A different approach to estimate nonlinear regression model using numerical methods

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G; Balasiddamuni, P

doi:10.1088/1757-899x/263/4/042122

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Method of estimating the parameter of the nonlinear regression model has been identified as a critical issue in the utilization of the nonlinear regression models. Reference [3] described some computational methods based on numerical analysis to estimate the parameters of nonlinear regression model. In this study, two nonlinear regression models are studied: the logistic growth regression model and the asymptotic growth regression.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Asymptotic and Logistics Growth Models on A Chemist Data

Biu

Nwakuya

Tubona³

2022

EJMATH

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This research considers two growth models; asymptotic growth model and logistic growth model. Both models were compared to establish a better model for modelling and prediction based on a Chemist data on the percentage concentration of isomers versus time for each Isomerization of α-Pinene at 189.50C. Results from the growth curve shows a non-linear relationship between the response (time of isomerization) and the independent variables (percentage of concentration) for all the four isomers considered. Based on the four isomers four different quadratic regressions of second-order were fitted. The problem of the initial parameters was addressed by second-order regression techniques since the models considered have three parameters to be estimated before the iterative approach was used. Estimation of parameters was done using modified version of the Levenberg-Marquardt Algorithm in Gretl statistical software. The results from both models were compared based on Aikaike Information Criteri (AIC), Bayesian Information Criteria (BIC), Mean Squared Error (MSE) and R-square. The Asymptotic Growth Model was identified to be a more adequate model for modelling and predicting growth patterns for three isomers (Dipentene, Pyronene and Dimer) while logistic growth model was seen to be a better model for predicting growth patterns of one isomer (Allo-Ocimene). This study will go a long way in directing Chemists and researchers in that field in choosing the appropriate model for their research.

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Section: Introductionmentioning

confidence: 99%

Assessment of Asymptotic and Logistics Growth Models on A Chemist Data

Biu

Nwakuya

Tubona³

2022

EJMATH

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“…Snezana S. Djordjevic ( 2019) presented a review of some unconstrained optimization methods based on the line search techniques. Mahaboob et al (2017) proposed a different approach to estimate nonlinear regression models using numerical methods also based on the line search techniques. Mohammad, Waziri, and Santos (2019) have briefly reviewed methods for solving NLS problems, paying special attention to the structured quasi-Newton methods which are the family of the search line techniques.…”

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confidence: 99%

A Review of Well-Known Robust Line Search and Trust Region Numerical Optimization Algorithms for Solving Nonlinear Least-Squares Problems

Kiseta

Akumoso

2021

ISR

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The conditional, unconditional, or the exact maximum likelihood estimation and the least-squares estimation involve minimizing either the conditional or the unconditional residual sum of squares. The maximum likelihood estimation (MLE) approach and the nonlinear least squares (NLS) procedure involve an iterative search technique for obtaining global rather than local optimal estimates. Several authors have presented brief overviews of algorithms for solving NLS problems. Snezana S. Djordjevic (2019) presented a review of some unconstrained optimization methods based on the line search techniques. Mahaboob et al. (2017) proposed a different approach to estimate nonlinear regression models using numerical methods also based on the line search techniques. Mohammad, Waziri, and Santos (2019) have briefly reviewed methods for solving NLS problems, paying special attention to the structured quasi-Newton methods which are the family of the search line techniques. Ya-Xiang Yuan (2011) reviewed some recent results on numerical methods for nonlinear equations and NLS problems based on online searches and trust regions techniques, particularly on Levenberg-Marquardt type methods, quasi-Newton type methods, and trust regions algorithms. The purpose of this paper is to review some online searches and trust region's more well-known robust numerical optimization algorithms and the most used in practice for the estimation of time series models and other nonlinear regression models. The line searches algorithms considered are: Gradient algorithm, Steepest Descent (SD) algorithm, Newton-Raphson (NR) algorithm, Murray’s algorithm, Quasi-Newton (QN) algorithm, Gauss-Newton (GN) algorithm, Fletcher and Powell algorithm (FP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. While the only trust-region algorithm considered is the Levenberg-Marquardt (LM) algorithm. We also give some main advantages and disadvantages of these different algorithms.

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