventional historical functional linear model relates the current value of the functional response at time to all past values of the functional covariate up to time . Motivated by situations where it is more reasonable to assume that only recent, instead of all, past values of the functional covariate have an impact on the functional response, in this work we investigate the historical functional linear model with an unknown forward time lag into the history. In addition to estimating the bivariate regression coefficient function, we also aim to identify the historical time lag from the data, which is important in many applications. To this end, we propose an estimation procedure that uses the finite element method to conform naturally to the trapezoidal domain of the bivariate coefficient function. We use a nested group bridge penalty to facilitate simultaneous estimation of the bivariate coefficient function and the historical lag, and show that our proposed estimators are consistent. We demonstrate this method of estimation in a real data example investigating the effect of muscle activation recorded via the noninvasive electromyography (EMG) method on lip acceleration during speech production. In addition, we examine the finite sample performance of our proposed method in comparison with the conventional approach to estimation via simulation studies.

On partial least‐squares estimation in scalar‐on‐function regression models

AbstractScalar‐on‐function regression, where the response is scalar valued and the predictor consists of random functions, is one of the most important tools for exploring the functional relationship between a scalar response and functional predictor(s). The functional partial least‐squares method improves estimation accuracy for estimating the regression coefficient function compared to other existing methods, such as least squares, maximum likelihood, and maximum penalized likelihood. The functional partial least‐squares method is often based on the SIMPLS or NIPALS algorithm, but these algorithms can be computationally slow for analyzing a large dataset. In this study, we propose two modified functional partial least‐squares methods to efficiently estimate the regression coefficient function under the scalar‐on‐function regression. In the proposed methods, the infinite‐dimensional functional predictors are first projected onto a finite‐dimensional space using a basis expansion method. Then, two partial least‐squares algorithms, based on re‐orthogonalization of the score and loading vectors, are used to estimate the linear relationship between scalar response and the basis coefficients of the functional predictors. The finite‐sample performance and computing speed are evaluated using a series of Monte Carlo simulation studies and a sugar process dataset.

Dynamic prediction of multivariate functional data based on Functional Kernel Partial Least Squares

With the flourishment of sensing technology, a huge mass of functional data can be acquired to describe the manufacturing process and predict the product quality. But these data simultaneously bring in modeling challenges of multi-type data, high-dimensional variables, data irregularity, and complex correlations. To address these challenges, this work proposes the Functional Kernel Partial Least Squares (FKPLS) methodology, which is a function-on-function regression. The FKPLS method first smooths the discrete sequences to continuous functions via functional data analysis (FDA) to retain the dynamic characteristics of variables, and then relies on basis function expansion to estimate the regression coefficient functions in order to avoid the ill-posed problem in directly estimating the functional eigenequation. An artificial dataset and a real-world steelmaking process are used to validate the effectiveness of the FKPLS method. The results demonstrate lower mean relative prediction error of the FKPLS method than the traditional methods, which is no more than 0.36% on simulation data and no more than 14.88% on industrial data. As the regression coefficients are functions, the FKPLS method is also effective in predicting dynamic mapping between predictors and responses.

Multiwave validation sampling for error-prone electronic health records.

Electronic health record (EHR) data are increasingly used for biomedical research, but these data have recognized data quality challenges. Data validation is necessary to use EHR data with confidence, but limited resources typically make complete data validation impossible. Using EHR data, we illustrate prospective, multiwave, two-phase validation sampling to estimate the association between maternal weight gain during pregnancy and the risks of her child developing obesity or asthma. The optimal validation sampling design depends on the unknown efficient influence functions of regression coefficients of interest. In the first wave of our multiwave validation design, we estimate the influence function using the unvalidated (phase 1) data to determine our validation sample; then in subsequent waves, we re-estimate the influence function using validated (phase 2) data and update our sampling. For efficiency, estimation combines obesity and asthma sampling frames while calibrating sampling weights using generalized raking. We validated 996 of 10,335 mother-child EHR dyads in six sampling waves. Estimated associations between childhood obesity/asthma and maternal weight gain, as well as other covariates, are compared to naïve estimates that only use unvalidated data. In some cases, estimates markedly differ, underscoring the importance of efficient validation sampling to obtain accurate estimates incorporating validated data.

Escape from air pollution: How does air quality in the place of residence shape tourism consumption?

Air quality has been demonstrated to be an important determinant influencing tourist decision making. In this paper, we investigate the effect of air quality in the place of origin on a resident’s tourism consumption and the moderating effect of household income on this relationship. We develop a conceptual framework to rationalize the effect and empirically examine it at the household level using China Labor-force Dynamics Survey data from 2016. The results show that poor ambient air quality increases tourism consumption. Furthermore, this relationship becomes stronger for the higher-income group: One standard deviation increase in the Air Quality Index would increase tourism expenditure as much as a 22.56% increase in family income. The methods of instrumental variable and functional-coefficient regression were employed for robustness analysis. These findings contribute to the literature by providing a new perspective for tourism demand studies and direct implications for tourism management and policy making.

Adaptive smoothing spline estimator for the function-on-function linear regression model

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the R package adass, openly available online on CRAN.

A robust scalar-on-function logistic regression for classification

Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor. Most of the methods used to estimate this model are based on the least-squares type estimators. However, the least-squares estimator is seriously hindered by outliers, leading to biased parameter estimates and an increased probability of misclassification. This paper proposes a robust partial least squares method to estimate the regression coefficient function in the scalar-on-function logistic regression. The regression coefficient function represented by functional partial least squares decomposition is estimated by a weighted likelihood method, which downweighs the effect of outliers in the response and predictor. The estimation and classification performance of the proposed method is evaluated via a series of Monte Carlo experiments and a strawberry puree data set. The results obtained from the proposed method are compared favorably with existing methods.

Truncated estimation in functional generalized linear regression models

Functional generalized linear models investigate the effect of functional predictors on a scalar response. An interesting case is when the functional predictor is thought to exert an influence on the conditional mean of the response only through its values up to a certain point in the domain. In the literature, models with this type of restriction on the functional effect have been termed truncated or historical regression models. A penalized likelihood estimator is formulated by combining a structured variable selection method with a localized B-spline expansion of the regression coefficient function. In addition to a smoothing penalty that is typical for functional regression, a nested group lasso penalty is also included which guarantees the sequential entering of B-splines and thus induces the desired truncation on the estimator. An optimization scheme is developed to compute the solution path efficiently when varying the truncation tuning parameter. The convergence rate of the coefficient function estimator and consistency of the truncation point estimator are given under suitable smoothness assumptions. The proposed method is demonstrated through simulations and an application involving the effects of blood pressure values in patients who suffered a spontaneous intracerebral hemorrhage.

Magnetic Fe3O4 nanoparticles loaded papaya (Carica papaya L.) seed powder as an effective and recyclable adsorbent material for the separation of anionic azo dye (Congo Red) from liquid phase: Evaluation of adsorption properties

Magnetic adsorbents have recently gotten a lot of attention because of their eco-friendliness, ease of separation, and inexpensive cost. In this work, a new magnetic Fe3O4 loaded papaya seed powder (Fe3O4-PSP) was successfully synthesized and utilized as a biosorbent to eliminate Congo Red (CR) from the liquid phase. The prepared Fe3O4-PSP was characterized by BET, FE-SEM/EDX, VSM, XRD, pHPZC, and FT-IR analysis. Batch tests were carried out to assess the influence of several adsorption factors like temperature (303–333 K), pH function (2.0–10.0), CR initial concentration (100–400 mg/L), Fe3O4-PSP mass (0.01–0.08 g/30 mL), and contact time (0–420 min). The pHPZC of Fe3O4-PSP was computed at 5.4. Four kinetic models were used to analyze the kinetic data, and the most appropriate model with an R2 value of 0.9991 was the pseudo-second-order. In accordance with the intra-particle diffusion model, the adsorption follows a three-step mechanism. The adsorption equilibrium data were examined using Dubinin-Radushkevich (D-R), Freundlich, Langmuir, and Temkin models and the adsorption data were well represented by the Langmuir isotherm (R2 = 0.9962). The saturated adsorption efficiency of Fe3O4-PSP calculated from the Langmuir model was 216.9 mg/g at 303 K. The data was examined using error and regression coefficient functions, such as the χ2 and SSE, to define the best-suitable isotherm and kinetic models. Hydrogen bonding and electrostatic interactions between CR and Fe3O4-PSP are responsible for the primary adsorption mechanism. The thermodynamic factors ΔSo (64.8 J/mol K), ΔGo (−1.1997 ∼ 3.1439 kJ/mol for 303 ∼ 333 K), and ΔHo (18.4 kJ/mol) revealed that the adsorption of CR onto Fe3O4-PSP was feasible, spontaneous, and endothermic. The saturation magnetization of Fe3O4-PSP was found to be 54.4 emu/g. An external magnetic field can regenerate and easily separate Fe3O4-PSP from an aqueous solution with no weight loss. According to the findings, Fe3O4-PSP is a potentially recyclable adsorbent for removing CR dye from contaminated water.

Spurious functional-coefficient regression models and robust inference with marginal integration

Functional-coefficient cointegrating models have become popular to model nonlinear nonstationarity in econometrics (Cai et al., 2009; Xiao, 2009). However, there is rare study on testing the existence of functional-coefficient cointegration. Consequently, functional-coefficient regressions involving nonstationary regressors may be spurious. This paper investigates the effect that spurious functional-coefficient regression has on the model diagnostics. We find that common characteristics of spurious regressions are manifest, including divergent local significance tests, random local goodness-of-fit, and local Durbin–Watson ratio converging to zero, complementing those discovered in spurious linear and nonparametric regressions (Phillips, 1986, 2009). In addition, spuriousness causes the divergences of the global significance tests proposed by Xiao (2009) and Sun et al. (2016), which are likely to produce misleading conclusions for practitioners when cointegration tests fail to reject a spurious regression. To resolve the problems, we propose a simple-to-implement inference procedure based on a semiparametric balanced regression, by augmenting regressors of the original spurious regression with lagged dependent variable and independent variables, with the aid of the marginal integration. This procedure achieves spurious regression detection via standard nonparametric inferential asymptotics, and is found robust to the true relationship between the integrated processes. The theoretical results are also corroborated by simulations.

Ethical Behavioural Disclosure and Financial Performance of Listed Industrial Goods Firms in Nigeria

Purpose: Interests in the nexus between ethical performance and financial performance have generated mixed results. However, despite the number and the variety of studies, the evidences available suggest not been comprehensively examined. Also, there is no sufficient effort to examine this relationship within the industrial good sector in Nigeria. This calls for further study.
 Design/Methodology: This study uses a functional coefficient regression technique to estimate panel-varying betas and alpha in three financial performance models. The empirical data were collected from the Nigerian Stock Exchange over a period of 2010-2019. Data were analyzed using random effects models after accounting for multicollinearity, heteroskedasticity, normality.
 Findings: Results show that human resource development disclosure and community service disclosure have significant positive effects on financial performance while environmental and product safety disclosures have significant negative effects on financial performance.
 Originality/Value: The study therefore concludes that ethical behavioural practices of listed industrial firms have significant effects on financial performance. The study recommends among others that industrial firms should redirect their ethical practices into human resource development and community services since their disclosures enhance financial performance.

Adsorption of cationic dyes, drugs and metal from aqueous solutions using a polymer composite of magnetic/β-cyclodextrin/activated charcoal/Na alginate: Isotherm, kinetics and regeneration studies

In this work, we successfully synthesized novel polymer gel beads based on functionalized iron oxide (Fe3O4), activated charcoal (AC) particles with β-cyclodextrin (CD) and sodium alginate (SA) polymer (Fe3O4/CD/AC/SA), by a simple, reproducible and inexpensive method. These beads proved to be versatile and strong adsorbents with magnetic properties and high adsorption capacity. The composites were characterized by Fourier transform infrared spectroscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy, vibrating sample magnetometry, adsorption at −196 °C, high resolution transmission electron microscopy, thermogravimetric analysis and point of zero charge measurements. Two dyes, two drugs and one metal were used to test the adsorption capability of the prepared polymer nanocomposite. The adsorbent showed good removal efficiencies for the studied pollutants, especially the cationic dyes and the metal, when compared to other low-cost adsorbents. The saturated adsorption capacity of Fe3O4/CD/AC/SA reached 5.882 mg g−1 for methyl violet (MV), 2.283 mg g−1 for brilliant green (BG), 2.551 mg g−1 for norfloxacin (NOX), 3.125 mg g−1 for ciprofloxacin (CPX), 10.10 mg g−1 for copper metal ion (Cu(II)). The adsorption isotherm studies showed that data fitted well with Langmuir and Temkin isotherms models. The kinetic data showed good correlation coefficient with low error function for the pseudo-second order kinetic model. The data analysis was carried out using error and regression coefficient functions for the estimation of best-fitting isotherm and kinetic models, namely: chi-square test (χ2) and sum of the squares of errors (SSE). The activation energy was found to be 47.68 kJ mol−1 for BG, 29.09 kJ mol−1 for MV, 28.93 kJ mol−1 for NOX, 4.53 kJ mol−1 for CPX and 17.08 kJ mol−1 for Cu(II), which represent chemisorption and physisorption behavior of sorbent molecules. The polymer composites can be regenerated and easily separated from aqueous solution without any weight loss. After regeneration, the Fe3O4/CD/AC/SA beads still have good adsorption capacities up to four cycles of desorption and adsorption. The results indicate that the polymer gel beads are promising adsorbents for the removal of different categories of toxicants (like dyes, drugs and metal) in single adsorbate aqueous systems. Thus, the novel Fe3O4/CD/AC/SA beads can be effectively employed for a large-scale applications as environmentally compatible materials for the adsorption of different categories of pollutants.

Meta-analysis of Total Effect Decomposition in the Presence of Multiple Mediators: The Example of Schizophrenia Treatment.

Causal mediation analysis addresses mechanistic questions by decomposing and quantifying effects operating through different pathways. Because most individual studies are underpowered to detect mediating effects, we outlined a parametric approach to meta-analyzing causal mediation and interaction analyses with multiple mediators, compared it with a bootstrap-based alternative, and discussed its limitations. We employed fixed- and random-effects multivariate meta-analyses to integrate evidence on treatment-mediators and mediators-outcome associations across trials. We estimated path-specific effects as functions of meta-analyzed regression coefficients; we obtained standard errors using the delta method. We evaluated the performance of this approach in simulations and applied it to assess the mediating roles of positive symptoms of schizophrenia and weight gain in the treatment effect of paliperidone ER on negative symptoms across four efficacy trials. Both simulations and the application showed that the meta-analytic approaches increased statistical power. In the application, we observed substantial mediating effects of positive symptoms (proportions mediated from fixed-effects meta-analysis: (Equation is included in full-text article.)). Weight gain may have beneficial mediating effects; however, such benefit may disappear at high doses when metabolic side effects were excessive. Meta-analyzing causal mediation analysis combines evidence from multiple sources and improves power. Targeting positive symptoms may be an effective way to reduce negative symptoms that are challenging to treat. Future work should focus on extending the existing methods to allow for more flexible modeling of mediation.

Empirical Likelihood for Generalized Functional-Coefficient Regression Models with Multiple Smoothing Variables under Right Censoring Data

Empirical likelihood as a nonparametric approach has been demonstrated to have many desirable merits for constructing a confidence region. The purpose of this article is to apply the empirical likelihood method to study the generalized functional-coefficient regression models with multiple smoothing variables when the response is subject to random right censoring. The coefficient functions with multiple smoothing variables can accommodate various nonlinear interaction effects between covariates. The empirical log-likelihood ratio of an unknown parameter is constructed and shown to have a standard chi-squared limiting distribution at the true parameter. Based on this, the confidence region of the unknown parameter can be constructed. Simulation studies are carried out to indicate that the empirical likelihood method performs better than a normal approximation-based approach for constructing the confidence region.

Parametric Modelling of M-Quantile Regression Coefficient Functions with Application to Small Area Estimation

Summary Small area estimation methods can be used to obtain reliable estimates of a parameter of interest within an unplanned domain or subgroup of the population for which only a limited sample size is available. A standard approach to small area estimation is to use a linear mixed model in which the heterogeneity between areas is accounted for by area level effects. An alternative solution, which has gained popularity in recent years, is to use M-quantile regression models. This approach requires much weaker assumptions than the standard linear mixed model and enables computing outlier robust estimators of the area means. We introduce a new framework for M-quantile regression, in which the model coefficients, β(τ), are described by (flexible) parametric functions of τ. We illustrate the advantages of this approach and its application to small area estimation. Using the European Union Survey on Income and Living Conditions data, we estimate the average equivalized household income in three Italian regions. The paper is accompanied by an R package Mqrcm that implements the necessary procedures for estimation, inference and prediction.

Data-driven model checking for errors-in-variables varying-coefficient models with replicate measurements

In this work, the adequacy check of errors-in-variables varying-coefficient models is investigated when replicate measurements are available. Estimation using the naive method that ignores measurement errors is biased. After the calibration of the estimators of the regression coefficient functions, we construct an empirical-process-based test statistic by the attenuation of corrected residuals. The asymptotic properties of the test statistic under the null hypothesis, global and various local alternatives are established. Simulation studies and real data analyses reveal that the proposed test performs satisfactorily.