A new approach for fitting growth models in random environment

PRAJNESHU PRAJNESHU; HIMADRI GHOSH

doi:10.56093/ijans.v87i12.79873

Authors

PRAJNESHU PRAJNESHU ICAR-Indian Agricultural Statistics Research Institute, New Delhi 110 012 India
HIMADRI GHOSH ICAR-Indian Agricultural Statistics Research Institute, New Delhi 110 012 India

https://doi.org/10.56093/ijans.v87i12.79873

Keywords:

Gompertz growth model, Pig weight data, SAS software package, Stochastic differential equation model

Abstract

Nonlinear growth models are widely employed in Animal sciences for describing growth of various species of
animals. Nonlinear estimation procedures are generally employed for estimation of parameters. However, one
limitation of these models is that they are applicable only when the data are available at equidistant epochs. Another limitation is that the fluctuations in the system cannot be satisfactorily explained simply by adding an error term to the deterministic formulation. The purpose of this article is to bring to the notice of Animal scientists the new approach of Stochastic differential equation modelling, which is capable of incorporating both the above aspects. The methodology is discussed by considering Gompertz growth model. Relevant SAS codes for fitting the model are developed. Finally, the methodology is illustrated on secondary monthly pig weight data, collected at the
piggery farm of Indian Veterinary Research Institute, Izatnagar, Bareilly, India.

Downloads

Download data is not yet available.

References

Cohen S and Elliott R J. 2015. Stochastic Calculus and Applications. 2nd edn. Birkhauser, Switzerland. DOI: https://doi.org/10.1007/978-1-4939-2867-5

Das P. 2015. ‘Estimation of growth parameters using nonlinear mixed effect model and comparison with fixed effect model in animals.’ M.Sc. thesis, Indian Agricultural Research Institute, New Delhi.

Filipe P A, Braumann C A, Brites N M and Roquete C J. 2013. Prediction for individual growth in a random environment, pp193–201. “Recent Developments in Modeling and Applications in Statistics”. (Eds) Oliveira P E, Temido M G, Henriques C and Vichi M. Springer, Berlin. DOI: https://doi.org/10.1007/978-3-642-32419-2_20

Ghosh H, Iquebal M A and Prajneshu 2011. Bootstrap study of parameter estimates for nonlinear Richards growth model through Genetic algorithm. Journal of Applied Statistics 38: 491–500. DOI: https://doi.org/10.1080/02664760903521401

Matis J H, Thomas R K, Wopke V D W, Alejandro C C, Matis T I and Grant W E. 2009. Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data. Ecological Modelling 220:1745–51. DOI: https://doi.org/10.1016/j.ecolmodel.2009.04.026

Oksendal B. 2003. Stochastic Differential Equations: An Introduction with Applications. 5th edn. Springer Science and Business Media, Berlin.

Prajneshu and Kandala V M. 2003. Mixed-influence nonlinear growth model. Journal of Indian Society of Agricultural Statistics 56: 19–24.

Prajneshu and Ravichandran S. 2003. A method for fitting of nonlinear Fox model in fisheries. Indian Journal of Animal Sciences 73: 329–31.

Seber G A F and Wild C J. 2003. Nonlinear Regression, John Wiley and Sons, New York.

Venugopalan R and Prajneshu. 1997. Von Bertalanffy growth model with autocorrelated errors. Indian Journal of Fisheries 44: 63–67.