Nonlinear Regression Analysis and Its Applications

Bates, Douglas M.; Watts, Donald G.

doi:10.1002/9780470316757

Cited by 2,571 publications

(227 citation statements)

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“…Mathematical monographs about non-linear regression analysis (Bates & Watts, 1988;Ratkowsky, 1990;Neter et al, 1996;Seber & Wild, 2003) point out the fact that by factorizing a product function the prerequisites are (i) the meaningful structure of the product function (ii) the univocal splitting regarding the factor functions as well as (iii) the verification that the obtained results yield plausible values.…”

Section: Verification Of the Results As Concentration Functions Of Thmentioning

confidence: 99%

“…Assuming the existence of a univocal solution, estimating a product function yields the factorization of the product (Bates & Watts, 1988;Ratkowsky, 1990;Neter et al, 1996;Seber & Wild, 2003).…”

Section: Principal Thoughtsmentioning

confidence: 99%

“…It is known that the result is different for the both ionic species. Concerning the mathematical approach, the values of the parameters in the factor functions of relationship (14) On principle, the parameter determination of the basic product function (14) should be possible from the optimal approximation of the existing experimental data for the concentration curve of the mean activity coefficients to the required power applying the non-linear regression analysis (Bates & Watts, 1988;Ratkowsky, 1990;Neter et al, 1996;Seber & Wild, 2003).…”

Section: The Mathematical Structure Of the Concentration Functionsmentioning

confidence: 99%

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Some Aspects on the Problem of Individual Activity Coefficients of Single-ion Species of Aqueous Strong Electrolytes

Ferse¹

2012

IJC

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Individual activity coefficients of single-ion species can neither be defined in thermodynamic terms nor determined experimentally. This does not mean that the individual activity of a single-ion species of an aqueous strong electrolyte does not have a real specifically individual effectiveness. Individual ion activity coefficients are required, for instance, for data about the potentials of single electrodes and liquid junction potentials in galvanic cells with transference. A purely mathematical method is written which allows the factorizing the mean activity coefficient into individual parts of the single-ion species. The experimentally accessible concentration curve of the mean activity coefficient is fitted with a quite new mathematical approach. The parameter set of the mathematical approach can be determined univocally and invariantly with the help of the asymptotic theory using corresponding approximations.Keywords: aqueous strong electrolytes, concentration dependence of activity coefficients, factorization of the mean activity coefficients, individual ion activity coefficients IntroducationThe analytical concentration "m" of a component within a real and homogeneous mixed phase has to be modified for the thermodynamic interpretation of equilibriums, according to Eq. (1):The modified concentration "a" is denoted as activity. The multiplicative term "γ" is known as activity coefficient. The activity coefficient considers all deviations from ideal behaviour of the component within the real mixed phase by forming of interaction forces.

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Section: Verification Of the Results As Concentration Functions Of Thmentioning

confidence: 99%

Section: Principal Thoughtsmentioning

confidence: 99%

Section: The Mathematical Structure Of the Concentration Functionsmentioning

confidence: 99%

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Some Aspects on the Problem of Individual Activity Coefficients of Single-ion Species of Aqueous Strong Electrolytes

Ferse¹

2012

IJC

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“…We examine these concepts further in the context of the asymptotic growth model applied to the BOD dataset found in Bates and Watts (1988). This is given by ( )…”

Section: Examplementioning

confidence: 99%

“…See [8]. Consider the nonlinear regression model ( ) η x β and the point on the surface at which the linear or tangent plane approximation is developed will affect the degree to which centering affects least squares based analysis of the model.…”

Section: Nonlinear Regression Models: Local Curvature Assessmentmentioning

confidence: 99%

Local Curvature and Centering Effects in Nonlinear Regression Models

Brimacombe¹

2016

OJS

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The effects of centering response and explanatory variables as a way of simplifying fitted linear models in the presence of correlation are reviewed and extended to include nonlinear models, common in many biological and economic applications. In a nonlinear model, the use of a local approximation can modify the effect of centering. Even in the presence of uncorrelated explanatory variables, centering may affect linear approximations and related test statistics. An approach to assessing this effect in relation to intrinsic curvature is developed and applied. Mis-specification bias of linear versus nonlinear models also reflects this centering effect.

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Temporal properties of the hemodynamic response in functional MRI

Kruggel

Cramon

1999

Hum. Brain Mapp.

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Today, most studies of cognitive processes using functional magnetic resonance imaging (fMRI) adopt an event-related experimental design. Highly flexible stimulation settings require new statistical models where not only the activation amount, but also the time course of the measured hemodynamic response is analyzed. It is possible to obtain statistically valid descriptions of single hemodynamic responses from a robust nonlinear estimation procedure. Focus is placed on the temporal behaviour of the hemodynamic response: relative temporal order, changes induced by modification of the experimental context, and interindividual differences. Example analyses from recent fMRI studies underline the usefulness of this approach.

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Nonlinear Regression Analysis and Its Applications

Cited by 2,571 publications

References 0 publications

Some Aspects on the Problem of Individual Activity Coefficients of Single-ion Species of Aqueous Strong Electrolytes

Some Aspects on the Problem of Individual Activity Coefficients of Single-ion Species of Aqueous Strong Electrolytes

Local Curvature and Centering Effects in Nonlinear Regression Models

Temporal properties of the hemodynamic response in functional MRI

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