Functional Regression Model Research Articles

Time-variant associations of ambulatory pulse rate with short-term neurologic functional outcomes following acute ischemic stroke.

This study aims to assess the associations of functional outcomes following acute ischemic stroke (IS) with ambulatory pulse rate (PR) and characterize the time-variant properties of the associations. The prospective cohort consisted of 1831 patients who had ambulatory blood pressure (BP) and PR monitoring following acute IS, and neurologic status evaluated at discharge and 3-month follow-up. The neurologic disability was defined as modified Rankin Scale ≥3. Logistic regression and generalized penalized functional regression models were used to examine the associations of ambulatory BP and PR with neurologic disability. Adjusting for covariates, the neurologic disability at discharge and 3-month was associated with high average 24-h, daytime, and nocturnal PR (odds ratio, OR = 1.20-1.34; p < 0.05 for all), high standard derivation of nocturnal PR (OR = 1.19 and 1.32; p < 0.05 for both), and low nocturnal PR decline (OR = 0.76 and 0.76; p < 0.05 for both). The OR functions of ambulatory PR on neurologic disability were "W-shaped" from 0 a.m. to 12 p.m., with ORs >1 in the wee hours and at noon, and ORs <1 before dawn and at night. The ambulatory BP profiles were not associated with neurologic disability at discharge or 3-month. The ambulatory PR is associated with the risk of short-term neurologic disability of stroke patients, with four different phases in a 24-h cycle. Ambulatory PR monitoring, especially nocturnal PR monitoring, has significant clinical implications for the prevention of short-term neurologic disability in stroke inpatients.

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space.

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).

Estimating Knee Movement Patterns of Recreational Runners Across Training Sessions Using Multilevel Functional Regression Models

Modern wearable monitors and laboratory equipment allow the recording of high-frequency data that can be used to quantify human movement. However, currently, data analysis approaches in these domains remain limited. This article proposes a new framework to analyze biomechanical patterns in sport training data recorded across multiple training sessions using multilevel functional models. We apply the methods to subsecond-level data of knee location trajectories collected in 19 recreational runners during a medium-intensity continuous run (MICR) and a high-intensity interval training (HIIT) session, with multiple steps recorded in each participant-session. We estimate functional intra-class correlation coefficient to evaluate the reliability of recorded measurements across multiple sessions of the same training type. Furthermore, we obtained a vectorial representation of the three hierarchical levels of the data and visualize them in a low-dimensional space. Finally, we quantified the differences between genders and between two training types using functional multilevel regression models that incorporate covariate information. We provide an overview of the relevant methods and make both data and the R code for all analyses freely available online on GitHub. Thus, this work can serve as a helpful reference for practitioners and guide for a broader audience of researchers interested in modeling repeated functional measures at different resolution levels in the context of biomechanics and sports science applications.

Nomogram of intra-abdominal infection after surgery in patients with gastric cancer: A retrospective study.

BackgroundSurgical resection is still the primary way to treat gastric cancer. Therefore, postoperative complications such as IAI (intra-abdominal infection) are major problems that front-line clinical workers should pay special attention to. This article was to build and validate IAI’s RF (regression function) model. Furthermore, it analyzed the prognosis in patients with IAI after surgery for stomach cancer. The above two points are our advantages, which were not involved in previous studies.MethodsThe data of this study was divided into two parts, the training data set and the validation data set. The training data for this article were from the patients treated surgically with gastric cancer in our center from December 2015 to February 2017. We examined IAI’s morbidity, etiological characteristics, and prognosis in the training data set. Univariate and multivariate logistic regression analyses were used to screen risk factors, establish an RF model and create a nomogram. Data from January to March 2021 were used to validate the accuracy of the RF model.ResultsThe incidence of IAI was 7.2%. The independent risk factors for IAI were hypertension (Odds Ratio [OR] = 3.408, P = 0.001), history of abdominal surgery (OR = 2.609, P = 0.041), combined organ excision (OR = 4.123, P = 0.010), and operation time ≥240 min (OR = 3.091, P = 0.005). In the training data set and validation data set, the area under the ROC curve of IAI predicted by the RF model was 0.745 ± 0.048 (P<0.001) and 0.736 ± 0.069 (P=0.003), respectively. In addition, IAI significantly extended the length of hospital stay but had little impact on survival.ConclusionsPatients with hypertension, combined organ excision, a history of abdominal surgery, and a surgical duration of 240 min or more are prone to IAI, and the RF model may help to identify them.

Learning and generalizing demonstration trajectoriesbased on elastic analysis and the functional regression model

Learning from demonstration (LfD) has been confirmed to be an effective method for solving humanoid trajectory-planning problems under dynamic scenarios. Demonstrations, as functional data, can have coupled spatial and temporal features, which need to be treated carefully under the framework of functional data analysis. Previous studies in LfD use a separate pre-processing step to decouple spatial and temporal features. To fully utilize the intrinsic functional feature of demonstrations, an elastic method is used to extract their spatial and temporal features. Based on the decoupled spatial feature, a functional regression model is built to generate dynamic trajectories under varying task parameters. Experiments on a JACO-2 manipulator are conducted by performing different skills and fulfilling related tasks dynamically with new task-parameters. Results demonstrate that a category of humanoid LfD problems can be solved with a theoretically unified and applicable method.

Effect of Resource Productivity of Maize-Based Farmers on Poverty Reduction in South West, Nigeria

The ability of Nigerian agriculture to perform its role in the development of the economy has been on the decline in the last three decades. Therefore, the 2030 Agenda’s historic commitment to rid the world of the twin scourges of poverty and hunger cannot become a reality if nothing is done about improving resource productivity so as to reduce poverty. This article examined the effect of resource productivity of maize-based farmers on poverty reduction in South-West, Nigeria. Multi-stage sampling procedure was used to select 180 respondents and data were collected with the aid of a structured questionnaire. The stochastic frontier production function, poverty index and probit regression model were used to analyze data from the study. Results showed that age, farming experience, cooperative membership, credit, extension visits, farm distance, and land ownership were significant determinants of efficiency of maize-based farmers. The poverty incidence, poverty gap and poverty severity were 42%, 50% and 11.2% respectively. Results further showed that efficiency and other variables were significant determinants of poverty among respondents in the study area. Policies that facilitate increased production of maize, increased level of education, increased cooperative membership, and access to credit are essential to help reducing poverty among maize-based farmers and among the rural poor in general. Keywords: Maize-based farmers; Poverty; Probit regression; Resource-productivity, Stochastic frontier analysis. DOI: 10.7176/JESD/13-20-09 Publication date: October 31 st 2022

Non-invasive Hemoglobin Measurement Predictive Analytics with Missing Data and Accuracy Improvement Using Gaussian Process and Functional Regression Model.

Recent use of noninvasive and continuous hemoglobin (SpHb) concentration monitor has emerged as an alternative to invasive laboratory-based hematological analysis. Unlike delayed laboratory based measures of hemoglobin (HgB), SpHb monitors can provide real-time information about the HgB levels. Real-time SpHb measurements will offer healthcare providers with warnings and early detections of abnormal health status, e.g., hemorrhagic shock, anemia, and thus support therapeutic decision-making, as well as help save lives. However, the finger-worn CO-Oximeter sensors used in SpHb monitors often get detached or have to be removed, which causes missing data in the continuous SpHb measurements. Missing data among SpHb measurements reduce the trust in the accuracy of the device, influence the effectiveness of hemorrhage interventions and future HgB predictions. A model with imputation and prediction method is investigated to deal with missing values and improve prediction accuracy. The Gaussian process and functional regression methods are proposed to impute missing SpHb data and make predictions on laboratory-based HgB measurements. Within the proposed method, multiple choices of sub-models are considered. The proposed method shows a significant improvement in accuracy based on a real-data study. Proposed method shows superior performance with the real data, within the proposed framework, different choices of sub-models are discussed and the usage recommendation is provided accordingly. The modeling framework can be extended to other application scenarios with missing values.

Dynamic evolution and influencing factors of coupling coordination between innovation environment and transformation development of resource-based cities in Gansu province, China

Studying the internal relationship between the innovation environment and the transformation development of resource-based cities from the perspective of coupling and coordination helps reveal the mechanism between them, which is of great significance to sustainable development of resource-based cities. This study reconstructs the index system for innovative environment and transformation development. We used the coupling coordination degree model, Epanechnikov function, and panel quantile regression model to analyze the coupling coordination level, dynamic evolution characteristics, and influencing factors of innovative environment and transformation development of resource-based cities in Gansu Province from 2009 to 2019. The study shows that the innovation environment index and the transformation development index of resource-based cities increased significantly during the study period. The innovation environment index of resource-based cities has been greatly improved, showing a dynamic evolution trend of rapid growth and development characteristics of “low-level, fast growth”. There are differences in the characteristics of transformation development in resource-based cities, but on the whole, it shows a trend of increasing fluctuation. The state of coupling coordination has changed from a severely unbalanced state to a moderately unbalanced state; some cities have turned to a low-level coordination state, and the overall trend is presented to optimize the process continuously. The quantile regression results show that the level of economic development and industrial structure has a significant positive effect on improving the coupling coordination degree of the two. The degree of government intervention has a negative impact. The level of capital investment has a negative effect at a high score but has no significant impact at a low score. This study tries to provide a scientific basis for formulating the policy of coordinated development between an innovation environment and transformation development of resource-based cities and also provides a reference for high-quality development of other resource-based cities.

Shape-constrained estimation in functional regression with Bernstein polynomials

Shape restrictions on functional regression coefficients such as non-negativity, monotonicity, convexity or concavity are often available in the form of a prior knowledge or required to maintain a structural consistency in functional regression models. A new estimation method is developed in shape-constrained functional regression models using Bernstein polynomials. Specifically, estimation approaches from nonparametric regression are extended to functional data, properly accounting for shape-constraints in a large class of functional regression models such as scalar-on-function regression (SOFR), function-on-scalar regression (FOSR), and function-on-function regression (FOFR). Theoretical results establish the asymptotic consistency of the constrained estimators under standard regularity conditions. A projection based approach provides point-wise asymptotic confidence intervals for the constrained estimators. A bootstrap test is developed facilitating testing of the shape constraints. Numerical analysis using simulations illustrates improvement in efficiency of the estimators from the use of the proposed method under shape constraints. Two applications include i) modeling a drug effect in a mental health study via shape-restricted FOSR and ii) modeling subject-specific quantile functions of accelerometry-estimated physical activity in the Baltimore Longitudinal Study of Aging (BLSA) as outcomes via shape-restricted quantile-function on scalar regression (QFOSR). R software implementation and illustration of the proposed estimation method and the test is provided.

Subgroup analysis for high-dimensional functional regression

Subgroup analysis for scalar data has been well studied in the literature. However, less has been done on functional data, especially on high-dimensional functional regression. In this study, we develop a high-dimensional functional regression model for simultaneous estimation and subgroup identification for a heterogeneous population. Under mild conditions, we establish the estimation and selection consistency of the proposed estimators. The proposed analysis allows the number of functional predictors and number of subgroups to increase as the sample size increases. Simulation studies demonstrate satisfactory performance of the proposed method, and it is also illustrated through a real application.

Functional data analysis with covariate-dependent mean and covariance structures.

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interestingresults.

A functional regression analysis of vessel source level measurements from the Enhancing Cetacean Habitat and Observation (ECHO) database.

Measurements of the source levels of 9880 passes of 3188 different large commercial ships from the Enhancing Cetacean Habitat and Observation (ECHO) program database were used to investigate the dependencies of vessel underwater noise emissions on several vessel design parameters and operating conditions. Trends in the dataset were analyzed using functional regression analysis, which is an extension of standard regression analysis and represents a response variable (decidecade band source level) as a continuous function of a predictor variable (frequency). The statistical model was applied to source level data for six vessel categories: cruise ships, container ships, bulk carriers, tankers, tugs, and vehicle carriers. Depending on the frequency band and category, the functional regression model explained approximately 25%-50% of the variance in the ECHO dataset. The two main operational parameters, speed through water and actual draft, were the predictors most strongly correlated with source levels in all of the vessel categories. Vessel size (represented via length overall) was the design parameter with the strongest correlation to underwater radiated noise for three categories of vessels (bulkers, containers, and tankers). Other design parameters that were investigated (engine revolutions per minute, engine power, design speed, and vessel age) had weaker but nonetheless significant correlations with source levels.

Estimation of Sound Speed Profiles Using a Random Forest Model with Satellite Surface Observations

Sound speed profile (SSP) inversion is usually performed by linear statistical regression, such as the single empirical orthogonal function regression (sEOF-r) model. However, due to the complex dynamic activities of the ocean, the relationship between parameters is not strictly linear, often resulting in an unsatisfactory inversion result. In this study, an algorithm based on the random forest (RF) integrated learning model, for SSP inversion, was proposed. Using the sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) data, the sound speed profile of the upper 1000 m layer in the South China Sea was reconstructed, and its accuracy was evaluated through the root mean square error (RMSE). The accuracy of the evaluation demonstrated that the RF model proposed here could reconstruct the SSP in the upper 1000 m layer better than the sEOF-r can. Compared with the latter, the average reconstruction accuracy of the RF model was improved by 0.56 m/s. The linear regression of the sEOF-r model fell short of expectations in the regression between surface and subsurface parameters. By removing the constraints of linear inversion, the nonlinear regression of the RF model showed a smaller RMSE and better robustness in the reconstruction process and was superior to the sEOF-r model at all depths. As a result, it provided an effective integrated learning model for SSP reconstruction.

Application of regression function model based on panel data in financial risk management of bank resource allocation

Abstract This paper studies the financial risk management of resource allocation of listed commercial banks in my country, starting from the fundamental influence of lender credit rating in the internal rating system of commercial banks, and analyzes the influence of a large number of subjective factors contained in the bank’s credit rating system on the rating effect. Influence. A sort-response panel regression function model with random effects (including random intercept terms and random coefficients) is proposed, and the rationality of the existing bank credit rating system is tested and analyzed. The experimental results show that the model’s prediction accuracy rate is 48.27%, and the percentage of prediction level error within two levels reaches 86.8%. The application of this model can find the redundant indicators of the existing system, which are highly fitted with the actual situation and can achieve quite ideal forecasting results, and provide a forecasting reference for the weight setting, which provides a basis for the revision of the bank’s credit rating system.

함수형 자료 기법을 활용한 로지스틱 회귀 모형과 응용

Stock prices around the world dramatically decreased in 2020 due to COVID-19. Although the general trend seemed to be rebounding in 2021, the degree of recovery might vary by industry. This paper intends to investigate the relationship between the type of the industry companies and the pattern of individual stock indexes for 2021. Specifically, we investigate whether the functional pattern of individual stock indexes can be an important factor that can distinguish the type of the industry company. Traditionally, the stock price data has been analyzed using a time series approach. However, with the recent development of automated devices, the interest on the functional data analysis has been increasing. If individual stock prices are assumed to be random functions defined above continuous time, functional data techniques can be applied. Following this approach, we propose to use a functional logistic regression model that can explain the type of the industry company with the pattern of individual stock prices especially for 2021.

The Functional Regression With Reconstructed Functions From Hybrid Principal Components Analysis: With EEG-fMRI Application

Objective: In this article, we reconstruct the hybrid data with hybrid principal component analysis (HPCA) as a feature extraction step and model them with functional regression as a modeling step, and comparing models and choose the best number of HPCA based on the prediction accuracy as an evaluation step. Method: We decompose the hybrid data to the eigencomponents with HPCA. The reconstructed data from HPCA were divided into the training and testing dataset. The function-on-function signal compression and scalar-on-function regressions were used. Three simulation scenarios and their applications in the neuroimaging datasets (EEG-fMRI) were studied. The number of HPCA was selected with the mean squared prediction error (MSPE). Result: The simulation shows that the raw data, reconstructed from the first and all HPCAs for the training dataset has median MSPE 0.1001, 0.0028, and 0.0174 respectively, and for the testing, the dataset has 0.3207, 0.1118, and 0.2484 respectively. The EEG-fMRI suggests that in both auditory and visual tasks and standard and target stimuli for different regions of the brain the first HPCA has the smallest MSPE. Conclusions: We conclude this method improves the prediction accuracy of the experiments with the EEG datasets. And we recommend that instead of using the functional PCA on the desired dimension, reconstruct the data with HPCA and average it on the other two dimensions for functional regression models.

SPF: A spatial and functional data analytic approach to cell imaging data.

The tumor microenvironment (TME), which characterizes the tumor and its surroundings, plays a critical role in understanding cancer development and progression. Recent advances in imaging techniques enable researchers to study spatial structure of the TME at a single-cell level. Investigating spatial patterns and interactions of cell subtypes within the TME provides useful insights into how cells with different biological purposes behave, which may consequentially impact a subject's clinical outcomes. We utilize a class of well-known spatial summary statistics, the K-function and its variants, to explore inter-cell dependence as a function of distances between cells. Using techniques from functional data analysis, we introduce an approach to model the association between these summary spatial functions and subject-level outcomes, while controlling for other clinical scalar predictors such as age and disease stage. In particular, we leverage the additive functional Cox regression model (AFCM) to study the nonlinear impact of spatial interaction between tumor and stromal cells on overall survival in patients with non-small cell lung cancer, using multiplex immunohistochemistry (mIHC) data. The applicability of our approach is further validated using a publicly available multiplexed ion beam imaging (MIBI) triple-negative breast cancer dataset.

Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma

Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient’s toxicity levels. In this work, a Functional covariate Cox Model (FunCM) to study the association between time-varying processes and a time-to-event outcome is proposed. FunCM first exploits functional data analysis techniques to represent time-varying processes in terms of functional data. Then, information related to the evolution of the functions over time is incorporated into functional regression models for survival data through functional principal component analysis. FunCM is compared to a standard time-varying covariate Cox model, commonly used despite its limiting assumptions that covariate values are constant in time and measured without errors. Data from MRC BO06/EORTC 80931 randomised controlled trial for treatment of osteosarcoma are analysed. Time-varying covariates related to alkaline phosphatase levels, white blood cell counts and chemotherapy dose during treatment are investigated. The proposed method allows to detect differences between patients with different biomarkers and treatment evolutions, and to include this information in the survival model. These aspects are seldom addressed in the literature and could provide new insights into the clinical research.

Model selection for functional linear regression with hierarchical structure

Scalar-on-function regression allows for a scalar response to be dependent on functional predictors; however, not much work has been done when interaction effects between the functional predictors are included. In this paper, we introduce a multiple functional linear regression model with interaction terms. Meanwhile, we enforce the hierarchical structure constraint on the model, that is, interaction terms can be selected into the model only if the associated main effects are in the model. Based on the functional principal component analysis and group smoothly clipped absolute deviation (SCAD) penalty, we propose a new penalized estimation procedure to select the important functional predictors and interactions while automatically obeying the hierarchical structure. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the model selection procedure are established under some regularity conditions. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies and a real data application.

Some non‐parametric regression models for interval‐valued functional data

The interval‐valued functional data belong to the category of symbolic data in which the values of each observation consist of two functions, a lower limit function and an upper limit function. This study introduces some functional non‐parametric approaches to fit a functional regression model on interval‐valued functional data. First, using kernel functions, two non‐parametric regression models are presented to predict a scalar interval‐valued response variable based on interval‐valued functional predictors. For this purpose, a local linear regression and a kernel regression estimator of the Nadaraya–Watson type are proposed. These approaches are based on two independent non‐parametric models, which may not hold in practice. Therefore, some non‐parametric methods are introduced, including bivariate functional Nadaraya–Watson, bivariate functional locally linear smoothing and another method based on bootstrap, which maintain selecting points randomly in the intervals of the proposed data. The applicability and advantages of the proposed models are investigated through simulation experiments and a real data example.