Nonlinear Regression Research Papers - Academia.edu (original) (raw)

Os modelos polinomiais são mais difundidos no meio florestal brasileiro na descrição do perfil de árvores devido à sua facilidade de ajuste e precisão. O mesmo não ocorre com os modelos não-lineares, os quais possuem maior dificuldade de... more

Os modelos polinomiais são mais difundidos no meio florestal brasileiro na descrição do perfil de árvores devido à sua facilidade de ajuste e precisão. O mesmo não ocorre com os modelos não-lineares, os quais possuem maior dificuldade de ajuste. Dentre os modelos não-lineares clássicos, na descrição do perfil, podem-se citar o de Gompertz, o Logístico e o de Weibull. Portanto, este estudo visou comparar os modelos lineares e não lineares para a descrição do perfil de árvores. As medidas de comparação foram o coeficiente de determinação (R²), o erro-padrão residual (s yx), o coeficiente de determinação corrigido (R²ajustado), o gráfico dos resíduos e a facilidade de ajuste. Os resultados ressaltaram que, dentre os modelos não-lineares, o que obteve melhor desempenho, de forma geral, foi o modelo Logístico, apesar de o modelo de Gompertz ser melhor em termos de erro-padrão residual. Nos modelos lineares, o polinômio proposto por Pires & Calegario foi superior aos demais. Ao comparar o...

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis... more

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method pre-sented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related non-linear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth’s climate system is the climate sen-sitivity: the change in global temperature due to doubling of atmospheric CO2 concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computa-tionally intensive nonlinear function is the MIT 2D climate model. 1. Introduction. A fundamental question in understanding the Earth’s cli-mate system is quan...

Mizolastine is a second generation antihistamine agent approved in Europe for the treatment of allergic rhinitis and skin conditions for which Sanofi~Synthélabo is developing a pediatric solution. Our objective was to design the... more

Mizolastine is a second generation antihistamine agent approved in Europe for the treatment of allergic rhinitis and skin conditions for which Sanofi~Synthélabo is developing a pediatric solution. Our objective was to design the population pharmacokinetic (PK) study of mizolastine pediatric solution in children. A bioavailability study of this solution compared to the marketed tablet was performed in 18 young volunteers. These PK data were analyzed by nonlinear regression using a two-compartment open model with zero-order absorption. From the estimated parameters, we designed population PK studies in two groups of children: 6 to 12 years and 2 to 6 years, respectively. To compare several population designs and to derive the optimal ones, we used the determinant of the Fisher information matrix of the population characteristics using a first-order expansion of the model. We have evaluated a “reference” population design with 10 samples (from 0.25 to 36 hr after drug intake) per child...

Based on permittivity changes, a new method to measure hematocrit (HCT) in extracorporeal blood systems is presented. Human blood samples were tested at different HCT levels pairing the values of permittivity change, obtained by means of... more

Based on permittivity changes, a new method to measure hematocrit (HCT) in extracorporeal blood systems is presented. Human blood samples were tested at different HCT levels pairing the values of permittivity change, obtained by means of a commercial impedance analyzer, with traditional centrifugation measurements. Data were correlated using both linear and nonlinear regression. When using the lineal model, the comparison

The so-called ‘least squares regression’ for mathematical modeling is a widely used technique. It’s so common that one might think nothing could be improved to the algorithm anymore. But it can. By minimizing the squares of the... more

The so-called ‘least squares regression’ for mathematical modeling is a widely used technique. It’s so common that one might think nothing could be improved to the algorithm anymore. But it can. By minimizing the squares of the differences between measured and predicted values not only in the vertical, but also in the horizontal direction. I call this ‘multidirectional regression’. The difference is very significant, especially for power function models, often used in biomedical sciences. And it makes the regression invariant if the dependent and independent variables are switched. This was a neglected problem with the traditional method. The Body Mass Index and the Corpulence Index and their correlation with body fat percentage are studied here as an example showing that this regression technique produces better results.

The equilibrium moisture contents (EMC) of pistachio were determined using the standard static-gravimetric method at 15, 25, 35 and 40°C for pistachio powder at 15, 35°C for pistachio kernel and pistachio nut for water activity (a w)... more

The equilibrium moisture contents (EMC) of pistachio were determined using the standard static-gravimetric method at 15, 25, 35 and 40°C for pistachio powder at 15, 35°C for pistachio kernel and pistachio nut for water activity (a w) ranging from 0.11 to 0.9. At a given water activity, the results show that the moisture content decreases with increasing temperature. The experimental sorption curves are then described by the BET, GAB, Henderson, Oswin, Smith and Halsey models. A nonlinear regression analysis method was used to evaluate the constants of the sorption equations. The Smith model was found to be suitable for describing the sorption curves. The isosteric heat of adsorption of water was determined as a function of moisture content from the equilibrium data at different temperatures using the Clasius–Clapeyron equation.

The kinetics of epoxidation of jatropha oil by peroxyacetic/peroxyformic acid, formed in situ by the reaction of aqueous hydrogen peroxide and acetic/formic acid, in the presence of an acidic ion exchange resin as catalyst in or without... more

The kinetics of epoxidation of jatropha oil by peroxyacetic/peroxyformic acid, formed in situ by the reaction of aqueous hydrogen peroxide and acetic/formic acid, in the presence of an acidic ion exchange resin as catalyst in or without toluene, was studied. The presence of an inert solvent in the reaction mixture appeared to stabilise the epoxidation product and minimise the side

A Monte Carlo method is presented to study the effect of systematic and random errors on computer models mainly dealing with experimental data. It is a common assumption in this type of models (linear and nonlinear regression, and... more

A Monte Carlo method is presented to study the effect of systematic and random errors on computer models mainly dealing with experimental data. It is a common assumption in this type of models (linear and nonlinear regression, and nonregression computer models) involving experimental measurements that the error sources are mainly random and independent with no constant background errors (systematic errors). However, from comparisons of different experimental data sources evidence is often found of significant bias or calibration errors. The uncertainty analysis approach presented in this work is based on the analysis of cumulative probability distributions for output variables of the models involved taking into account the effect of both types of errors. The probability distributions are obtained by performing Monte Carlo simulation coupled with appropriate definitions for the random and systematic errors. The main objectives are to detect the error source with stochastic dominance on the uncertainty propagation and the combined effect on output variables of the models. The results from the case studies analyzed show that the approach is able to distinguish which error type has a more significant effect on the performance of the model. Also, it was found that systematic or calibration errors, if present, cannot be neglected in uncertainty analysis of models dependent on experimental measurements such as chemical and physical properties. The approach can be used to facilitate decision making in fields related to safety factors selection, modeling, experimental data measurement, and experimental design.

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for para- metric conditional distributions. This test is formed on the basis of the integrated squared... more

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for para- metric conditional distributions. This test is formed on the basis of the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. This test is consistent, and has nontrivial

The so-called ‘least squares regression’ for mathematical modeling is a widely used technique. It’s so common that one might think nothing could be improved to the algorithm anymore. But it can. By searching the ‘least squares’ not... more

The so-called ‘least squares regression’ for mathematical modeling is a widely used technique. It’s so common that one might think nothing could be improved to the algorithm anymore. But it can. By searching the ‘least squares’ not just in the vertical direction. The first test results are very promising, and especially for power functions, often used in biomedical sciences, the conclusions you make from your data can change dramatically.

The adsorption behavior of nickel(II) from aqueous solution onto agricultural waste such as cashew nut shell (CNS) was investigated as a function of parameters such as solution pH, CNS dose, contact time, initial nickel(II) concentration... more

The adsorption behavior of nickel(II) from aqueous solution onto agricultural waste such as cashew nut shell (CNS) was investigated as a function of parameters such as solution pH, CNS dose, contact time, initial nickel(II) concentration and temperature. The Langmuir, Freundlich, Temkin and Dubinin–Radushkevich models were applied to describe the equilibrium isotherms using nonlinear regression analysis. The equilibrium data fits well for the both Langmuir and Freundlich adsorption isotherms. The Langmuir monolayer adsorption capacity of CNS was found to be 18.868 mg/g. Thermodynamic parameters such as ΔG°, ΔH° and ΔS° have also been evaluated and it has been found that the sorption process was feasible, spontaneous and exothermic in nature. Pseudo-first-order, pseudo-second-order and Elovich kinetic models were used to describe the kinetic data and the rate constants were evaluated. The result of the kinetic study shows that the adsorption of nickel(II) could be described by the pseudo-second-order equation, suggesting that the adsorption process is presumably chemisorption. The adsorption process was found to be controlled by both surface and pore diffusion, with surface diffusion at the earlier stages followed by pore diffusion at the later stages. Analysis of adsorption data using a Boyd kinetic plot confirmed that external mass transfer is the rate determining step in the sorption process. A single-stage batch adsorber was designed for different CNS dose/effluent volume ratios using the Freundlich equation.

Consider a random vector (X,Y)(X,Y)(X,Y) and let m(x)=E(Y∣X=x)m(x)=E(Y|X=x)m(x)=E(Y∣X=x). We are interested in testing H0:mincalMTheta,calG=gamma(cdot,theta,g):thetainTheta,gincalGH_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}H0:mincalMTheta,calG=gamma(cdot,theta,g):thetainTheta,gincalG for some known function gamma\gammagamma, some compact set... more

Consider a random vector (X,Y)(X,Y)(X,Y) and let m(x)=E(Y∣X=x)m(x)=E(Y|X=x)m(x)=E(Y∣X=x). We are interested in testing H0:mincalMTheta,calG=gamma(cdot,theta,g):thetainTheta,gincalGH_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}H0:mincalMTheta,calG=gamma(cdot,theta,g):thetainTheta,gincalG for some known function gamma\gammagamma, some compact set Thetasubset\Theta \subset ThetasubsetIR$^p$ and some function set calG{\cal G}calG of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linear model, a partial linear model, a single index model, but also the selection of explanatory variables can be considered as a special case of this hypothesis. To test this null hypothesis, we make use of the so-called marked empirical process introduced by \citeD and studied by \citeSt for the particular case of parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure. The asymptotic validity of the proposed test is established, and its finite sample performance is compared with other existing tests by means of a simulation study.

The purpose of this work is to develop empirical equations for describing the in vitro ganciclovir (GCV) release from PLGA microspheres and also to develop and characterize a formulation containing GCV loaded PLGA microspheres dispersed... more

The purpose of this work is to develop empirical equations for describing the in vitro ganciclovir (GCV) release from PLGA microspheres and also to develop and characterize a formulation containing GCV loaded PLGA microspheres dispersed in thermogelling PLGA-PEG-PLGA polymer gel. Effect of polymer chain length and polymer blending on GCV entrapment and release from PLGA microspheres is also examined. PLGA microspheres of GCV were prepared from two polymers PLGA 6535 (d,l-lactide:glycolideColon, two colons65:35, Mw=45,000-75,000 Da) and Resomer RG 502H (d,l-lactide:glycolideColon, two colons50:50, Mw=8000 Da) and a 3:1 mixture. PLGA-PEG-PLGA polymer was synthesized and characterized. In vitro GCV release studies were conducted with microspheres and microspheres dispersed in 23% w/v PLGA-PEG-PLGA solution. Polymer blended microspheres entrap more GCV (72.67+/-2.49%) than both PLGA 6535 (51.37+/-2.7%) and Resomer RG 502H (47.13+/-1.13%) microspheres. In vitro drug release data was fit ...