Assessment of Asymptotic and Logistics Growth Models on A Chemist Data
##plugins.themes.bootstrap3.article.main##
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.
References
-
Kutner MH, Nachtshien CJ, Neters Li W. Applied Linear Statistical Methods. 5th ed. McGraw-Hill Irwin; 2005.
Google Scholar
1
-
Biu EO, Wonu N. Estimation of Parameters of Two Non-linear Regression Models Using Assumed Values: Reciprocal Power Regression Models. Asian Research Journal of Mathematic.2019;15(4): 1-19.
Google Scholar
2
-
Mahaboob B, Venkateswarlu B, Mokeshrayalu G, Balasiddamuni P. A different approach to estimate nonlinear regression model using numerical methods. Conf. Series: Materials Science and Engineering. 2017; 263.
Google Scholar
3
-
Hossain MdJ, Hossain MR, Datta D, Islam MdS. Mathematical Modelling of Bangladesh Population Growth. Journal of Statistics and Management System. 2015; 18(3): 289-300.
Google Scholar
4
-
Wei H, Jiang Y, Zhang Y. A Review of Two Population Growth Models and an Analysis of Factors Affecting the Chinese Population Growth. Asian Journal of Economic Modelling. 2015; 3(1): 8-20.
Google Scholar
5
-
Tkachenko N, Weissmann J.D, Petersen WP, Lake G, Zollikofer CPE, Callegari S. Individual-based modelling of population growth and diffusion in discrete time. PLoS ONE. 2017; 12(4): 0176101.
Google Scholar
6
-
Suherman MM, Rakhmawati RM, Andriani H, Suyitno S, Junaidi I. The Application of Differential Equation of Verhulst Population Model on Estimation of Bandar Lampung Population. IOP Conf. Series: Journal of Physics. 2019; 1155: 0120.
Google Scholar
7
-
Birch CPD. A new generalized logistic sigmoid growth equation compared with the Richards growth equation. Ann. Bot. 1999; 83: 713–723.
Google Scholar
8
-
Yin X, Lantinga EA, Schapendonk AHCM, Zhong X. Some quantitative relationships between leaf area index and canopy nitrogen content and distribution. Ann. Bot. 2003; 91: 893–903.
Google Scholar
9
-
Valent F, Schiava F, Savonnito C, Gallo T, Brusaferro S, Barbone F. Risk factors for fatal road accidents in Udine, Italy. Accident Analysis & Prevention. 2002; 34: 71–84.
Google Scholar
10
-
Christopher YS. Logistic growth modelling of COVID-19 proliferation in China and its international implications. International Journal of Infectious Disease. 2020; 96: 582-589.
Google Scholar
11
-
Ahmed SRA. Using logistic regression models to determine factors affecting diabetes in red sea state. International Journal of Statistics and Applied Mathematics. 2019; 4(4): 12-17.
Google Scholar
12
-
Francois D, Youness M. Growth Models with Oblique Asymptote. Mathematical Modelling and Analysis. 2013; 18(2): 204-218
Google Scholar
13
-
Pommerening A, Muszta A. Methods of modelling relative growth rate. Forest Ecosystems. 2015; 2.
Google Scholar
14