scholarly journals Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Maja Marasović ◽  
Tea Marasović ◽  
Mladen Miloš
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Kinetic Parameters ◽  
Nonlinear Regression ◽  
Ordinary Least Squares ◽  
Parameters Estimation ◽  
Accurate Estimation ◽  
Robust Estimator ◽  
Enzyme Kinetic ◽  
Linearization Methods

Accurate estimation of essential enzyme kinetic parameters, such as Km and Vmax, is very important in modern biology. To this date, linearization of kinetic equations is still widely established practice for determining these parameters in chemical and enzyme catalysis. Although simplicity of linear optimization is alluring, these methods have certain pitfalls due to which they more often then not result in misleading estimation of enzyme parameters. In order to obtain more accurate predictions of parameter values, the use of nonlinear least-squares fitting techniques is recommended. However, when there are outliers present in the data, these techniques become unreliable. This paper proposes the use of a robust nonlinear regression estimator based on modified Tukey’s biweight function that can provide more resilient results in the presence of outliers and/or influential observations. Real and synthetic kinetic data have been used to test our approach. Monte Carlo simulations are performed to illustrate the efficacy and the robustness of the biweight estimator in comparison with the standard linearization methods and the ordinary least-squares nonlinear regression. We then apply this method to experimental data for the tyrosinase enzyme (EC 1.14.18.1) extracted from Solanum tuberosum, Agaricus bisporus, and Pleurotus ostreatus. The results on both artificial and experimental data clearly show that the proposed robust estimator can be successfully employed to determine accurate values of Km and Vmax.

Kinetic parameters estimation in an anaerobic digestion process using successive quadratic programming

2005 ◽  
Vol 52 (1-2) ◽  
pp. 419-426 ◽  
Author(s):  
C.A. Aceves-Lara ◽  
E. Aguilar-Garnica ◽  
V. Alcaraz-González ◽  
O. González-Reynoso ◽  
J.P. Steyer ◽  
...  
Keyword(s):  
Experimental Data ◽  
Anaerobic Digestion ◽  
Quadratic Programming ◽  
Kinetic Parameters ◽  
Parameters Estimation ◽  
Fixed Bed Reactor ◽  
Accurate Estimation ◽  
Successive Quadratic Programming ◽  
Anaerobic Digestion Process ◽  
Digestion Process

In this work, an optimization method is implemented in an anaerobic digestion model to estimate its kinetic parameters and yield coefficients. This method combines the use of advanced state estimation schemes and powerful nonlinear programming techniques to yield fast and accurate estimates of the aforementioned parameters. In this method, we first implement an asymptotic observer to provide estimates of the non-measured variables (such as biomass concentration) and good guesses for the initial conditions of the parameter estimation algorithm. These results are then used by the successive quadratic programming (SQP) technique to calculate the kinetic parameters and yield coefficients of the anaerobic digestion process. The model, provided with the estimated parameters, is tested with experimental data from a pilot-scale fixed bed reactor treating raw industrial wine distillery wastewater. It is shown that SQP reaches a fast and accurate estimation of the kinetic parameters despite highly noise corrupted experimental data and time varying inputs variables. A statistical analysis is also performed to validate the combined estimation method. Finally, a comparison between the proposed method and the traditional Marquardt technique shows that both yield similar results; however, the calculation time of the traditional technique is considerable higher than that of the proposed method.

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

Calibration of stormwater quality regression models: a random process?

2010 ◽  
Vol 62 (4) ◽  
pp. 875-882 ◽  
Author(s):  
A. Dembélé ◽  
J.-L. Bertrand-Krajewski ◽  
B. Barillon
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Regression Models ◽  
Linear Models ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Sets ◽  
Data Set ◽  
Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

scholarly journals Nonlinear quantile regression to describe the dry matter accumulation of garlic plants

2020 ◽  
Vol 50 (1) ◽  
Author(s):  
Guilherme Alves Puiatti ◽  
Paulo Roberto Cecon ◽  
Moysés Nascimento ◽  
Ana Carolina Campana Nascimento ◽  
Antônio Policarpo Souza Carneiro ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Dry Matter ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Dry Matter Accumulation ◽  
Over Time

ABSTRACT: The objective of this study was to adjust nonlinear quantile regression models for the study of dry matter accumulation in garlic plants over time, and to compare them to models fitted by the ordinary least squares method. The total dry matter of nine garlic accessions belonging to the Vegetable Germplasm Bank of Universidade Federal de Viçosa (BGH/UFV) was measured in four stages (60, 90, 120 and 150 days after planting), and those values were used for the nonlinear regression models fitting. For each accession, there was an adjustment of one model of quantile regression (τ=0.5) and one based on the least squares method. The nonlinear regression model fitted was the Logistic. The Akaike Information Criterion was used to evaluate the goodness of fit of the models. Accessions were grouped using the UPGMA algorithm, with the estimates of the parameters with biological interpretation as variables. The nonlinear quantile regression is efficient for the adjustment of models for dry matter accumulation in garlic plants over time. The estimated parameters are more uniform and robust in the presence of asymmetry in the distribution of the data, heterogeneous variances, and outliers.

scholarly journals A New Approach in Regression Analysis for Modeling Adsorption Isotherms

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Dana D. Marković ◽  
Branislava M. Lekić ◽  
Vladana N. Rajaković-Ognjanović ◽  
Antonije E. Onjia ◽  
Ljubinka V. Rajaković
Keyword(s):  
Least Squares ◽  
Error Function ◽  
Weighted Least Squares ◽  
Equilibrium Concentration ◽  
Ordinary Least Squares ◽  
Parameters Estimation ◽  
Percentage Error ◽  
Parameter Estimates ◽  
Simple Method ◽  
Orthogonal Distance Regression

Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart’s percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

Lumping Kinetics of Hydrodesulfurization for Crude Longkou Shale Oil

2013 ◽  
Vol 798-799 ◽  
pp. 12-16
Author(s):  
Xun Tang ◽  
Shu Yuan Li ◽  
Chang Tao Yue ◽  
Ji Lai He ◽  
Yue E Gong
Keyword(s):  
Experimental Data ◽  
Nitrogen Content ◽  
Kinetic Parameters ◽  
Nonlinear Regression ◽  
Kinetic Models ◽  
Correction Coefficient ◽  
Shale Oil ◽  
Optimal Model ◽  
Apparent Activation Energies ◽  
Kinetics Of

New lumping kinetic models, considering the effects of the nitrogen content in product and the correction coefficient of LHSV, were proposed to describe the hydrodesulfurization of crude Longkou shale oil. The kinetic parameters were obtained using nonlinear regression of the experimental data which were conducted in a bench-scale trick-bed reactor with NiW/Al2O3 catalyst at various conditions. The results show that the 4-lump model is the optimal model. The values of apparent activation energies of lumps 1, 2, 3 and 4 are 51.14, 62.64, 130 and 166.42kJ/mol, respectively. The validation and application of the 4-lump model were also investigated.

scholarly journals Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot and other methods

1974 ◽  
Vol 139 (3) ◽  
pp. 721-730 ◽  
Author(s):  
Athel Cornish-Bowden ◽  
Robert Eisenthal
Keyword(s):  
Least Squares ◽  
Kinetic Parameters ◽  
Kinetic Data ◽  
Experimental Error ◽  
Preceding Paper ◽  
Enzyme Kinetic ◽  
Confidence Limits ◽  
Method Of Least Squares ◽  
Linear Plot ◽  
Least Squares Estimates

The statistical implications of the direct linear plot for enzyme kinetic data, described in the preceding paper (Eisenthal & Cornish-Bowden, 1974), are discussed for the case of the Michaelis–Menten equation. The plot is shown to lead directly to non-parametric confidence limits for the kinetic parameters, V and Km, which depend on far less sweeping assumptions about the nature of experimental error than those implicit in the method of least squares. Median estimates of V and Km can also be defined, which are shown to be more robust than the least-squares estimates in a wide variety of experimental situations.

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