Merging Spline Approximations with Analysis of Nonlinear Regression Models

Questa nota intende dare alcuni criteri generali per costruire stime di parametri da funzioni curve cubiche. Tali funzioni sono particolarmente utili nell'analisi di modelli non lineari per le loro proprieta di convergenza (Ahlberg e altri, 1967). Illustra quindi l'effetto dei coefficienti di correlazione multipla sulle proprieta delle stime quando il modello lineare sottinteso e una funzione esponenziale a tre parametri. Esempi numerici sono gia stati pubblicati dall'Autore (1982, 1984).

Wiley-Interscience Paperback Series Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression -Technometrics [This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students. -Mathematical Reviews [This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. book also includes pseudocode for computing algorithms.

Random norming aids analysis of non-linear regression models with sequential informative dose selection

Analytical expressions based on the physics of the aerothermodynamics processes of a gas turbine engine facilitate a systematic approach to analysis and synthesis of model based controllers. An analytical linear model that can more accurately capture the engine dynamics during aggressive transient maneuvers has been proposed in the literature. The model is based on analytical linearization of a nonlinear model at both equilibrium and nonequilibrium conditions. Such an analytical linear model, however, still requires a complete knowledge of the current state vector for estimation of the linear model coefficients. This paper explores the potential for using linear model state estimates from the current time step in order to arrive at new linear model coefficients for the next time step. The fidelity of the linear models so obtained is evaluated by comparing transient responses with those from a nonlinear model and a detailed numerical linear model. Also, the fidelity of the analytical linear model is compared with that of piecewise linear models considered in the literature. Numerical simulations are carried out using a nonlinear separate flow twin spool turbofan engine model in the Numerical Propulsion System Simulation (NPSS) platform.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Spectral knowledge-based regression for laser-induced breakdown spectroscopy quantitative analysis

Estimation of high-spatial resolution clear-sky longwave downward and net radiation over land surfaces from MODIS data

Implied volatility is (almost) past-dependent: Linear vs non-linear models

This paper examines the estimation of a global nonlinear gas turbine model using NARMAX techniques. Linear models estimated on small-signal data are first examined and the need for a global nonlinear model is established. A nonparametric analysis of the engine nonlinearity is then performed in the time and frequency domains. The information obtained from the linear modelling and nonlinear analysis is used to restrict the search space for nonlinear modelling. The nonlinear model is then validated using large-signal data and its superior performance illustrated by comparison with a linear model. This paper illustrates how periodic test signals, frequency domain analysis and identification techniques, and time-domain NARMAX modelling can be effectively combined to enhance the modelling of an aircraft gas turbine.

The pharmacokinetic parameters were estimated and the pharmacokinetic models of aprindine were evaluated in patients. Two pharmacokinetic models were used, comprising a linear elimination model and a non-linear elimination model, both one-compartment models in which first-order absorption is assumed. Twenty-two serum levels of patients in terms of TDM were measured and the pharmacokinetic parameters were estimated using the simple pool method. The pharmacokinetic parameters estimated using a linear model were ka= 0.244 (hr-1), ke=0.020 (hr-1) and Vd=1.778 (1/kg), while those using a non-linear model were ka=0.666 (hr-1), Km=2.022 (μg/ml), Vmax=0.106 (mg/hr/kg) and Vd=2.754 (1/kg).The non-linear model was more suitable than the linear model for the AIC (linear model:-12.59, non-linear model:-19.61). The parameters estimated using the non-linear model were therefore more accurate and were found to have a smaller bias than those estimated using the linear model.

Ensuring the structural integrity of Steam Generator (SG) U-bend tube arrays during out-of-plane earthquakes is crucial. Rationalization of the design code is desired considering the increasing trend of design earthquake level. As a rationalization evaluation method, a primary stress criterion of tube arrays obtained from a limit analysis using a nonlinear model which can precisely consider the load sharing mechanism of the tubes by modeling all tubes and anti-vibration-bars (AVBs) is under consideration, and a response analysis is conducted using the equivalent linear model of the nonlinear model and response spectrum method. In this study, a response analysis method which can simultaneously evaluate the response displacement and bending strain distribution using an equivalent linear model and bending strain correction coefficient was proposed. The concept of the proposed method is that the macroscopic response (displacement and strain distributions) of the tube bundle is obtained by the response spectrum method using the equivalent linear model. The nonlinear behavior in which the strain per deformation just above the upper tube support plate (TSP) increases due to the change in the contact state between the tube and the TSP, which cannot be evaluated by the linear model directly, is corrected using the bending strain correction coefficient calculated based on the single tube analysis. The proposed method is validated by comparing the seismic test results obtained based on a full-scale mock-up consisting of square arrayed SG tubes. From the seismic test and pseudo static analysis using the nonlinear model, it was confirmed that near upper tube support plate (TSP) where high stress occurs as the out-of-plane response of the tube bundle increases, a change in contact occurs, resulting in the tube bundle only in contact with the upper surface of the TSP to also enter into contact with the lower surface of the TSP, and that the strain per deformation increases nonlinearly. In the linear model constructed in the previous study, the linear spring is defined at the contact point between the AVBs and the tube, whereas the non-contact point is free. In order to accurately predict stress, an evaluation method considering the contact state at the TSP is required. Therefore, a linear spring was defined only at the contact point at the moment of linearization at the top and bottom contact surfaces of the TSP, and the stiffness of the spring thereof was calculated as the equivalent stiffness from the contact force and gap displacement at the moment of linearization. This equivalent stiffness was also set for the AVB-tube contact point. Theoretically, responses such as deformed shape or strain distribution at the linearization moment, pseudo static analysis of the equivalent linear model and original nonlinear model are consistent. Furthermore, the bending strain correction coefficient, which can be calculated only by nonlinear analysis of a single tube, is set so that the response evaluation becomes conservative. The natural frequency of out-of-plane first mode obtained by the eigenvalue analysis of the equivalent linear model were well consistent with the seismic test. Bending strains of out-of-plane first mode obtained by the response spectrum method using the typical design damping ratio of 8% were larger than the test results. Furthermore, the response displacement was also well consistent with the measured values. Therefore, the proposed method can simultaneously evaluate the displacement response and the bending strain distribution by the response spectrum method. In addition, the natural frequencies of the out-of-plane second-mode were well consistent with the measured values in the linear model which is applied to the evaluation of the out-of-plane second or more higher mode. In conclusion, it was confirmed that the proposed method is applicable as a seismic response evaluation method that includes safety margins.

In this chapter we consider dependent data but move from the linear models of Chap.8 to general regression models. As in Chap.6, we consider generalized linear models (GLMs) and, more briefly, nonlinear models. We first give an outline of this chapter. In Sect.9.2 we describe three motivating datasets to which we return throughout the chapter. The GLMs discussed in Sect.6.3 can be extended to incorporate dependences in observations on the same unit; as with the linear model, an obvious way to carry out modeling in this case is to introduce unit-specific random effects. Within a GLM a natural approach is for these random effects to be included on the linear predictor scale. The resultant conditional models are known as generalized linear mixed models (GLMMs), and these are introduced in Sect.9.3. In Sects.9.4 and9.5 we describe likelihood and conditional likelihood methods of estimation, with Sect.9.6 devoted to a Bayesian treatment. Section9.7 illustrates some of the flexibility of GLMMs by describing and applying a particular model for spatial dependence. An alternative random effects specification, based on conjugacy, is described in Sect.9.8. An important approach to the modeling and analysis of dependent data that is philosophically different from the random effects formulation is via marginal models and generalized estimating equations (GEE), and these are the subject of Sect.9.9. In Sect.9.10, a second GEE approach is described in which the estimating equations for the mean are supplemented with a second set for the variances/covariances. For GLMMs, extra care must be taken with parameter interpretation, and Sect.9.11 discusses this issue, emphasizing how interpretation differs between conditional and marginal models. In PartII of the book, which focused on independent data, Chap.7 was devoted to models for binary data. For dependent data, models binary data are less well developed, and so we do not devote a complete chapter to their description. However, Sect.9.12 introduces the modeling of dependent binary data, and, subsequently, Sects.9.13 and 9.14 describe conditional (mixed) and marginal models for binary data. Section 9.15 considers how nonlinear models, as defined in Sect.6.10, can be extended to the dependent data case. For such models, many applications concentrate on inference for units, and so the introduction of random effects is again suggested. We refer to the resultant class of models as nonlinear mixed models (NLMMs). Section9.16 considers issues related to the parameterization of the nonlinear model. Inference for nonlinear mixed models via likelihood and Bayes approaches is covered in Sects.9.17 and9.18, while GEE is briefly considered in Sect.9.19. The assessment of assumptions for general regression models is described in Sect.9.20, with concluding comments contained in Sect.9.21. Additional references appear in Sect.9.22.

Population pharmacokinetic study of tacrolimus in pediatric patients with primary nephrotic syndrome: A comparison of linear and nonlinear Michaelis–Menten pharmacokinetic model

Extraction of battery parameters using a multi-objective genetic algorithm with a non-linear circuit model

Purpose: To assess the impact of using breathing adapted radiotherapy on contralateral breast (CB) dose, to relate the thorax shape with the dose to the organs at risk (OARs) and to predict the risk for induced malignancies in CB using linear and non-linear models, following tangential irradiation of breast. Material and methods. Sixteen patients with stage I-II breast cancer treatment planned with tangential fields using deep inspiration breath hold (DIBH) and free breathing (FB) techniques were included in this analysis. The dose results mainly based on DVH analysis were compared. Four parameters were defined to describe thoracic shape. Excess relative risk (ERR) for cancer induction in CB, employing linear and non-linear models was calculated. Results. Average CB volumes exposed to a dose of 1 Gy is 1.3 times higher in DIBH plans than in FB plans. No significant difference in average V3Gy and V5Gy for DIBH and FB plans is observed. The average mean CB dose for DIBH and FB plans is 0.33 and 0.28 Gy, respectively. No correlation between thorax shape parameters and mean OARs dose is observed. The estimated average mean ERR with linear model is lower in FB plans (0.12) than for the DIBH plans (0.14). The estimated ERR with non-linear model is 0.14 for DIBH plans and 0.15 for FB plans. Conclusion. No significant difference in CB dose between DIBH and FB plans is observed. The four thorax shape parameters defined in this study can not be related to the dose at OARs using DIBH and FB radiation techniques. The ERR estimates for secondary CB cancer are nearly the same for FB and DIBH planning when using a linear and non-linear risk prediction models.