Partially Linear Models Research Articles

Bayesian Adaptive Lasso for the Partial Functional Linear Spatial Autoregressive Model

This study introduces a partial functional linear spatial autoregressive model which can explore the relationship between a scalar spatially dependent response variable and predictive variables containing both multiple scalar covariates and a functional covariate. With approximating to the functional coefficient by Karhunen–Loève representation, we propose a Bayesian adaptive Lasso method to simultaneously estimate unknown parameters and select important covariates in the model, which can be performed by combining the Gibbs sampler and the Metropolis–Hastings algorithm. Some simulation studies are conducted and the results show that the proposed Bayesian method behaves well.

Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms

Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.

Weighted composite asymmetric Huber estimation for partial functional linear models

<abstract><p>In this paper, we first investigate a new asymmetric Huber regression (AHR) estimation procedure to analyze skewed data with partial functional linear models. To automatically reflect distributional features as well as bound the influence of outliers effectively, we further propose a weighted composite asymmetric Huber regression (WCAHR) estimation procedure by combining the strength across multiple asymmetric Huber loss functions. The slope function and constant coefficients are estimated through minimizing the combined loss function and approximating the slope function with principal component analysis. The asymptotic properties of the proposed estimators are derived. To realize the WCAHR estimation, we also develop a practical algorithm based on pseudo data. Numerical results show that the proposed WCAHR estimators can well adapt to the different error distributions, and thus are more useful in practice. Two real data examples are presented to illustrate the applications of the proposed methods.</p></abstract>

Estimation and group variable selection for additive partial linear models withwavelets and splines

In this paper we study sparse high dimensional additive partial linear models with nonparametric additive components of heterogeneous smoothness. We review several existing algorithms that have been developed for this problem in the recent literature, highlighting the connections between them, and present some computationally efficient algorithms for fitting such models. To achieve optimal rates in large sample situations we use hybrid P-splines and block wavelet penalisation techniques combined with adaptive (group) LASSO-like procedures for selecting the additive components in the nonparametric part of the models. Hence, the component selection and estimation in the nonparametric part may be viewed as a functional version of estimation and grouped variable selection. This allows to take advantage of several oracle results which yield asymptotic optimality of estimators in high-dimensional but sparse additive models. Numerical implementations of our procedures for proximal like algorithms are discussed. Large sample properties of the estimates and of the model selection are presented and the results are illustrated with simulated examples and a real data analysis. Keywords: Additive models, Backfitting, Penalisation, Proximal algorithms, Squared group-LASSO, Splines, Wavelets

Robust estimation for partial functional linear regression models based on FPCA and weighted composite quantile regression

Abstract In this paper, we consider a novel estimation for partial functional linear regression models. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. An efficient estimation based on principal component basis function approximation is used for minimizing the proposed weighted composite quantile regression (WCQR) objective function. Since the proposed WCQR involves a vector of weights, we develop a computational strategy for data-driven selection of the optimal weights. Under some mild conditions, the theoretical properties of the proposed WCQR method are obtained. The simulation study and a real data analysis are provided to illustrate the numerical performance of the resulting estimators.

Identification of subgroups via partial linear regression modeling approach.

In clinical trials, treatment effects often vary from subject to subject. Some subjects may benefit more than others from a specific treatment. One of the aims of subgroup analysis is to identify if there are subgroups of subjects with differential treatment effects. As in standard analysis, we first test if subgroups with differential treatment effects exist; if they do, we classify the subjects into different subgroups based on their covariate profiles; otherwise, we conclude no subgroups have differential treatment effects in this population. Existing methods utilize regression models, particularly linear models, for such analysis. However, in practice, not all effects of covariates on responses are linear. To address this issue, the article proposes a more flexible model, the partial linear model with a nonlinear monotone function to describe some specific effects of covariates and with a linear component to describe the effects of other covariates, develops model-fitting algorithm and derives model asymptotics. We then utilize the Wald statistic to test the existence of subgroups and the Neyman-Pearson rule to classify subjects into the subgroups. Simulation studies are conducted to evaluate the finite sample performance of the proposed method by comparing it with the commonly used linear models. Finally, we apply the methods to analyzing a real clinicaltrial.

Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

This research includes the Bayesian estimation of the parameters of the multivariate partial linear regression model when the random error follows the matrix-variate generalized modified Bessel distribution and found the statistical test of the model represented by finding the Bayes factor criterion, the predictive distribution under assumption that the shape parameters are known. The prior distribution about the model parameters is represented by non-informative information, as well as the simulate on the generated data from the model by a suggested way based on different values ​​of the shape parameters, the kernel function used in the generation was a Gaussian kernel function, the bandwidth (Smoothing) parameter was according to the rule of thumb. It found that the posterior marginal probability distribution of the location matrix and the predictive probability distribution is a matrix-t distribution with different parameters, the posterior marginal probability distribution of the scale matrix is proper distribution but it does not belong to the conjugate family, Through the Bayes factor criterion, it was found that the sample that was used in the generation process was drawn from a population that does not belong to the generalized modified Bessel population.

Comparison of Some Semi-parametric Methods in Partial Linear Single-Index Model

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

Bayesian model selection in additive partial linear models via locally adaptive splines

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model while simultaneously determining whether nonzero additive components should be represented as linear or non-linear components in the final model. In this paper, we propose a Bayesian model selection method that is facilitated by a carefully specified class of models, including the choice of a prior distribution and the nonparametric model used for the nonlinear additive components. We employ a series of latent variables that determine the effect of each variable among the three possibilities (no effect, linear effect, and nonlinear effect) and that simultaneously determine the knots of each spline for a suitable penalization of smooth functions. The use of a pseudo-prior distribution along with a collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo samplers, both for model selection and for fitting the preferred model. Our method and algorithm are deployed on a suite of numerical studies and are applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methods in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates.

Association of PAF and its Metabolic Enzymes with GGT and the Fatty Liver Index in Healthy Volunteers.

Platelet-activating-factor (PAF) is a lipid inflammatory mediator implicated in liver disease. Its main biosynthetic enzymes are cytidine diphosphate (CDP)-choline: 1-alkyl-2-acetyl-sn-glycerol-cholinephosphotransferase (PAF-CPT) and acetyl-coenzyme A: lyso-PAF-acetyltransferases (Lyso-PAF-AT). At the same time, PAF acetylhydrolase (PAF-AH) and lipoprotein-associated phospholipase A2 (Lp-PLA2 ) degrade PAF. To explore the relation of PAF metabolism with liver diseases and non-alcoholic fatty liver disease, as reflected by the fatty liver index (FLI). In 106 healthy volunteers, PAF concentration, the activity of its metabolic enzymes and gamma-glutamyl transferase (GGT) were measured in whole blood, leukocytes and serum, respectively and the FLI was calculated. Partial correlations and linear regression models were used. In males, serum GGT activity was positively correlated with abdominal fat (as assessed by analysis of a manually defined region of interest in dual-energy X-ray absorptiometry), triacylglycerols, bound-PAF and Lp-PLA2 , while the FLI was positively correlated with Lp-PLA2 activity. In females, serum GGT activity was negatively associated with high-density lipoprotein cholesterol (HDL-C) (age adjusted correlations, all p<0.05). Lp-PLA2 was a significant determinant of serum GGT activity in males after controlling for age, low- density lipoprotein cholesterol (LDL-C) and abdominal fat. The addition of bound-PAF in the model significantly increased the explained variance of serum GGT activity (total variance explanation 30%). Bound-PAF and Lp-PLA2 activity predicted serum GGT activity while Lp-PLA2 was also related to FLI. Our findings shed light on the metabolic pathways linking Lp-PLA2 to other atherosclerosis and/or oxidative markers, such as HDL-C, LDL-C, GGT and FLI and underline the important role of PAF.

Estimation on functional partially linear single index measurement error model

In this article, we investigate the functional partially linear single index model when measurement error exists in covariates. The main purpose of this article is to correct the biased estimators caused by additive error and construct the asymptotic properties of unknown parameters and function in model. Asymptotic distribution of the parametric component and the convergence rates of the nonparametric part are obtained under some regularity conditions. Compared with existing literatures in this field, such as functional partially linear and semi-functional partial linear regression model with measurement error, good performance in Tecator data analysis illustrates the advantages of the model and the significance of the proposed methodology. In this process, functional slice inverse regression is applied to estimate the functional single index parameter to improve computational efficiency. Furthermore, a simulation study is also carried out for demonstration.

Research on the Calculation Method of Harmonic Contribution in the Case of Dominant System-side Harmonics

Existing methods for quantifying the responsibility of harmonic sources assume a dominant user side and use a harmonic source equivalence circuit to calculate the equivalent system impedance and background harmonic voltage, which in turn assesses the harmonic contribution of that source to the bus of concern. For users who actively participate in harmonic governance, it is very important to evaluate the responsibility of injecting harmonics into users. This paper assumes system-side is dominant, constructs a partial linear regression model and a constant impedance model, and tracks the regression error. The equivalent fundamental impedance is doubly screened to calculate the harmonic impedance for the corresponding number of times, which in turn quantifies the harmonic voltage duty. The results of simulation and the analysis of measured data show that this method has simple calculation model, small regression error (0.0037), high accuracy and practical engineering significance.

Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline

Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline

Combining Remote Sensing and Meteorological Data for Improved Rice Plant Potassium Content Estimation

Potassium (K) plays a significant role in the formation of crop quality and yield. Accurate estimation of plant potassium content using remote sensing (RS) techniques is therefore of great interest to better manage crop K nutrition. To improve RS of crop K, meteorological information might prove useful, as it is well established that weather conditions affect crop K uptake. We aimed to determine whether including meteorological data into RS-based models can improve K estimation accuracy in rice (Oryza sativa L.). We conducted field experiments throughout three growing seasons (2017–2019). During each year, different treatments (i.e., nitrogen, potassium levels and plant varieties) were applied and spectra were taken at different growth stages throughout the growing season. Firstly, we conducted a correlation analysis between rice plant potassium content and transformed spectra (reflectance spectra (R), first derivative spectra (FD) and reciprocal logarithm-transformed spectra (log [1/R])) to select correlation bands. Then, we performed the genetic algorithms partial least-squares and linear mixed effects model to select important bands (IBs) and important meteorological factors (IFs) from correlation bands and meteorological data (daily average temperature, humidity, etc.), respectively. Finally, we used the spectral index and machine learning methods (partial least-squares regression (PLSR) and random forest (RF)) to construct rice plant potassium content estimation models based on transformed spectra, transformed spectra + IFs and IBs, and IBs + IFs, respectively. Results showed that normalized difference spectral index (NDSI (R1210, R1105)) had a moderate estimation accuracy for rice plant potassium content (R2 = 0.51; RMSE = 0.49%) and PLSR (FD-IBs) (R2 = 0.69; RMSE = 0.37%) and RF (FD-IBs) (R2 = 0.71; RMSE = 0.40%) models based on FD could improve the prediction accuracy. Among the meteorological factors, daily average temperature contributed the most to estimating rice plant potassium content, followed by daily average humidity. The estimation accuracy of the optimal rice plant potassium content models was improved by adding meteorological factors into the three RS models, with model R2 increasing to 0.65, 0.74, and 0.76, and RMSEs decreasing to 0.42%, 0.35%, and 0.37%, respectively, suggesting that including meteorological data can improve our ability to remotely sense plant potassium content in rice.

Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions.

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

Estimating equivalence scales and non-food needs in Egypt: Parametric and semiparametric regression modeling.

This paper investigated the appropriate specifications of Engel curves for non-food expenditure categories and estimated the deprivation indices of non-food needs in rural areas using a semi parametric examination of the presence of saturation points. The study used the extended partial linear model (EPLM) and adopted two estimation methods—the double residual estimator and differencing estimator—to obtain flexible shapes across different expenditure categories and estimate equivalence scales. We drew on data of the Egyptian Household Income, Expenditure, and Consumption Survey (HIEC). Our paper provides empirical evidence that the rankings of most non-food expenditure categories is of rank three at most. Rural households showed high economies of scale in non-food consumption, with child’s needs accounting for only 10% of adult’s non-food needs. Based on semi-parametrically estimated consumption behavior, the tendency of non-food expenditure categories to saturate did not emerge. While based on parametrically estimated consumption behavior, rural areas exhibited higher deprivation indices in terms of health and education expenditure categories, which indicates the need to design specific programs economically targeting such vulnerable households.

Generalized partial linear models with nonignorable dropouts

Generalized partial linear models with nonignorable dropouts

Bayes estimators of a multivariate generalized hyperbolic partial regression model

The matrix-variate generalized hyperbolic distribution belongs to the family of heavy-tailed mixed probability distributions and is considered to be one of the continuous skewed probability distributions. This distribution has wide applications in the field of economics, especially in stock modeling. This paper includes estimation the parameters of the multivariate semi-parametric regression model represented by the multivariate partial linear regression model when the random error follows the matrix-variate generalized hyperbolic distribution, using the Bayesian method when non???informative prior information is available and under the assumption that the shape parameters and the skewness matrix are known. In addition, the bandwidth parameter is estimated by a suggested way based on the normal distribution rule and the proposed kernel function based on the mixed Gaussian kernel function and studying the findings on the generated data in a way suggested for the model, comparing the estimators depending on the criterion of the mean sum of squares error. The two researchers concluded that the proposed kernel function is better than the Gaussian kernel function in estimate the parameters.

Isotonic quadriceps endurance is better associated with daily physical activity than quadriceps strength and power in COPD: an international multicentre cross-sectional trial

Knowledge about modifiable determinants of daily physical activity (PA) in patients with chronic obstructive pulmonary disease (COPD) is crucial to design effective PA interventions. The present study aimed to determine the contribution of quadriceps strength, power and endurance to daily PA in COPD. Additionally, for quadriceps endurance, we also aimed to determine to what extent the association varies according to the mode of movement (isotonic, isometric, or isokinetic). Using a multicentre cross-sectional trial design we determined the contribution of quadriceps function to daily PA (steps, sedentary time and time spent doing moderate-to-very-vigorous physical activity [MVPA]) using bivariate and partial Pearson correlation analysis (r) and multiple linear regression models (ΔR2). Pre-determined controlling factors were sex, age, body mass index (BMI), COPD-assessment test, forced expiratory volume in one second in percent of the predicted value (FEV1pred), and distance walked on the 6-minute walk test. Eighty-one patients with COPD (mean ± SD: age 67 ± 8 years, FEV1pred 57 ± 19%, daily steps 4968 ± 3319, daily sedentary time 1016 ± 305 min, and MVPA time 83 ± 45 min) were included. Small to moderate bivariate correlations (r = .225 to .452, p < .05) were found between quadriceps function and measures of PA. The best multiple linear regression models explained 38–49% of the variance in the data. Isotonic endurance was the only muscle contributor that improved all PA models; daily steps (ΔR2 = .04 [relative improvement 13%] p = .026), daily sedentary time (ΔR2 = .07 [23%], p = .005) and MVPA-minutes (ΔR2 = .08 [20%], p = .001). Isotonic endurance was also independently associated with most PA variables, even when controlling for strength, power or isometric-isokinetic endurance properties of the muscle (r = .246 to .384, p < .05). In contrast, neither strength, power, isometric-or isokinetic endurance properties of the muscle was independently associated with PA measures when controlling for isotonic endurance (r = .037 to .219, p > .05). To conclude, strength, power, and endurance properties of the quadriceps were low to moderately associated with PA in patients with COPD. Isotonic quadriceps endurance was the only quadriceps property that was independently associated with the different measures of PA after controlling for a basic set of known determinants of PA, quadriceps strength or power, or isometric or isokinetic quadriceps endurance. Future longitudinal studies should investigate its potential as a modifiable determinant of PA.