Parameters Of Linear Model Research Articles

Mixed effect machine learning: A framework for predicting longitudinal change in hemoglobin A1c.

Accurate and reliable prediction of clinical progression over time has the potential to improve the outcomes of chronic disease. The classical approach to analyzing longitudinal data is to use (generalized) linear mixed-effect models (GLMM). However, linear parametric models are predicated on assumptions, which are often difficult to verify. In contrast, data-driven machine learning methods can be applied to derive insight from the raw data without a priori assumptions. However, the underlying theory of most machine learning algorithms assume that the data is independent and identically distributed, making them inefficient for longitudinal supervised learning. In this study, we formulate an analytic framework, which integrates the random-effects structure of GLMM into non-linear machine learning models capable of exploiting temporal heterogeneous effects, sparse and varying-length patient characteristics inherent in longitudinal data. We applied the derived mixed-effect machine learning (MEml) framework to predict longitudinal change in glycemic control measured by hemoglobin A1c (HbA1c) among well controlled adults with type 2 diabetes. Results show that MEml is competitive with traditional GLMM, but substantially outperformed standard machine learning models that do not account for random-effects. Specifically, the accuracy of MEml in predicting glycemic change at the 1st, 2nd, 3rd, and 4th clinical visits in advanced was 1.04, 1.08, 1.11, and 1.14 times that of the gradient boosted model respectively, with similar results for the other methods. To further demonstrate the general applicability of MEml, a series of experiments were performed using real publicly available and synthetic data sets for accuracy and robustness. These experiments reinforced the superiority of MEml over the other methods. Overall, results from this study highlight the importance of modeling random-effects in machine learning approaches based on longitudinal data. Our MEml method is highly resistant to correlated data, readily accounts for random-effects, and predicts change of a longitudinal clinical outcome in real-world clinical settings with high accuracy.

Coverage probabilities of confidence intervals for the slope parameter of linear regression model when the error term is not normally distributed

Confidence interval for the slope parameter based on the t-statistic is not appropriate when the error term is not normally distributed. In this paper, we examine some existing methods for the interval estimation of the slope parameter and suggest new methods for giving better coverage accuracy. The following methods are considered: the standard t, the bootstrap-t, and three intervals based on the transformations of the t-statistic. The results for the Exponential and Weibull distributions and for the real data set are presented. The simulation study shows that these introduced intervals give better results than existing methods.

ОЦІНКА СТАНУ ДЕЦЕНТРАЛІЗАЦІЇ МІСЦЕВИХ БЮДЖЕТІВ УКРАЇНИ

Необхідною умовою формування ефективного місцевого самоврядування є децентралізація влади. Тому важливо поглибити теоретико-методичні засади оцінки стану децентралізації місцевих бюджетів України. Встановлено, що оцінка стану децентралізації місцевих бюджетів вимагає використання комплексу показників, які б найповніше характеризували фінансову децентралізацію. Запропоновано розподілити показники оцінки стану децентралізації місцевих бюджетів за трьома критеріями: впливу децентралізації на формування доходів місцевих бюджетів; децентралізації місцевих бюджетів згідно з бюджетною класифікацією; залежності місцевих бюджетів від міжбюджетних трансфертів.Запропоновано систему окремих показників, які можна використовувати для оцінки стану децентралізації місцевих бюджетів, і визначено критерії оцінки впливу децентралізації на формування доходів місцевих бюджетів згідно із запропонованою методикою розрахунку. За результатами аналізу окремих показників оцінки стану децентралізації місцевих бюджетів встановлено, що такий аналіз не дає загального уявлення про стан їх децентралізації, тому авторами розраховано показники за окремими критеріями з використанням вагових коефіцієнтів.Обгрунтовано, що параметри моделі лінійного тренду для критеріїв оцінки впливу децентралізації на формування доходів місцевих бюджетів свідчать про велику визначеність процесу їх спадання. Протягом останніх років простежується тенденція до зниження критеріїв оцінки впливу децентралізації на формування доходів місцевих бюджетів. Встановлено нестабільну тенденцію до зміни критеріїв оцінки децентралізації місцевих бюджетів згідно з бюджетною класифікацією. При цьому параметри моделі лінійного тренду для субіндексів критеріїв оцінки залежності місцевих бюджетів від міжбюджетних трансфертів говорять про велику визначеність їх спадної тенденції.У процесі дослідження розроблено систему показників для визначення стану децентралізації місцевих бюджетів. Апробація методики розрахунку інтегрального показника підтвердила можливість її використання для аналізу стану децентралізації місцевих бюджетів.

Online system identification of mini cropped delta UAVs using flight test methods

The current manuscript presents the longitudinal and lateral directional online parameter estimation of two unmanned aerial vehicles (UAVs) using sequential Least Squares formulation in frequency domain. The two fixed wing UAVs share a similar cropped delta planform and differ in their cross sectional geometries, one with a rectangular and the other being a reflex airfoil cross sections respectively. Recursive Fourier Transform algorithm has been used to convert the flight data in time domain to frequency domain which is measured by means of a dedicated on-board data acquisition system capable of on-board logging and telemetry to ground station. The combination of Sequential Least Squares with Recursive Fourier Transform (SLS-RFT) in frequency domain can be used to carry out online parameter estimation. An attempt has been made to check the applicability of the current method to estimate parameters from the generated flight data of the two UAVs using both conventional as well as random control inputs. Results showed that the parameters estimated, using SLS-RFT, from the linear flight data are consistent and in close agreement with the obtained parameters from full scale wind tunnel testing of UAVs. It was also observed that the estimates from the manoeuvres with multistep control inputs converged faster compared to the parameters obtained from the manoeuvres with slow varying control surface deflections. The time varying linear aerodynamic parametric model of SLS-RFT was able to capture the dynamics of the flights with nonlinear aerodynamics. Certain limitations of the current online system identification method were also observed with estimating parameters from the flight data of UAVs performing near stall manoeuvres. The estimated parameters using SLS-RFT are also compared with the results obtained from batch methods namely classical Maximum Likelihood (ML) and neural based Neural–Gauss–Newton (NGN) methods.

Foetal ultrasound measurement imputations based on growth curves versus multiple imputation chained equation (MICE)

Ultrasound measures are valuable for epidemiologic studies of risk factors for growth restriction. Longitudinal measurements enable investigation of rates of change and identification of windows where growth is impacted more acutely. However, missing data can be problematic in these studies, limiting sample size, ability to characterise windows of vulnerability, and in some instances creating bias. We sought to compare a parametric linear mixed model (LMM) approach to multiple imputation in this setting with multiple imputation by chained equation (MICE) methodology. Ultrasound scans performed for clinical purposes were abstracted from women in the LIFECODES birth cohort (n=1003) if they were close in time to three study visits (median 18, 26, and 35weeks' gestation). We created imputed datasets using LMM and MICE and calculated associations between demographic factors and ultrasound parameters cross-sectionally and longitudinally. Results were compared with a complete-case analysis. Most participants had ultrasounds at 18weeks' gestation, and ~50% had measurements at 26 and 35weeks; 100% had birthweight. Associations between demographic factors and ultrasound measures were similar in magnitude, but more precise, when either imputed datasets were used, compared with a complete-case analysis, in both the cross-sectional or longitudinal analyses. MICE, though ignoring the non-linear features of the trajectory and within subject correlation, is able to provide reasonable imputation of foetal growth data when compared to LMM. Because it simultaneously imputes missing covariate data and does not require specification of variance structure as in LMM, MICE may be preferable for imputation in this setting.

Color Contrast-Preserving Decolorization.

Decolorization is to convert a color image into a gray scale image while preserve image features like salient structure and chrominance contrast. The sign of the color contrast is crucial for the decolorization algorithm and is usually determined in existing works by giving a strict defined color order or twomode weak order. In this paper, a fast computation on color order is achieved via a simple global mapping which is introduced in a linear parametric model using an extended structure transfer filter. The values of the parameters are obtained via an elegant approximation method. A local decolorization algorithm is finally designed on basis of the global linear mapping so that both color and spatial information are preserved robustly and accurately. Experimental results show that the proposed decolorization algorithms obtain a good performance among existing quality metrics for the decolorization. In addition, the proposed global decolorization algorithm is friendly to mobile devices with limited computational resource.

The carbon balance of a Scots pine forest following severe windthrow: Comparison of reforestation techniques

Even though windthrows are the main disturbance type in European forests, their impact on forest carbon balance is generally understudied. In order to close this knowledge gap, we took advantage of a tornado event, which occurred in July 2012 in Trzebciny Forest District in northwest Poland. The main objective of this study was to determine how two completely different reforestation techniques in windthrow areas impact net ecosystem production (NEP) of this Scots pine forest ecosystem under similar meteorological conditions. The two techniques were: conventional (“Tlen I” site): uprooted stumps pulled out and removed from the site followed by ploughing, and non-conventional (“Tlen II” site): all stumps left on the site to decompose with no ploughing. Therefore, we measured carbon dioxide (CO2) fluxes using the eddy covariance (EC) technique for four continuous years. Our results indicate that both sites became significant carbon (C) sources after the windthrow (up to 575 ± 56 g C m−2 y-1 in the first year, Tlen I). However, the Tlen I (conventional technique) lost over 30% less C than Tlen II during the 2015–2016 observation period. In contrast to existing knowledge, ploughing as done at Tlen I, did not substantially increase CO2 emission, as compared to local soil ripping (non-conventional technique). The decrease in net C emission, estimated on the basis of linear model parameters, was almost five times greater at Tlen I than at Tlen II. We thus hypothesize that the annual NEP at conventionally reforested windthrow site will reach C neutrality (NEP = 0) six years after windthrow at most, while at the non-conventionally managed area it will probably take ca. 18 years. So far then, the currently widely applied conventional reforestation technique in wind-disturbed Polish forest appeared to be more effective in decreasing C losses than a technique that leaves stumps to decompose and avoids ploughing.

Identification and analysis of nonlinear dynamics of inertial actuators

Abstract This paper presents an experimental study of the nonlinear dynamics of electrodynamic proof mass actuators. When inertial actuators are used in velocity feedback controllers, their nonlinear dynamics can affect the stability margin of the feedback loop. Thus, it is crucial to identify the nonlinearity sources and to build reliable models that can be implemented in the stability analysis. Firstly, the underlying linear model parameters of an inertial actuator are identified for small excitation signals. The inductance losses at high frequencies due to eddy currents have also been included in the electrical impedance model. Secondly, the nonlinear model of the inertial actuator is determined using the detection, characterisation and identification process. Finally, a numerical analysis is carried out to highlight the implications of nonlinear dynamics of inertial actuators. The proposed methodology is applied to several electromagnetic proof mass actuators, including when the proof mass is not accessible to be directly instrumented.

Inference in Linear Regression Models with Many Covariates and Heteroscedasticity

ABSTRACTThe linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker–White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online.

Dynamic Data Modeling of SCR De-NOx System Based on NARX Neural Network

Targeting at the selective catalytic reduction (SCR) de-NOx system of a coal-fired unit, a NARX-neural-network-based dynamic data modeling method was proposed. Firstly, analyzed the main factors affecting the operation characteristics of SCR de-NOx system. According to the characteristics of operational data, insignificant variables were excluded to simplify the model input variables. Secondly, the dynamic characteristics of the SCR de-NOx system near an equilibrium point were described by using a linear multivariable model of second-order inertia plus pure delay. The nonlinearity of the system was reflected in the change of linear model parameters. Based on this principle, determined the order and the pure lag time of input variables. Lastly, a NARX-neural-network model was developed on the basis of the actual operating data and the validity of the model was confirmed in comparison with the operation data of the SCR de-NOx system of the coal-fired unit.

Models of alien species richness show moderate predictive accuracy and poor transferability

Robust predictions of alien species richness are useful to assess global biodiversity change. Nevertheless, the capacity to predict spatial patterns of alien species richness remains largely unassessed. Using 22 data sets of alien species richness from diverse taxonomic groups and covering various parts of the world, we evaluated whether different statistical models were able to provide useful predictions of absolute and relative alien species richness, as a function of explanatory variables representing geographical, environmental and socio-economic factors. Five state-of-the-art count data modelling techniques were used and compared: Poisson and negative binomial generalised linear models (GLMs), multivariate adaptive regression splines (MARS), random forests (RF) and boosted regression trees (BRT). We found that predictions of absolute alien species richness had a low to moderate accuracy in the region where the models were developed and a consistently poor accuracy in new regions. Predictions of relative richness performed in a superior manner in both geographical settings, but still were not good. Flexible tree ensembles-type techniques (RF and BRT) were shown to be significantly better in modelling alien species richness than parametric linear models (such as GLM), despite the latter being more commonly applied for this purpose. Importantly, the poor spatial transferability of models also warrants caution in assuming the generality of the relationships they identify, e.g. by applying projections under future scenario conditions. Ultimately, our results strongly suggest that predictability of spatial variation in richness of alien species richness is limited. The somewhat more robust ability to rank regions according to the number of aliens they have (i.e. relative richness), suggests that models of aliens species richness may be useful for prioritising and comparing regions, but not for predicting exact species numbers.

Zonotope-based recursive estimation of the feasible solution set for linear static systems with additive and multiplicative uncertainties

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear static models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in an application to health monitoring of marine engines. Furthermore, PAZI algorithm applied to mini-batches of measurement data leads itself to further analysis of the relation between the estimation results at different iterations. In addition, an example of identifying time-varying parameters is also reported.

Application of Chosen Methods of Robust Estimation: Baarda’s and Huber’s in Search for Outliers in the Real Estate Market Modeling

Abstract In the article, an attempt was made to compile a dataset which was devoid of outliers, on the example of Cracovian apartment market. Robust estimation was the tool which was used, but only its two methods were considered: Baarda’s and Huber’s. Huber’s method belongs to the so-called active methods which means that it allows to eliminate gross errors during the estimation of the parameters of multiple linear regression where a unit price is called a dependent variable or forecasted one. Baarda’s method is a passive method which is based on statistical tests and allows, after determining the parameters of a multiple linear regression model, to indicate the observations which may be burdened with gross errors. Thus both mentioned algorithms differ from each other substantially. In this publication, Baarda’s and Huber’s methods were compared in the context of their effectiveness for the analyzed dataset, and as tools of preparing the data for further analysis. The results showed that Baarda’s method is more appropriate for the analyzed dataset than Huber’s algorithm, but it does not mean that the active method is worse.

Fundos de Investimento: Performance Aplicando Modelo Carhart e Análise Envoltória de Dados

Resumo Este estudo avalia o desempenho de fundos de investimento brasileiros em ações, comparando retornos reais e indicadores paramétricos e não paramétricos de performance. A estimativa de desempenho e classificação dos fundos foi realizada com base na observação dos retornos reais e dos alfas obtidos do modelo de regressão linear paramétrica, de Carhart. Os indicadores foram comparados com os scores de eficiência relativa da análise envoltória de dados, do modelo não paramétrico de Banker, Charnes e Cooper. Os alfas foram estimados considerando os impactos dos fatores de mercado, tamanho, valor e momento nos retornos reais de cada fundo e os scores, tendo como insumos risco sistêmico, recursos disponíveis, custos e risco total, e, como produto de análise, os retornos. Identificou-se queda de performance dos fundos, apontada pela literatura, alta correlação dos alfas com os retornos reais, baixa correlação dos scores com retornos e mais baixa correlação entre alfas e scores. Isso indica que a escolha da medida de avaliação a ser utilizada consiste em uma importante etapa da seleção de ativos. Montaram-se, ainda, carteiras teóricas pautadas na eficiência e alfas identificando-se performance superior das carteiras baseada na eficiência, sendo que nenhuma delas superou a carteira de mercado.

Magnitude and Temporal Variability of Inter-stimulus EEG Modulate the Linear Relationship Between Laser-Evoked Potentials and Fast-Pain Perception.

The level of pain perception is correlated with the magnitude of pain-evoked brain responses, such as laser-evoked potentials (LEP), across trials. The positive LEP-pain relationship lays the foundation for pain prediction based on single-trial LEP, but cross-individual pain prediction does not have a good performance because the LEP-pain relationship exhibits substantial cross-individual difference. In this study, we aim to explain the cross-individual difference in the LEP-pain relationship using inter-stimulus EEG (isEEG) features. The isEEG features (root mean square as magnitude and mean square successive difference as temporal variability) were estimated from isEEG data (at full band and five frequency bands) recorded between painful stimuli. A linear model was fitted to investigate the relationship between pain ratings and LEP response for fast-pain trials on a trial-by-trial basis. Then the correlation between isEEG features and the parameters of LEP-pain model (slope and intercept) was evaluated. We found that the magnitude and temporal variability of isEEG could modulate the parameters of an individual's linear LEP-pain model for fast-pain trials. Based on this, we further developed a new individualized fast-pain prediction scheme, which only used training individuals with similar isEEG features as the test individual to train the fast-pain prediction model, and obtained improved accuracy in cross-individual fast-pain prediction. The findings could help elucidate the neural mechanism of cross-individual difference in pain experience and the proposed fast-pain prediction scheme could be potentially used as a practical and feasible pain prediction method in clinical practice.

Ultrasound elastography reliably identifies altered mechanical properties of burned soft tissues

Although burn injury to the skin and subcutaneous tissues is common in both civilian and military scenarios, a significant knowledge gap exists in quantifying changes in tissue properties as a result of burns. In this study, we present a noninvasive technique based on ultrasound elastography which can reliably assess altered nonlinear mechanical properties of a burned tissue. In particular, ex vivo porcine skin tissues have been exposed to four different burn conditions: (i) 200°F for 10s, (ii) 200°F for 30s, (iii) 450°F for 10s, and (iv) 450°F for 30s. A custom-developed instrument including a robotically controlled ultrasound probe and force sensors has been used to compress the tissue samples to compute two parameters (C10 and C20) of a reduced second-order polynomial hyperelastic material model. The results indicate that while the linear model parameter (C10) does not show a statistically significant difference between the test conditions, the nonlinear model parameter (C20) reliably identifies three (ii–iv) of the four cases (p<0.05) when comparing burned with unburned tissues with a classification accuracy of 60–87%. Additionally, softening of the tissue is observed because of the change in structure of the collagen fibers. The ultrasound elastography-based technique has potential for application under in vivo conditions, which is left for future work.

Iterative weighted estimation based on variance modelling in linear regression models

ABSTRACTThe estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset.

Applying functional data analysis to assess tele-interpersonal psychotherapy's efficacy to reduce depression

ABSTRACTThe use of parametric linear mixed models and generalized linear mixed models to analyze longitudinal data collected during randomized control trials (RCT) is conventional. The application of these methods, however, is restricted due to various assumptions required by these models. When the number of observations per subject is sufficiently large, and individual trajectories are noisy, functional data analysis (FDA) methods serve as an alternative to parametric longitudinal data analysis techniques. However, the use of FDA in RCTs is rare. In this paper, the effectiveness of FDA and linear mixed models (LMMs) was compared by analyzing data from rural persons living with HIV and comorbid depression enrolled in a depression treatment randomized clinical trial. Interactive voice response systems were used for weekly administrations of the 10-item Self-Administered Depression Scale (SADS) over 41 weeks. Functional principal component analysis and functional regression analysis methods detected a statistically significant difference in SADS between telphone-administered interpersonal psychotherapy (tele-IPT) and controls but linear mixed effects model results did not. Additional simulation studies were conducted to compare FDA and LMMs under a different nonlinear trajectory assumption. In this clinical trial with sufficient per subject measured outcomes and individual trajectories that are noisy and nonlinear, we found FDA methods to be a better alternative to LMMs.

Enhanced Cross-Component Linear Model for Chroma Intra-Prediction in Video Coding.

Cross-Component Linear Model (CCLM) for chroma intra-prediction is a promising coding tool in Joint Exploration Model (JEM) developed by the Joint Video Exploration Team (JVET). CCLM assumes a linear correlation between the luma and chroma components in a coding block. With this assumption, the chroma components can be predicted by the Linear Model (LM) mode, which utilizes the reconstructed neighbouring samples to derive parameters of a linear model by linear regression. This paper presents three new methods to further improve the coding efficiency of CCLM. First, we introduce a multi-model CCLM (MM-CCLM) approach, which applies more than one linear models to a coding block. With MM-CCLM, reconstructed neighbouring luma and chroma samples of the current block are classified into several groups, and a particular set of linear model parameters is derived for each group. The reconstructed luma samples of the current block are also classified to predict the associated chroma samples with the corresponding linear model. Second, we propose a multi-filter CCLM (MF-CCLM) technique, which allows the encoder to select the optimal down-sampling filter for the luma component with the 4:2:0 colour format. Third, we present a LM-angular prediction (LAP) method, which synthesizes the angular intra-prediction and the MM-CCLM intra-prediction into a new chroma intra coding mode. Simulation results show that 0.55%, 4.66% and 5.08% BD rate savings in average on Y, Cb and Cr components respectively, are achieved for All Intra (AI) configurations with the proposed three methods. MM-CCLM and MF-CCLM have been adopted into the JEM by JVET.

On‐line estimation of switched reluctance motor parameters

SummaryThis paper addresses the problem of on‐line parameter estimation of switched reluctance motors and provides, to the best of the authors' knowledge, the first result that takes into account the dynamics of both electrical and mechanical subsystems. Based on a widely‐used standard model of the motor and establishing a reasonable structure for modeling the unknown load torque, a linear parametric model is derived and a 2‐stage identification scheme is proposed and implemented with the recursive least‐squares algorithm with forgetting factor. It is assumed that stator voltages and currents and rotor position and speed are available through measurements. Numerical simulations and experimental tests are included for a 3‐phase 12/8 switched reluctance motor. The results show a good performance of the proposed methodology, and the estimated parameters are validated through their use in a closed‐loop control scheme. Key features of the proposed solution are that it does not rely on locked‐rotor tests nor does it assume previous knowledge of the magnetization curves of the motor. The estimation scheme is intended to improve the performance and efficiency of currently available control algorithms, and it is potentially useful for the design of selfcommissioning switched reluctance drives, ie, drives that can automatically adjust the controller parameters for a wide range of motors and loads.