Nonlinear Least Squares Estimation

Hartley, H. O.; Booker, Aaron H

doi:10.1214/aoms/1177700171

Cited by 91 publications

(15 citation statements)

References 5 publications

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“…Due to the nonlinear nature of the response function, we adopt the nonlinear least squares approach (NLS; Hartley and Booker 1965). NLS has been widely used in nonlinear regression (Bates and Watts 1988), and a common application in marketing has been the estimation of the Bass diffusion model (Bass, Krishnan, and Jain 1994;Srinivasan and Mason 1986).…”

Section: Parameter Estimationmentioning

confidence: 99%

The Dynamics of Goal Revision: A Cybernetic Multiperiod Test-Operate-Test-Adjust-Loop (TOTAL) Model of Self-Regulation

Wang

Mukhopadhyay

2011

Journal of Consumer Research

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This research presents a comprehensive conceptual model of the dynamics of goal revision over multiple periods. First, based on an integrative literature review, we derive four principles that govern how individuals update their goals over time (monotonicity, diminishing sensitivity, aspiration maximization, and performance satisficing). We then integrate these principles logically as well as mathematically into a goal-discrepancy response function. Next, we advance existing cybernetic models of self-regulation by synthesizing the four principles and the response function info a Test-Operate-Tesf-Adjusf-Loop (TOTAL) model, which captures the dynamics of goal revision in self-regulation. We report four laboratory experiments fhat demonstrate initial support for the postulates of our model and conclude with a discussion of limitations and future directions.A goal is defined as a "wisbed-for end that is considered to be attainable" (Geen 1995), and it is well accepted that people set goals to motivate themselves toward desired ends (Austin and Vancouver 1996;Locke and Latham 1990;Soman and Cheema 2004;Vohs, Baumeister, and Tice 2008). As they strive toward their goals after setting them (Bagozzi and Dholakia 1999;Thaler and Shefrin 1981), people may recalibrate the original goal, representing an adjustment in the wished-for end. Sometimes the shift is upward. For example, someone who sets and then achieves a goal to run Chen Wang is a doctoral student in marketing at

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Section: Parameter Estimationmentioning

confidence: 99%

The Dynamics of Goal Revision: A Cybernetic Multiperiod Test-Operate-Test-Adjust-Loop (TOTAL) Model of Self-Regulation

Wang

Mukhopadhyay

2011

Journal of Consumer Research

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“…(K is a Michaelis-type constant, n is the degree of the equation). It is shown by eliminating the constant K from expressions for two observations that, if Vi and Vj are velocities observed at concentrations Ci and Cj = aCi, respectively (where (Y is constant throughout an experiment), then they are related through a hyperbolic expression: Yj = LVi/(M+vi), (14) where M=V/(cu"-I) and L=Mti. Consequently, the parameters n and V can be evaluated by all methods applicable to the hyperbola, including linearizations.…”

Section: Methods Of Parameter Eliminationmentioning

confidence: 99%

New linear plots for the separate estimation of Michaelis—Menten parameters

Fajszi

Endrényi

1974

FEBS Letters

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“…A subroutine was included in the programme to define the parameters of the model (the rate constants and A,, the dose input) and the equations for cumulative excretion of dye An iterative process of non-linear regression is carried out (Hartley & Booker, 1965).…”

Section: Computational Techniquesmentioning

confidence: 99%

Pharmacokinetic model for the successive demethylation and biliary secretion of methyl orange in the rat

O'Reilly

Pitt

Ryan

1971

British J Pharmacology

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Summary1. A one-compartment pharmacokinetic model was developed in which a drug underwent two successive metabolical reactions (for example, metabolism followed by conjugation) and free drug and both metabolites were excreted. 2. Techniques were described whereby graphical estimates of the first-order rate constants may be derived from cumulative excretion data on the drug and its metabolites. Computer simulation techniques were used to show that the experimental data permit reasonably accurate estimation of the rate constants of the model by graphical and computer methods. 3. Tritiated methyl orange (2 mg) was administered to five groups of six rats with biliary cannulation. The bile produced by each animal was collected at hourly intervals for 6 h and the amounts of methyl orange and its metabolites, 4'sulpho-4-methylaminoazobenzene and 4'sulpho-4-aminoazobenzene, determined by thin layer chromatography and radioactive counting techniques. 4. The data were analysed graphically and with an iterative digital computer programme to yield the first-order rate constants for the successive demethylation steps in the metabolism of methyl orange. The removal of the first methyl group had a rate constant of 0-684+0-142 h-1 (+S.D.) and the second methyl group 100+0-302 h-1. The rate constant for biliary excretion of the free methyl orange was 0-164+0-042 h-1,-for the monomethyl derivative 0-672+ 0-461 h-i, and for the demethylated metabolite 6-413 + 3.222 h-1.

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Nonlinear Least Squares Estimation

Cited by 91 publications

References 5 publications

The Dynamics of Goal Revision: A Cybernetic Multiperiod Test-Operate-Test-Adjust-Loop (TOTAL) Model of Self-Regulation

The Dynamics of Goal Revision: A Cybernetic Multiperiod Test-Operate-Test-Adjust-Loop (TOTAL) Model of Self-Regulation

New linear plots for the separate estimation of Michaelis—Menten parameters

Pharmacokinetic model for the successive demethylation and biliary secretion of methyl orange in the rat

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