An insight into technology diffusion of tractor through Weibull growth model

Most of the technological innovation diffusion follows an S-shaped curve. But, in many practical situations this may not hold true. To this end, Weibull model was proposed to capture the diffusion of new technological innovation, which does not follow any specific pattern. Nonlinear growth models pl...

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Bibliographic Details
Published in:Journal of applied statistics 2018-03, Vol.45 (4), p.682-696
Main Authors: Gurung, Bishal, Singh, K. N., Shekhawat, Ravindra Singh, Yeasin, Md
Format: Article
Language:English
Subjects:
Computer simulation
Economic models
Genetic algorithms
Gompertz model
Growth models
Innovations
logistic model
Mathematical models
Parameter estimation
S curves
Statistical methods
technology diffusion
Weibull growth model
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Summary:Most of the technological innovation diffusion follows an S-shaped curve. But, in many practical situations this may not hold true. To this end, Weibull model was proposed to capture the diffusion of new technological innovation, which does not follow any specific pattern. Nonlinear growth models play a very important role in getting an insight into the underlying mechanism. These models are generally 'mechanistic' as the parameters have meaningful interpretation. The nonlinear method of estimation of parameters of Weibull model fails to converge. Taking this problem into consideration, we propose the use of a powerful technique of genetic algorithm for parameter estimation. The methodology is also validated by simulation study to check whether parameter estimates are closer to the real value. For illustration purpose, we model the tractor density time-series data of India as a whole and some major states of India. It is seen that fitted Weibull model is able to capture the technology diffusion process in a reasonable manner. Further, comparison is also made with Logistic and Gompertz model; and is found to perform better for the data sets under consideration.
ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2017.1289504