Semiparametric Additive Model Research Articles

What I Like! The Joint Impact of Attitude, Perceived Quality, and Experience on Brand Loyalty: Semi-Parametric Additive Mixed Modeling

Abstract Several psychological brand performance indicators that predict a brand’s intermediate market share have been identified. So far, rating studies have exclusively investigated brand effects in terms of linear relationships, and their specific and possibly nonlinear interactions have yet to be examined in comparison. Hence, we investigated the relative importance of three well-established psychological performance indicators, attitude toward the brand, perceived quality, and brand experience, in predicting brand loyalty. A sample of 1,077 participants completed an online survey and rated subsets of 105 international brands from various product and service industries. Relations between attitude, perceived quality, and experience in predicting loyalty toward a brand were analyzed using semi-parametric additive mixed regression models. We replicated that all three predictors significantly impacted brand loyalty and revealed a pronounced nonlinear relationship between attitude and loyalty. The inclusion of nonlinear interactions between predictors improved model fit. In particular, the nonlinear interaction between perceived quality and attitude substantially impacted brand loyalty. In addition, these effects differ by type of industry, specifically fast-moving consumer goods, automotive, fashion, electronics, and finance/insurance. These findings draw attention to nonlinear patterns between specific psychological features of brands. Future research should address nonlinear effects and the specific interactions of other essential predictors of brand equity.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Dynamic linkages between human capital, natural resources, and economic growth – Impact on achieving sustainable development goals

This study examines the impact of economic growth, trade dynamics, natural resources, human capital, and sustainable development from 1990 to 2022. To capture the complexity of these factors, we utilize a Novel Dynamic Semi-parametric Additive Panel model. Additionally, we employ a Dynamic panel thresholds model to explore the sensitivity of natural resources to economic development across various indices, addressing a gap in previous nonlinear technique studies. Our findings diverge from conventional financial development and economic growth theories. While increasing money may boost trade and development, it could hinder sustainable development. Interestingly, the relationship between financial market expansion, economic improvement, and natural resource use follows an inverse “U-shaped” non-linear pattern. Furthermore, the expansion of the financial sector significantly affects the interplay between human capital and natural resources. As thresholds of growth in financial markets rise, economic growth contributes more to sustainable development, mitigating its negative impact. Several implications emerge, particularly regarding minimizing energy deprivation through global economic and developmental strategies.

Group Selection and Shrinkage: Structured Sparsity for Semiparametric Additive Models

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection. This work introduces structured sparse estimators that combine group subset selection with shrinkage. To accommodate sophisticated structures, our estimators allow for arbitrary overlap between groups. We develop an optimization framework for fitting the nonconvex regularization surface and present finite-sample error bounds for estimation of the regression function. As an application requiring structure, we study sparse semiparametric additive modeling, a procedure that allows the effect of each predictor to be zero, linear, or nonlinear. For this task, the new estimators improve across several metrics on synthetic data compared to alternatives. Finally, we demonstrate their efficacy in modeling supermarket foot traffic and economic recessions using many predictors. These demonstrations suggest sparse semiparametric additive models, fit using the new estimators, are an excellent compromise between fully linear and fully nonparametric alternatives. All of our algorithms are made available in the scalable implementation grpsel. Supplementary materials for this article are available online.

Variational inference: uncertainty quantification in additive models

Markov chain Monte Carlo (MCMC)-based simulation approaches are by far the most common method in Bayesian inference to access the posterior distribution. Recently, motivated by successes in machine learning, variational inference (VI) has gained in interest in statistics since it promises a computationally efficient alternative to MCMC enabling approximate access to the posterior. Classical approaches such as mean-field VI (MFVI), however, are based on the strong mean-field assumption for the approximate posterior where parameters or parameter blocks are assumed to be mutually independent. As a consequence, parameter uncertainties are often underestimated and alternatives such as semi-implicit VI (SIVI) have been suggested to avoid the mean-field assumption and to improve uncertainty estimates. SIVI uses a hierarchical construction of the variational parameters to restore parameter dependencies and relies on a highly flexible implicit mixing distribution whose probability density function is not analytic but samples can be taken via a stochastic procedure. With this paper, we investigate how different forms of VI perform in semiparametric additive regression models as one of the most important fields of application of Bayesian inference in statistics. A particular focus is on the ability of the rivalling approaches to quantify uncertainty, especially with correlated covariates that are likely to aggravate the difficulties of simplifying VI assumptions. Moreover, we propose a method, where we combine both advantages of MFVI and SIVI and compare its performance. The different VI approaches are studied in comparison with MCMC in simulations and an application to tree height models of douglas fir based on a large-scale forestry data set.

Martingale-residual-based greedy model averaging for high-dimensional current status data.

Current status data are a type of failure time data that arise when the failure time of study subject cannot be determined precisely but is known only to occur before or after a random monitoring time. Variable selection methods for the failure time data have been discussed extensively in the literature. However, the statistical inference of the model selected based on the variable selection method ignores the uncertainty caused by model selection. To enhance the prediction accuracy for risk quantities such as survival probability, we propose two optimal model averaging methods under semiparametric additive hazards models. Specifically, based on martingale residuals processes, a delete-one cross-validation (CV) process is defined, and two new CV functional criteria are derived for choosing model weights. Furthermore, we present a greedy algorithm for the implementation of the techniques, and the asymptotic optimality of the proposed model averaging approaches is established, along with the convergence of the greedy averaging algorithms. A series of simulation experiments demonstrate the effectiveness and superiority of the proposed methods. Finally, a real-data example is provided as an illustration.

Shape restricted additive hazards models: Monotone, unimodal, and U-shape hazard functions.

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time-dependent covariate with monotone or U-shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

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

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

Quality design based on kernel trick and Bayesian semiparametric model for multi-response processes with complex correlations

ABSTRACT Processes or products are typically complex systems with numerous interrelated procedures and interdependent components. This results in complex relationships between responses and input factors, as well as complex nonlinear correlations among multiple responses. If the two types of complex correlations in the quality design cannot be properly dealt with, it will affect the prediction accuracy of the response surface model, as well as the accuracy and reliability of the recommended optimal solutions. In this paper, we combine kernel trick-based kernel principal component analysis, spline-based Bayesian semiparametric additive model, and normal boundary intersection-based evolutionary algorithm to address these two types of complex correlations. The effectiveness of the proposed method in modeling and optimisation is validated through a simulation study and a case study. The results show that the proposed Bayesian semiparametric additive model can better describe the process relationships compared to least squares regression, random forest regression, and support vector basis regression, and the proposed multi-objective optimisation method performs well on several indicators mentioned in the paper.

Determinants and spatial patterns of anaemia and haemoglobin concentration among pregnant women in Nigeria using structured additive regression models

Anaemia which is a condition that describes low haemoglobin (Hb) levels has been recognized as a major public health problem amongst pregnant women in many sub-Saharan African countries including Nigeria. The causes of maternal anaemia which are interconnected and complex vary between countries and can vary within a country. This study aimed to investigate the spatial pattern and identify demographic and socio-economic determinants associated with anaemia amongst Nigerian pregnant women aged 15–49 years using data from the 2018 Nigeria Demographic and Health Survey (NDHS). This study utilized chi-square tests of independence and semiparametric structured additive models to describe the relationship between the presumed factors and anaemia status or Hb level while also taking spatial effects at state level into account. The Gaussian and Binomial distributions were used for Hb level and anaemia status respectively. The overall observed prevalence of anaemia in pregnant women and average Hb level in Nigeria were 64% and 10.4 (SD = 1.6) g/dL respectively while the prevalence of mild, moderate and severe anaemia were 27.2%, 34.6% and 2.2% respectively. Higher education, older age, and currently breastfeeding were associated with higher Hb level. Low education, being unemployed and recently having a sexually transmitted infection were identified as risk factors for maternal anaemia. Body mass index (BMI) and household size had a nonlinear effect on Hb level while BMI and age were nonlinearly related to odds of anaemia. Bivariate analysis indicated that living in rural area, low wealth class, using unsafe water and non-usage of internet were significantly associated with increased risk of anaemia. Maternal anaemia prevalence was highest in the South Eastern part of Nigeria with Imo state producing the highest prevalence of maternal anaemia while Cross River state yielded the lowest prevalence of maternal anaemia. The spatial effects associated with states were significant but unstructured indicating that states in close proximity do not necessarily share similar spatial effects. Hence, unobserved characteristics shared by states in close proximity do not influence maternal anaemia and Hb level. The findings from this study can undoubtedly help in the planning and designing of anaemia interventions that match local conditions taking into consideration the aetiology of anaemia in Nigeria.

A survey of smoothing techniques based on a backfitting algorithm in estimation of semiparametric additive models

AbstractThis paper aims to present an overview of Semiparametric additive models. An estimation of the finite‐parameters of semiparametric regression models that involve additive nonparametric components is explained, including their historical background. In addition, three different smoothing techniques are considered in order to show the working procedures of the estimators and to explore their statistical properties: smoothing splines, kernel smoothing and local linear regression. These methods are compared with respect to both their theoretical and practical behaviors. A simulation study and a real data example are carried out to reveal the performances of the three methods. Accordingly, the advantages and disadvantages of each method regarding semiparametric additive models are presented based on their comparative scores using determined evaluation metrics for loss of information.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Models > Semiparametric Models

Modeling the dynamic influences of economic growth and financial development on energy consumption in emerging economies: Insights from dynamic nonlinear approaches

This article evaluates the dynamic impacts of economic growth and financial development on energy consumption in emerging economies from 1998 to 2019. The total financial development and its submeasures of financial institution and financial market development are applied in consideration of the different dimensions of financial development. In doing so, we apply a new dynamic semiparametric additive panel model to address potential dynamicity and nonlinearity. Moreover, the dynamic panel threshold model is recommended to explore the dynamic threshold effect of income growth on energy pressure under different financial development indicators, complementing the gap in the existing research on nonlinear mechanisms regarding this topic. Our findings do not indicate the presence of the EKC hypothesis but verify that income growth can reinforce energy pressure. Total financial improvement and financial market development both display an inverted “U-shaped” nonlinear influence on energy expenditure, while financial institution development can directly ease energy pressure. We also find that financial development performs a significant threshold effect in the linkage between income growth and energy expenditure. The higher the total financial development and financial market development levels are, the stronger the contribution of economic growth on energy pressure; however, the unfavorable influence of economic growth on energy pressure is receded with the increase in financial institution development. Some policy implications are provided for reducing energy poverty through optimizing economic and financial advancement.

The Environmental Kuznets Curve in a long-term perspective: Parametric vs semi-parametric models

Empirical studies of the EKC hypothesis may be very sensitive to datasets, specifications, and functional forms. The aim of this paper is to investigate the long-run relationship among CO2 emissions, real GDP, and energy consumption using a panel of 9 advanced economies from 1870 to 2008 using both parametric and semi-parametric additive models. While at the panel level the results provide support to the Environmental Kuznets Curve (EKC) only in the post-1950s period, at the individual country level the inverted U-shaped relationship between CO2 and real GDP is validated for a subset of countries only. However, when a semi-parametric regression framework is applied an inverse U-shaped pattern becomes clear for all countries of the sample, except Canada. Empirical findings indicate that relaxing the restrictions associated with parametric regression models may be critical for the question of investigating the existence of the EKC.

Augmented weighting estimators for the additive rates model under multivariate recurrent event data with missing event type.

Multivariate recurrent event data are frequently encountered in biomedical and epidemiological studies when subjects experience multiple types of recurrent events. In practice, the event type information may be missing due to a variety of reasons. In this article, we consider a semiparametric additive rates model for multivariate recurrent event data with missing event types. We develop the augmented inverse probability weighting technique to handle event types that are missing at random. The nonparametric kernel-assisted proposals for the missing mechanisms are studied. The resulting estimator is shown to be consistent and asymptotically normal. Extensive simulation studies and a real data application are provided to illustrate the validity and practical utility of the proposed method.

A Genetic Association Test Accounting for Skewed X-Inactivation With Application to Biotherapy Immunogenicity in Patients With Autoimmune Diseases.

Despite being assayed on commercialized DNA chips, the X chromosome is commonly excluded from genome-wide association studies (GWAS). One of the reasons is the complexity to analyze the data taking into account the X-chromosome inactivation (XCI) process in women and in particular the XCI process with a potentially skewed pattern. This is the case when investigating the role of X-linked genetic variants in the occurrence of anti-drug antibodies (ADAs) in patients with autoimmune diseases treated by biotherapies. In this context, we propose a novel test statistic for selecting loci of interest harbored by the X chromosome that are associated with time-to-event data taking into account skewed X-inactivation (XCI-S). The proposed statistic relies on a semi-parametric additive hazard model and is straightforward to implement. Results from the simulation study show that the test provides higher power gains than the score tests from the Cox model (under XCI process or its escape) and the Xu et al.'s XCI-S likelihood ratio test. We applied the test to the data from the real-world observational multicohort study set-up by the IMI-funded ABIRISK consortium for identifying X chromosome susceptibility loci for drug immunogenicity in patients with autoimmune diseases treated by biotherapies. The test allowed us to select two single nucleotide polymorphisms (SNPs) with high linkage disequilibrium (rs5991366 and rs5991394) located in the cytoband Xp22.2 that would have been overlooked by the Cox score tests and the Xu et al.'s XCI-S likelihood ratio test. Both SNPs showed a similar protective effect for drug immunogenicity without any occurrence of ADA positivity for the homozygous females and hemizygous males for the alternative allele. To our knowledge, this is the first study to investigate the association between X chromosome loci and the occurrence of anti-drug antibodies. We think that more X-Chromosome GWAS should be performed and that the test is well-suited for identifying X-Chromosome SNPs, while taking into account all patterns of the skewed X-Chromosome inactivation process.

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin.

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan-Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccinestudy.

Detection of Cognitive Impairment after Critical Illness with the Medicare Annual Wellness Visit: A Cohort Study.

Rationale: Cognitive impairment after critical illness is common in observational studies of older intensive care unit (ICU) survivors. The rate of screening for and diagnosis of cognitive impairment in ICU survivors in nonresearch settings is unknown. Objectives: To determine how often cognitive impairment was detected in older adults in the year after critical illness at an academic medical center as part of 1) the Medicare Annual Wellness Visit (AWV) and 2) routine clinical care. Methods: This study was a retrospective cohort study conducted at an urban academic medical center. The study included 696 patients aged 65 years and older admitted to the medical ICU between October 1, 2016, and October 1, 2018, and discharged alive. Patients were also required to have a health system-affiliated primary care provider. Patients were followed for 1 year. We defined cognitive impairment detected in the AWV as either an indicated diagnosis of cognitive impairment or dementia or patient, family, or provider indication of memory concerns during the AWV. We modeled the incidence of AWV completion and the detection of cognitive impairment using semiparametric additive models accounting for the competing risk of death. Results: Over 1 year of follow-up, the cumulative incidence of mortality was 23.0% (95% confidence interval [CI], 19.9-26.1%), with 24.7% (95% CI, 21.5-27.9%) completing the AWV. The cumulative incidence of cognitive impairment first detected through the AWV was 3.4% (95% CI, 1.8-5.0%) at 1 year, with a higher cumulative incidence for diagnoses of cognitive impairment or dementia first indicated via encounter diagnosis codes or the electronic health record problem list (5.9%; 95% CI, 3.9-7.9%). Conclusions: The results of our study suggest that the currently implemented AWV is unlikely to be an adequate mechanism for detecting cognitive impairment in a high-risk population such as those recovering from critical illness.

Semiparametric additive frailty hazard model for clustered failure time data

This article proposes a flexible semiparametric additive frailty hazard model under clustered failure time data, where frailty is assumed to have an additive effect on the hazard function. When there is no frailty, this model degenerates into a semiparametric additive hazard model. Our method can deal simultaneously with both time‐varying and constant covariate effects. The estimate of the covariate effects does not rely on the frailty distribution. The time‐varying coefficient is estimated by utilizing the local linear technique, while we can obtain a ‐consistency convergence rate of the constant‐coefficient estimate by integration. Another advantage of the estimator is that it has a closed form. We establish large sample properties of the estimator and conduct simulation studies under various scenarios to demonstrate its performance. The proposed method is applied to real data for illustration.

Dynamic Impact of Environmental Regulation on Environmental Performance in China: New Evidence from a Semiparametric Additive Panel Analysis

Environmental protection is the core of sustainable economic development, and environmental policy plays a key role in achieving protection goals. Therefore, it is extremely crucial to evaluate the effectiveness of environmental policies. Existing studies mainly focus on the average impact of environmental policies on environmental pollution but ignore their dynamic impact, which is prone to misestimate the effect of environmental policies. To make up for the deficiency, a semiparametric additive panel data model is used to explore the dynamic impact of China’s sewage charging policy on environmental performance at each level of the levy. The results show that the relationship between sewage charge level and environmental degeneration is an “M-shaped” pattern, indicating that the current sewage charge policy is not absolutely effective. Moreover, the results also reveal an “N-shaped” linkage between economic growth and environmental pollution, indicating that economic development is not sustainable. Moreover, the factors of energy consumption, population growth, and industrialization contribute to increasing environmental degeneration. Although technological development has a positive impact on environmental performance, its impact is insignificant. This study could provide new evidence for strengthening environmental regulatory reform and promoting green economic development.

Additive rates model for recurrent event data with intermittently observed time-dependent covariates.

Various regression methods have been proposed for analyzing recurrent event data. Among them, the semiparametric additive rates model is particularly appealing because the regression coefficients quantify the absolute difference in the occurrence rate of the recurrent events between different groups. Estimation of the additive rates model requires the values of time-dependent covariates being observed throughout the entire follow-up period. In practice, however, the time-dependent covariates are usually only measured at intermittent follow-up visits. In this paper, we propose to kernel smooth functions involving time-dependent covariates across subjects in the estimating function, as opposed to imputing individual covariate trajectories. Simulation studies show that the proposed method outperforms simple imputation methods. The proposed method is illustrated with data from an epidemiologic study of the effect of streptococcal infections on recurrent pharyngitis episodes.