Volume 6, Issue 5, October 2020, Page: 153-162
Discrete Weibull and Artificial Neural Network Models in Modelling Over-dispersed Count Data
Kipkorir Collins, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Waititu, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Oct. 2, 2020;       Accepted: Oct. 20, 2020;       Published: Oct. 26, 2020
DOI: 10.11648/j.ijdsa.20200605.15      View  60      Downloads  60
Abstract
In modelling count data, the use of least square regression models suffers several methodological limitations and statistical properties in instances of discrete, non-negative integer count of a dependent variable. Unlike the classical regression model, count data models are non-linear with many properties of the response variable relating to discreteness, non-linearity and deal with non-negative values only. A good starting point for modelling count data is the Poisson regression model since it lends itself well with the nature properties of count data. However, the limitation of equi-dispersion renders it inappropriate for modelling over-dispersed data. Negative Binomial regression model has been widely used and considered as the default regression model for over-dispersed count data. This model is a modification of Poisson regression model and though widely used, it might not be the best model for over-dispersion and other models have been found to perform better. Over-dispersion in this study was defined relative to the Poisson model. This study models over-dispersed count data using discrete Weibull regression model and artificial neural network model with a median neuron in the hidden layer. After fitting the two models on simulated data and real data, the artificial neural network model outperformed the discrete Weibull regression model. Application on data set from German health survey gave RMSE of DW regression model as 69.0668 and 35.5652 for the artificial neural network.
Keywords
Over-dispersion, Count, Discrete Weibull, Artificial Neural Network
To cite this article
Kipkorir Collins, Anthony Waititu, Anthony Wanjoya, Discrete Weibull and Artificial Neural Network Models in Modelling Over-dispersed Count Data, International Journal of Data Science and Analysis. Vol. 6, No. 5, 2020, pp. 153-162. doi: 10.11648/j.ijdsa.20200605.15
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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