Nonparametric Smooth Functions Research Articles

The Factors Driving the Spatial Variation in the Selection of Spawning Grounds for Sepiella japonica in Offshore Zhejiang Province, China

Due to overfishing and marine pollution, the status of fishery resources and the ecological environment in the sea areas have considerably changed. The proliferation and release of fishery resources have become the main means of human intervention to maintain and conserve the resource populations. The annual output of Sepiella japonica (S. japonica), once one of the four major seafood species in the East China Sea, has now recovered to a level of 4000 t. However, do the traditional spawning grounds of S. japonica still exist? Have the spawning grounds shifted? These scientific questions are worthy of attention. Based on the survey data of fishery resources and environment at 120 stations in coastal Zhejiang waters from 2015 to 2022, the spatial and temporal distribution and resource center of gravity of S. japonica in springtime were analyzed. Random forest (RF) was used to explain the importance of six environmental variables, including water depth, sea surface temperature, sea surface salinity, chlorophyll a, pH, and dissolved oxygen. The generalized additive model (GAM) nonparametric smoothing function was used to analyze the relationship between environmental factors and the distribution of S. japonica inhabiting the offshore areas of Zhejiang province, and the effects of environmental factors on spawning habitat selection of S. japonica were revealed. This study found that there was a significant interannual variation in S. japonica resources, with an overall increasing trend in the resource. The spawning grounds were mainly distributed in the Jiushan Islands Marine Reserve, the Dachen Islands Marine Reserve, and their nearby sea areas. The resource peaked at latitude 28.3° N. Additionally, the most important variables affecting the distribution of S. japonica were depth of water, followed by sea surface salinity, pH, dissolved oxygen, sea surface temperature, and chlorophyll a. S. japonica mainly inhabited sea areas with a depth of 15~25 m and a sea surface salinity of 26~32. When the pH ranged from 7.6 to 8.3, dissolved oxygen ranged from 6 to 9 mg/L, sea surface temperature ranged from 14 to 17 °C, and chlorophyll a ranged from 2.5 to 5 µg/L, S. japonica was more likely to be present. This study provides insights into the spatial distribution of S. japonica in offshore Zhejiang province, offering a reference for the rational utilization and scientific protection of this resource.

Bayesian and Classical Semi-parametric Estimation of the Balanced Longitudinal Data Model

The primary objective of this study is to employ semi-parametric regression techniques in the balanced longitudinal data model. Where the parametric regression models are plagued by the problem of strict constraints, while non-parametric regression models, despite their flexibility, suffer from the problem of the curse of dimensionality. Consequently, semi-parametric regression presents a suitable solution to address the problems in parametric and non-parametric regression methods. The advantage of this model is that it contains all the positive properties included in the previous two models such as containing strict restrictions in its parametric component, complete flexibility in its non-parametric component, and clarity of the interaction between its parametric and non-parametric components. According to the above, two methods were used to estimate a semi-parametric balanced longitudinal data model. The first is the Bayesian estimating method; the second is the Speckman method, which estimated the unknown nonparametric smoothing function by employing the kernel smoothing Nadaraya & Watson method. The Aim was to make a comparison between the Bayesian estimation method and the classical estimation method. Based on simulation experiments conducted on three different sample sizes (50, 100, and 200), it was concluded that the Bayes method is best at the variance levels (1,5). In contrast, the Profile least square method is best at the variance level (10).

Semi-parametric Model to Study the Risk Factors of Tuberculosis among Adult men in South Africa

Background: Understanding the relationship between tuberculosis and the risk factors of tuberculosis is vital to be able to address them. Even though tuberculosis is curable and preventable, it remains a public threat, especially in low- and middle-income countries. There are more cases of men infected with tuberculosis compared to women. Methods: This study determines the risk factors that influence TB infection among adult men in South Africa. The Generalized Additive Mixed Models that incorporate a nonparametric smooth additive function were used to analyze the 2016 South African Demographic Health Survey. The Generalized Additive Model and Generalized Additive Mixed Model were compared to find the most suitable model. Results: The finding reveals that the significant determinates associated with tuberculosis were: region, primary education compared to secondary, race, health, weight, and wealth index, which were modeled parametrically. The conclusion is that only the interaction effect of age and number of times away from home were significant in variables modeled non-parametrically. Conclusion: In conclusion, the South African government needs to intervene on men living in Western Cape, Eastern Cape, Northern Cape, Free State, and men with poor health - to reduce South Africa’s infections. The government should also implement programs that will teach and discourage lower body mass index. Thus, targeting the factors that have a positive significant effect among adult men can help to reduce the risk of having tuberculosis.

Health effect assessment of PM2.5 pollution due to vehicular traffic (case study: Isfahan)

IntroductionAir pollution is the most challenging issue in megacities worldwide. Isfahan is the third most populated city in Iran, and its pollution is a leading cause of many diseases and deaths, and economic problems every year. Root cause analysis of air pollution can help the government and legislators make laws for reducing air pollution. As critical factors play an important role in fine particulate matter (PM2.5) emission, traffic parameters should be essential in air pollution modeling. MethodsThe generalized additive model (GAM), as a flexible statistical model, is implemented to demonstrate non-linear and linear relationships between response and predictive variables by nonparametric smooth functions. Traffic counts and meteorological and spatial variables were considered independent variables in this research. Regarding evaluating the health outcomes of air pollution due to traffic, the AirQ+ model is implemented. ResultsThis research was applied for Isfahan in the two years from 2018 to 2020 based on experimental data. The results indicated that the models could explain 54%–69% of PM2.5 concentrations in different areas. In Isfahan's southern and central regions, the effect of traffic on PM2.5 pollution was more. Low values of temperature also affected concentration pollution. Moreover, the model was estimated seasonally for further investigation. Also, annual premature mortality attributed to PM2.5 due to traffic is 150 and 157 cases over two years. ConclusionsThe results show the health impacts of air pollution due to vehicular PM2.5 emissions are remarkable.

Kernel estimator and predictor of partially linear mixed-effect errors-in-variables model

This paper considers the partially linear mixed-effect model relating a response Y to predictors with mean function which is a combination of the linear mixed-effect model and the nonparametric smooth function. The proposed model contains an additive measurement error in X. Taavoni and Arashi (Kernel estimation in semiparametric mixed-effect longitudinal modelling. Statist Papers. 2019. Available from: https://doi.org/10.1007/s00362-019-01125-8.) approximated the nonparametric function by the profile kernel method, and made use of the weighted least squares to estimate the regression coefficients when measurement error was ignored. We derive a simple modification of their estimators by correction for attenuation stems from measurement error and demonstrate that the linear parts estimator is asymptotically normal.

Multivariate t semiparametric mixed-effects model for longitudinal data with multiple characteristics

Semiparametric mixed-effects models (SMM) have received increasing attention in recent years because of the greater flexibility in analysing longitudinal trajectories. However, the normality assumption of SMM may be unrealistic when outliers occur in the data. This paper presents a semiparametric extension of the multivariate t linear mixed-effects model (MtLMM), called the multivariate t semiparametric mixed model (MtSMM). To be specific, the MtSMM incorporates a parametric linear function related to the fixed covariate effects and random effects which have a joint multivariate t distribution together with an arbitrary nonparametric smooth function to capture the unexpected patterns. A computationally analytical EM-based algorithm is developed for carrying out maximum likelihood estimation of the MtSMM. Simulation studies and a real example concerning the analysis of PBCseq data are used to investigate the empirical behaviour of the proposed methodology.

Kernel estimation in semiparametric mixed effect longitudinal modeling

HIV damages the immune system by targeting the CD4 cells. Hence CD4 count data modeling is important in the analysis of HIV infection. This paper considers a semiparametric mixed effects model for the analysis of CD4 longitudinal data. The model is a natural extension to the linear mixed and semiparametric models that uses parametric linear model to present the covariate effects and an arbitrary nonparametric smooth function to model the time effect and account for the within subject correlation using random effects. We approximate the nonparametric function by the profile kernel method, and make use of the weighted least squares to estimate the regression coefficients. Under some regularity conditions, the asymptotic normality of the resulting estimator is established and the performance is compared with the backfitting method. Although, two estimators share the same asymptotic variance matrix for independent data, it is shown that, backfitting often produces larger bias and variance than the profile-kernel method, asymptotically. Consequently, the use of backfitting method is no longer advised in semiparametric mixed effect longitudinal model. For practical implementation and also improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed methods are compared through a simulation study and the analysis of CD4 data.

A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS

ABSTRACTWe propose a new semiparametric Weibull cure rate model for fitting nonlinear effects of explanatory variables on the mean, scale and cure rate parameters. The regression model is based on the generalized additive models for location, scale and shape, for which any or all distribution parameters can be modeled as parametric linear and/or nonparametric smooth functions of explanatory variables. We present methods to select additive terms, model estimation and validation, where all computational codes are presented in a simple way such that any R user can fit the new model. Biases of the parameter estimates caused by models specified erroneously are investigated through Monte Carlo simulations. We illustrate the usefulness of the new model by means of two applications to real data. We provide computational codes to fit the new regression model in the R software.

Additive mixed models to study the effect of tree age and climatic factors on stem radial growth of Eucalyptus trees

The effect of tree age and climatic variables on stem radial growth of two hybrid clones of Eucalyptus was determined using longitudinal data from eastern South Africa. The stem radius of was measured weekly as the response variable. In addition to tree age, average weekly temperature, solar radiation, relative humidity and wind speed were simultaneously recorded with total rainfall at the site. An additive mixed effects model that incorporates a non-parametric smooth function was used. The results of the analysis indicate that the relationship between stem radius and each of the covariates can be explained by nonlinear functions. Models that account for the effect of clone and season together with their interaction in the parametric part of the additive mixed model were also fitted. The interaction between clone and season was not significant in all cases. For analyzing the joint effect all the covariates, additive mixed models that included two or more covariates were fitted. A significant effect of tree age was found in all cases. Although tree age was the key determinant of stem radial growth, weather variables also had a significant effect that was dependent on season.

Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model

Nonlinear effects between explanatory and response variables are increasingly present in new surveys. In this paper, we propose a flexible four-parameter semi-parametric cure rate survival model called the sinh Cauchy cure rate distribution. The proposed model is based on the generalized additive models for location, scale and shape, for which any or all parameters of the distribution are parametric linear and/or nonparametric smooth functions of explanatory variables. The new model is used to fit the nonlinear behavior between explanatory variables and cure rate. The biases of the cure rate parameter estimates caused by not incorporating such non-linear effects in the model are investigated using Monte Carlo simulations. We discuss diagnostic measures and methods to select additive terms and their computational implementation. The flexibility of the proposed model is illustrated by predicting lifetime and cure rate proportion as well as identifying factors associated to women diagnosed with breast cancer.

A flexible semiparametric regression model for bimodal, asymmetric and censored data

ABSTRACTIn this paper, we propose a new semiparametric heteroscedastic regression model allowing for positive and negative skewness and bimodal shapes using the B-spline basis for nonlinear effects. The proposed distribution is based on the generalized additive models for location, scale and shape framework in order to model any or all parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. We motivate the new model by means of Monte Carlo simulations, thus ignoring the skewness and bimodality of the random errors in semiparametric regression models, which may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. An iterative estimation process and some diagnostic methods are investigated. Applications to two real data sets are presented and the method is compared to the usual regression methods.

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis

ABSTRACTThe gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

Generating Health Estimates by Zip Code: A Semiparametric Small Area Estimation Approach Using the California Health Interview Survey

We propose a method to meet challenges in generating health estimates for granular geographic areas in which the survey sample size is extremely small. Our generalized linear mixed model predicts health outcomes using both individual-level and neighborhood-level predictors. The model's feature of nonparametric smoothing function on neighborhood-level variables better captures the association between neighborhood environment and the outcome. Using 2011 to 2012 data from the California Health Interview Survey, we demonstrate an empirical application of this method to estimate the fraction of residents without health insurance for Zip Code Tabulation Areas (ZCTAs). Our method generated stable estimates of uninsurance for 1519 of 1765 ZCTAs (86%) in California. For some areas with great socioeconomic diversity across adjacent neighborhoods, such as Los Angeles County, the modeled uninsured estimates revealed much heterogeneity among geographically adjacent ZCTAs. The proposed method can increase the value of health surveys by providing modeled estimates for health data at a granular geographic level. It can account for variations in health outcomes at the neighborhood level as a result of both socioeconomic characteristics and geographic locations.

Kernel density surface modelling as a means to identify significant concentrations of vulnerable marine ecosystem indicators.

The United Nations General Assembly Resolution 61/105, concerning sustainable fisheries in the marine ecosystem, calls for the protection of vulnerable marine ecosystems (VME) from destructive fishing practices. Subsequently, the Food and Agriculture Organization (FAO) produced guidelines for identification of VME indicator species/taxa to assist in the implementation of the resolution, but recommended the development of case-specific operational definitions for their application. We applied kernel density estimation (KDE) to research vessel trawl survey data from inside the fishing footprint of the Northwest Atlantic Fisheries Organization (NAFO) Regulatory Area in the high seas of the northwest Atlantic to create biomass density surfaces for four VME indicator taxa: large-sized sponges, sea pens, small and large gorgonian corals. These VME indicator taxa were identified previously by NAFO using the fragility, life history characteristics and structural complexity criteria presented by FAO, along with an evaluation of their recovery trajectories. KDE, a non-parametric neighbour-based smoothing function, has been used previously in ecology to identify hotspots, that is, areas of relatively high biomass/abundance. We present a novel approach of examining relative changes in area under polygons created from encircling successive biomass categories on the KDE surface to identify “significant concentrations” of biomass, which we equate to VMEs. This allows identification of the VMEs from the broader distribution of the species in the study area. We provide independent assessments of the VMEs so identified using underwater images, benthic sampling with other gear types (dredges, cores), and/or published species distribution models of probability of occurrence, as available. For each VME indicator taxon we provide a brief review of their ecological function which will be important in future assessments of significant adverse impact on these habitats here and elsewhere.

Catchability of snow crab (Chionoecetes opilio) by the eastern Bering Sea bottom trawl survey estimated using a catch comparison experiment

Catchability of the eastern Bering Sea (EBS) bottom trawl survey for snow crab (Chionoecetes opilio) was estimated from experimental data to provide a constraint on the survey catchability parameters in the stock assessment model. The experiment utilized a second fishing vessel to conduct side-by-side trawling with each of two survey vessels at 92 stations using an experimental trawl assumed to capture all crabs in its path. Trawl efficiency, or the captured proportion of crabs in the trawl path, was estimated for the 83-112 Eastern otter trawl from experimental data using a nonparametric smooth function of carapace width, sediment size, and depth. Survey catchability was then estimated as the catch-weighted average of the predicted trawl efficiency at all 275 survey stations where snow crabs were captured. The fitted model indicated that trawl selectivity was greater in sand than mud and greater in shallow water than deep. At a carapace widths >95 mm, the minimum commercial size limit, the estimated survey catchability of males is considerably less than previously reported.

Using semiparametric‐mixed model and functional linear model to detect vulnerable prenatal window to carcinogenic polycyclic aromatic hydrocarbons on fetal growth

Prenatal exposure to carcinogenic polycyclic aromatic hydrocarbons (c-PAHs) through maternal inhalation induces higher risk for a wide range of fetotoxic effects. However, the most health-relevant dose function from chronic gestational exposure remains unclear. Whether there is a gestational window during which the human embryo/fetus is particularly vulnerable to PAHs has not been examined thoroughly. We consider a longitudinal semiparametric-mixed effect model to characterize the individual prenatal PAH exposure trajectory, where a nonparametric cyclic smooth function plus a linear function are used to model the time effect and random effects are used to account for the within-subject correlation. We propose a penalized least squares approach to estimate the parametric regression coefficients and the nonparametric function of time. The smoothing parameter and variance components are selected using the generalized cross-validation (GCV) criteria. The estimated subject-specific trajectory of prenatal exposure is linked to the birth outcomes through a set of functional linear models, where the coefficient of log PAH exposure is a fully nonparametric function of gestational age. This allows the effect of PAH exposure on each birth outcome to vary at different gestational ages, and the window associated with significant adverse effect is identified as a vulnerable prenatal window to PAHs on fetal growth. We minimize the penalized sum of squared errors using a spline-based expansion of the nonparametric coefficient function to draw statistical inferences, and the smoothing parameter is chosen through GCV.

Abstract P379: Adiposity Tracking and Its Heritability: A Longitudinal Study of Rural Chinese Children and Adolescents

Objectives: Examine adiposity tracking and estimate its heritability in a large prospective cohort of pre-pubertal and pubertal rural Chinese children. Methods: This report included 1317 children and adolescents from the Anqing region of China, aged 6 to 18 years at baseline, who also completed follow-up visit 6 years later. Anthropometric measures included body mass index (BMI), waist circumference (WC), total body fat (TBF), percent body fat (%BF), trunk fat (TRF), and percent trunk fat (%TRF). Adiposity measures were obtained by dual-energy X-ray absorptiometry (DEXA). Locally weighted nonparametric smoothing function (SAS LOESS, SAS Institute, Cary, NC, USA) were used to describe (1) “tracking” of adiposity measurements from baseline to 6-year follow-up, and (2) gender differences in the growth of adiposity measurements across age. Structural equation modeling was used to estimate the heritability of tracking using the software Mx. Results: All anthropometric measures, except for %TRF, tracked significantly from baseline to follow-up in both genders. The middle baseline tertile, in general, had the lowest degree of tracking. Subjects in a high baseline tertile for BMI, TBF, %TBF, WC, and TRF were significantly more likely to be in the high tertile of TBF, %TBF, TRF at the follow-up. There was no good predictor for %TRF. Gender and pubertal status did not affect tracking, for TBF in females, and WC in the older age-group. The genetic correlation of BMI=0.60 (0.46-0.72); TBF=0.43 (0.29-0.55); %TBF=0.37 (0.23-0.50); WC=0.35 (0.11-0.56); TR=0.41 (0.27-0.54); and %TR=0.33 (0.07-0.59). Conclusion: The strong tracking of adiposity measures in this pediatric population underscores the importance of closely monitoring individuals with high BMI or adiposity over time; those in the medium tertile should also be monitored for upward trend due to their “mobility”. Only BMI showed a strong genetic correlation between baseline and followup, suggesting that environmental changes can influence adiposity depots. Our data raises the possibility that individuals at risk of adult obesity can be identified at early age so that early intervention can be initiated to prevent or mitigate obesity and related complications.

Association between temperature and daily mortality in Guangzhou, 2006-2009: a time-series study

To study the association between temperature and daily mortality from June 1, 2006 to December 31, 2009 in Guangzhou. Time series approach was used to estimate the impact of temperature on the rates of total and cause-specific daily mortality. We fitted generalized additive Poisson regression using non-parametric smooth functions to control for the long-term time trend, day of week, air pollution and other weather variables. A slight sloping U-like relationship between the total mortality and temperature was found, with an optimum average temperature (temperature with lowest mortality risk) value of 19.7°C in Guangzhou. For temperature above the optimum value, the relative risk of total mortality increased by 3.0% (RR=1.030, 95%CI: 1.011-1.050) for each increase of degree in Celsius. For average temperature below the optimum value, the relative risk of total mortality and diseases of circulatory system had a 3.3% (RR=0.967, 95%CI: 0.936-0.997) decrease and a 3.6% (RR=0.964, 95%CI: 0.935-0.994) increase, for each degree of Celsius increase, respectively. Our findings showed that the temperature had an impact on the daily mortality in Guangzhou. Countermeasures needed to be taken to reduce the temperature related mortality.

QUALITY AND ECONOMIES OF SCALE IN HIGHER EDUCATION: A SEMIPARAMETRIC SMOOTH COEFFICIENT ESTIMATION

I. INTRODUCTION Institutions of higher education comprise knowledge creation (research) and knowledge dissemination (teaching). Thus, the university's mission is to deliver quality undergraduate and graduate education and to expand the frontier of academic research. Numerous studies (Verry and Layard 1975; Cohn, Rhine, and Santos 1989; deGroot McMahon, and Volkin 1991; Nelson and Hevert 1992; Lloyd, Morgan, and Williams 1993; Dundar and Lewis 1995; Koshal and Koshal 1995, 1999) have investigated, as in the case of firms, the multiple-product cost function of producing the vector of outputs on undergraduate and graduate education and research. The cost structure of higher education is studied via the scale economies and the scope economies of the cost function. However, these measures of scale and scope economies may be elusive if the quality dimension of colleges and universities is not considered. Without taking into account the quality variation, in the short-run, a university can reduce the average cost of operation by lowering the quality. Universities with more congested educational facilities are substituting facility utilization for capital; universities with a higher student/faculty ratio and less research engagement are substituting quality of education for quantity of undergraduate and graduate enrollment. The consequence is an upward bias in estimating the economies of scale and scope. This conclusion is consistent with the early studies of Nelson and Hevert (1992) which showed that failure to control for class size in cost function may result in specification bias, and an economy of scale is evident if class size is allowed to expand. Quality of higher education is multidimensional. Quality in instruction, faculty research, and the quality of educational environment are all significant factors determining the long-run university cost structure and the crucial determinants of the scale and scope economies of higher education. How and to what extent quality affects a university's operating cost depends on the goal and orientation of the institutions. Higher quality increases the university's cost of operation. But, in a large research-oriented university, a disproportional share of the budget often benefits the graduate, not the undergraduate program. It is unrealistic to assume that quality affects only the average cost and that the marginal costs of various educational programs are independent of quality. Quality is unlikely to be simply a neutral cost-shifting factor. The purpose of this paper is to propose a university cost function and a semiparametric-estimating technique that treats quality as a nonneutral cost-shifting factor, which directly affects the marginal cost of outputs in undergraduate and graduate education. More precisely, the marginal costs of outputs are specified as a nonparametric smooth function of quality. A semiparametric specification of university cost is applied to 56 comprehensive and science/technology universities in Taiwan over the period 2000-2003. II. SEMIPARAMETRIC COST FUNCTION AND ESTIMATION TECHNIQUE Following the conventional multiproduct cost specification for higher education (Cohn, Rhine, and Santos 1989; deGroot, McMahon, and Volkin 1991; Lloyd, Morgan, and Williams 1993; Dundar and Lewis 1995; Koshal and Koshal 1995, 1999), the total cost (C) is specified as a quadratic function of outputs, undergraduate and graduate enrollments. However, the quadratic cost function is modified by allowing for the coefficients to be functions of quality in the following form: (1) C = [[beta].sub.0](Q) + [k.summation over i=1] [[beta].sub.i](Q)[Y.sub.i] + (1/2) X [k.summation over i=1], [k.summation over j=1], [[beta].sub.ij](Q)[Y.sub.i][Y.sub.j] + [m.summation over i=1], [[alpha].sub.i][Z.sub.i] + [epsilon] where C is the total cost of producing k educational outputs (Y), and [Z.sub.i] is the ith institutional characteristics. …

Robust likelihood inference for regression parameters in partially linear models

A robust likelihood approach is proposed for inference about regression parameters in partially-linear models. More specifically, normality is adopted as the working model and is properly corrected to accomplish the objective. Knowledge about the true underlying random mechanism is not required for the proposed method. Simulations and illustrative examples demonstrate the usefulness of the proposed robust likelihood method, even in irregular situations caused by the components of the nonparametric smooth function in partially-linear models.