Partially Linear Models Research Articles

Kernel density estimation for partial linear multivariate responses models

We propose a kernel density based estimation by constructing a nonparametric kernel version of the maximum profile likelihood estimator for partial linear multivariate responses regression models. The method proposed in this article makes use of multivariate kernel smoothing nonparametric techniques to estimate the unknown multivariate density function. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. We illustrate our proposals through simulations and an analysis of the energy efficiency data. Our analysis provides strong evidence that the proposed kernel density based estimator is superior than the profile least squares estimator, particularly for multimodal or heavy-tailed distributions of the model errors.

Modelling and applications for non-stationary time series in the presence of trend and period

In this paper, we study the estimation of the non-stationary time series in the presence of trend and period. We write the classical decomposition time series model as a partial linear model with an unknown parameter. Then we approximate the trend term with B-spline and obtain the estimators of the period, periodic sequence and trend. The asymptotic behaviors of the estimators are given in our paper, including the consistency of period estimation and the asymptotic behavior of the estimated periodic sequence and trend. We illustrate the superiority of our method through simulations and the applications to two real data examples show the utility of our method.

Foveal changes in aquaporin-4 antibody seropositive neuromyelitis optica spectrum disorder are independent of optic neuritis and not overtly progressive.

Foveal changes were reported in aquaporin-4 antibody (AQP4-Ab) seropositive neuromyelitis optica spectrum disorder (NMOSD) patients; however, it is unclear whether they are independent of optic neuritis (ON), stem from subclinical ON or crossover from ON in fellow eyes. Fovea morphometry and a statistical classification approach were used to investigate if foveal changes in NMOSD are independent of ON and progressive. This was a retrospective longitudinal study of 27 AQP4-IgG + NMOSD patients (49 eyes; 15 ON eyes and 34 eyes without a history of ON [NON eyes]), follow-up median (first and third quartile) 2.32 (1.33-3.28), and 38 healthy controls (HCs) (76 eyes), follow-up median (first and third quartile) 1.95 (1.83-2.54). The peripapillary retinal nerve fibre layer thickness and the volume of combined ganglion cell and inner plexiform layer as measures of neuroaxonal damage from ON were determined by optical coherence tomography. Nineteen foveal morphometry parameters were extracted from macular optical coherence tomography volume scans. Data were analysed using orthogonal partial least squares discriminant analysis and linear mixed effects models. At baseline, foveal shape was significantly altered in ON eyes and NON eyes compared to HCs. Discriminatory analysis showed 81% accuracy distinguishing ON vs. HCs and 68% accuracy in NON vs. HCs. NON eyes were distinguished from HCs by foveal shape parameters indicating widening. Orthogonal partial least squares discriminant analysis discriminated ON vs. NON with 76% accuracy. In a follow-up of 2.4 (20.85) years, no significant time-dependent foveal changes were found. The parafoveal area is altered in AQP4-Ab seropositive NMOSD patients suggesting independent neuroaxonal damage from subclinical ON. Longer follow-ups are needed to confirm the stability of the parafoveal structure over time.

Detection the symmetry or asymmetry of model errors in partial linear models

In this paper, we propose a residual-based estimator of k-th correlation coefficient between the density function and distribution function of a continuous variable for partial linear regression models, and further we use this k-th correlation coefficient to test whether the density function of the true model error is symmetric or not. First, we propose a moment based estimator of k-th correlation coefficient and present its asymptotic results. Second, we consider statistical inference of k-th correlation coefficient by using the empirical likelihood method, and the empirical likelihood statistic is shown to be asymptotically distributed as Chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators.

Variable selection for partially linear models via Bayesian subset modeling with diffusing prior

Most existing methods of variable selection in partially linear models (PLM) with ultrahigh dimensional covariates are based on partial residuals, which involve a two-step estimation procedure. While the estimation error produced in the first step may have an impact on the second step, multicollinearity among predictors adds additional challenges in the model selection procedure. In this paper, we propose a new Bayesian variable selection approach for PLM. This new proposal addresses those two issues simultaneously as (1) it is a one-step method which selects variables in PLM, even when the dimension of covariates increases at an exponential rate with the sample size, and (2) the method retains model selection consistency, and outperforms existing ones in the setting of highly correlated predictors. Distinguished from existing ones, our proposed procedure employs the difference-based method to reduce the impact from the estimation of the nonparametric component, and incorporates Bayesian subset modeling with diffusing prior (BSM-DP) to shrink the corresponding estimator in the linear component. The estimation is implemented by Gibbs sampling, and we prove that the posterior probability of the true model being selected converges to one asymptotically. Simulation studies support the theory and the efficiency of our methods as compared to other existing ones, followed by an application in a study of supermarket data.

Study of Some Factors Affecting on the Chickenpox Cases by Using the Partial Linear Regression Model

Chickenpox is classified as a transmission disease, especially young ages from three months to 15 years old. This study clarifies the effect of the area, population, and the number of the health centers on the number of cases of chickenpox disease in the Rusafa district, Baghdad, Iraq. We use the Partial Linear Model (PLM) that divides the independent variables into two parts (parametric and non-parametric). Moreover, choosing the best model that represents data of the chickenpox disease, using criteria (R2, Bic, Aic) from six models. The results of the study show a positive relation between the number of cases and number of health centers.

A projection-based consistent test incorporating dimension-reduction in partial linear models

A projection-based consistent test incorporating dimension-reduction in partial linear models

Age estimation of barramundi (

The age of whole otoliths from barramundi (Lates calcarifer) obtained from the southern Gulf of Carpentaria were estimated using Fourier transform near-infrared (FT-NIR) spectroscopy. Otoliths from 1716 barramundi collected in 2006, 2009 and 2012–2015 were used in this study. Partial least-squares regression models (PLS-R) and multiple linear regression models (MLR) were developed from the diffuse reflectance spectra and the age was obtained from traditional sectioned otoliths. Calibration models were built up over consecutive years (2012–2015) by using a subset of the samples and used to predict the age of the remaining samples and samples from the following year. Results suggest that when seasonal (temporal) variability is incorporated into the calibration model, FT-NIR has the ability to predict barramundi age (validation R2 ranged from 0.73 to 0.78; RMSEP ranged from 6.92 to 7.64 months). The predicted age class was within 1 year of the reference age in over 96% of the samples. These models were also able to predict the age of otoliths from 2006 and 2009, which were retrieved from long-term storage (validation R2 ranged from 0.77 to 0.84; RMSEP ranged from 8.66 to 10.88 months). The results from this study have shown the potential for barramundi from the southern Gulf of Carpentaria to be aged quickly and accurately by using FT-NIR.

Identification for partially linear regression model with autoregressive errors

The semiparametric partial linear models are often used in real data analysis for its flexibility and parsimony. Statistical inference of this model is restricted with two conditions: (i) the linear and nonlinear parts are known in advance, (ii) the errors are independent. However, in practice, this is unreasonable to artificially determine which subset of variables have linear effect on the response and which have nonlinear effect. In addition, the assumption of errors being independent may be incorrect for time series data. Therefore, it is of great interest to develop some efficient methods to distinguish linear components from nonlinear ones with correlated errors. In this paper, we develop a method for identifying linear and nonlinear components, and estimate the coefficients of error structure. The performance of the proposed method is examined by simulation study and analyses a real data set for an illustration.

Financing innovative development of the African economies: the role of digitalization and financial innovations

The article examines the relationship between financial innovation (mobile banking) variables in sub-Saharan Africa. Mobile banking (also known as mobile money) is one of the main financial innovations in the sub-Saharan region, and it is a system through which non-bank residents (residents without bank accounts, etc.) receive financial services. The overall importance of financial innovation in today’s digital and knowledge-based economy, and indeed, innovative development, inspired this study. Using a partial linear regression model, we analysed the International Monetary Fund data set, the World Bank’s national economic data, and mobile banking data from GSMA for the period from 2011 to 2017. A negative correlation was found between these variables and growth, as well as financial development, but a positive relationship was established between financial development and economic development. This positive relationship re-confirms the argument that financial development affects economic growth. It is recommended that policy makers develop and implement the necessary policy tools that can promote this form of financial innovation, and thus link its benefits to the national economy in general.

Locally efficient semiparametric estimator for zero-inflated Poisson model with error-prone covariates

Overdispersion is a common phenomenon in count or frequency responses in Poisson models. For example, number of car accidents on a highway during a year period. A similar phenomenon is observed in electric power systems, where cascading failures often follows some distribution with inflated zero. When the response contains an excess amount of zeros, zero-inflated Poisson (ZIP) is the most favourable model. However, during the data collection process, some of the covariates cannot be accessed directly or are measured with error among numerous disciplines. To the best of our knowledge, little existing work is available in the literature that tackles the population heterogeneity in the count response while some of the covariates are measured with error. With the increasing popularity of such outcomes in modern studies, it is interesting and timely to study zero-inflated Poisson models in which some of the covariates are subject to measurement error while some are not. We propose a flexible partial linear single index model for the log Poisson mean to correct bias potentially due to the error in covariates or the population heterogeneity. We derive consistent and locally efficient semiparametric estimators and study the large sample properties. We further assess the finite sample performance through simulation studies. Finally, we apply the proposed method to a real data application and compare with existing methods that handle measurement error in covariates.

The Environmental Kuznets Curve with Recycling: A Partially Linear Semiparametric Approach

This paper is the first to study a comparatively new Environmental Kuznets Curve which traces empirically the relationship between environmental abatement and real GDP. Our model is a partial linear semi parametric model that allows for two way fixed effects to eliminate the bias arising from two sources. We use data for recycling and real GDP, for fifty states of the United States for the years between 1988 and 2017. We find evidence that this relationship is characterized by an increasing curve which confirms the existence of a J curve, a finding that agrees with the predictions from recent theoretical models.

Association between cardiorespiratory fitness and cardiometabolic risk factors in Brazilian children and adolescents: the mediating role of obesity parameters

ABSTRACT Background There is a lack of clarity as to which obesity parameters may be more important in the association between cardiorespiratory fitness (CRF) and cardiometabolic risk factors (CMRF). Aim To verify the mediating role of different obesity parameters on the association between CRF and CMRF in normal weight and overweight/obese children and adolescents. Methods This cross-sectional study comprised 999 children and adolescents (534 boys) aged 7–14 years from the south of Brazil. Body mass index (BMI), waist circumference (WC), waist-to-height ratio (WHtR) and percentage of body fat were assessed. Participants were classified as normal weight, overweight and obese according to BMI. CRF was evaluated by the 6-minute run/walk test. . A continuous CMRF score was calculated by summing the Z-scores of the following variables: systolic and diastolic blood pressure, glucose, total cholesterol, high-density lipoprotein cholesterol and triglycerides. Data analysis was performed using partial correlation and linear regression models. Results BMI, WC, WHtR and percentage of body fat mediated the relationship between CRF and CMRF in overweight/obese boys and girls but not those of normal weight. Additionally, the percentage of the influence of each obesity parameter was 20% for BMI and WC, 16% for percentage of body fat and 18% for WHtR in girls. For boys, the mediation effect was 25% for BMI, 26% for WC, 28% for percentage of body fat and 25% for WHtR. Conclusion Adiposity plays a central role in CMRF; therefore, maintaining an adequate weight status should be an important objective of health-promoting programmes in early age. Abbreviations: CMRF, cardiometabolic risk factors; CRF, cardiorespiratory fitness; BMI. body mass index; HDL-c, high-density lipoprotein cholesterol, PROCESS PROESP-Br, Projeto Esporte Brasil; SPSS, Package for Social Sciences; TC, total cholesterol; TG, triglycerides; WC, waist circumference; WHtR, waist-to-height ratio; %BF, percentage of body fat.

Using the Generalized Partial Linear Regression Model to Determine Climatic Factor Effect on Dust Storms in Baghdad Governorate

The phenomenon of dust that occurs in Iraq is one of the phenomena that cannot be completely controlled or partially processed in a short time. It also works to know how some climatic factors such as the average wind speed, relative humidity, atmospheric pressure above sea level, and the maximum temperature which represent explanatory (independent) variables , respectively. The effects on the number of occurrences of dust storms represent the adopted variable (Y) in Baghdad Governorate for the period from 2008 to mid-2013. The researchers used the Generalized Partial Linear Regression Model (GPLRM) consist of fourteen models, after determining the best link function for each model. Then we compared these models to determine the best model that represents this data with the best representation using the Akaike information criterion (AIC), the Schwartz information criterion (BIC), and the determination Coefficient criterion . We also used the program (i- xplore) in the calculation, and we have concluded that the best model is the model in which the variable relative humidity and the maximum temperature in the parametric part, i.e., linear and stable. On the other hand, the variable average wind speed and the variable atmospheric pressure above sea level are non-parametric and their behavior is non-linear and unstable. The researchers consider that Baghdad Governorate suffers from this negative phenomenon as well as in general in Iraq. Besides, the effect of the variable relative humidity is a decreasingly negative effect, while the effect of the variable maximum temperature, it is an increasingly positive effect.

Modal regression based robust empirical likelihood and variable selection for partial linear models with longitudinal data

Modal regression based robust empirical likelihood and variable selection for partial linear models with longitudinal data

Estimation in Partial Functional Linear Spatial Autoregressive Model

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.

Prediction of the xanthine oxidase inhibitory activity of celery seed extract from ultraviolet–visible spectrum using machine learning algorithms

Xanthine oxidase inhibitory activity of celery seed extract was predicted from UV–Vis spectrum using five different algorithms: multiple linear regression, artificial neural network, support vector regression, random forest and partial linear regression. The optimal parameters of each model established by these methods were examined carefully and the best model was selected. The results showed that the model obtained by partial linear regression had the best quality with coefficient of determination R2 = 0.9618, correlation coefficient of leave-one-out cross validation Q2 = 0.8746, average absolute deviation MAD = 0.0671, root mean square error RMSE = 0.0761 and the accuracy of the model with train and test were 99.29% and 96.69%, respectively. Our findings suggest that this model could be an effective method for rapidly determining xanthine oxidase inhibitory activity of herbal medicine, particularly celery seed extract from UV–Vis spectra. However, more investigations are required in order to improve the performance of the partial linear regression model.

Partial functional linear regression with autoregressive errors

In the presented paper, we introduce a partial functional linear model, where a scalar response variable is explained by a multivariate random variable and a functional random variable, and the relationship between the scalar response and both of the predictors is linear. Besides, the model has autoregressive errors. To estimate the model, we first expand the functional predictor and functional regression parametric on the functional principal component basis, and then estimate the coefficients for multivariate and functional regression parametric by a generalized least squares method. Theoretical properties are presented including the asymptotical normality for the multivariate coefficient and the optimal convergence rate for the functional regression parametric. Simulation studies are used to illustrate these characteristics. The proposed method is also applied on the power forecasting of photovoltaic systems data set.

A Typological Concept to Predict the Nitrogen Release from Organic Fertilizers in Farming Systems

The prediction of nitrogen (N) mineralization or immobilization in organic fertilizers is an important tool to optimize fertilizer use, especially in intensive agricultural systems. Our aim was to derive a model to predict the N mineralization/immobilization from readily available information on the properties of organic fertilizers in farming practice. On the basis of a literature review, a characterization of organic fertilizers was performed, revealing a large variance in fertilizer properties within the defined categories and subcategories. A partial linear model was derived and used for the prediction of N mineralization/immobilization based on the type of fertilizer and the carbon (C) to organic nitrogen (Norg) ratio. Depending on the previously defined category, a strong mineralization (e.g., plant- and animal-based commercial fertilizers) or a predominant immobilization (e.g., compost and slurries) was detected. For a total of seven main categories and their subcategories, individual models were developed. This work shows that the mineralization properties of organic fertilizers can be sufficiently predicted through a simple classification into a fertilizer category and through the C to Norg ratio.

Corrigendum to "Partial least squares and linear support vector regression chemometric models for analysis of Norfloxacin and Tinidazole with Tinidazole impurity" [Spectrochim. Acta A: Mol. Biomol. Spectrosc. Volume 239, 5 October 2020, 118513

Corrigendum to "Partial least squares and linear support vector regression chemometric models for analysis of Norfloxacin and Tinidazole with Tinidazole impurity" [Spectrochim. Acta A: Mol. Biomol. Spectrosc. Volume 239, 5 October 2020, 118513