Somnath Mukhopadhyay Information and Decision Sciences Department

1. Examining Factors and Predictive Validity of a New Set of Global Internet Diffusion Models Including Neural Networks Somnath Mukhopadhyay Information and Decision Sciences Department The University of Texas at El Paso

2. Introduction • Global International Growth • Traditional Diffusion Models • Neural Network Model • Research Method • Results • Conclusion and Future Research

3. Global Adoption of the Internet • Rapid Growth Globally • Inadequate capacity planning caused by inaccurate prediction of growth • Alternative approach required (Rai et al. 1998) • Significant past research on traditional diffusion models (Gurbaxani, 1990; Mahajan et al. 1990, Venkatraman et al. 1994, Rai et al. 1998)

4. Traditional Diffusion Models • Imitation Theory of Growth • S-shaped curves • Total number of potential adopters and current level of adopters • Two s-shaped curves: Gompertz and Logistic • Exponential Model with ever increasing growth function

5. Limitation of Traditional Diffusion Models • Growth function must be predetermined • Not flexible enough to respond to external factors influencing the growth • Difficult to optimize parameters for nonlinear functional relationship • Does not perform well on new samples even when the models fit calibration samples

6. Pure Diffusion Model Logistic Model: log(( 1/Intt ) – 1/u) = b0+b1*t where, the upper limit (u) is restricted to 1000. Gompertz Model: • log( Intt ) = b0*log(y*)+b1*log(Intt-1) where, b0, b1 are constants and y* is the equilibrium level.

7. Neural Network Models • Connectionist theory of pattern seeking in data • Functional relationship determined by going through the data • Flexible enough to respond to sudden changes in data • No assumption of parametric distribution required

8. Nonlinear Regression Form of a Feed-forward one layered NN

9. Research Method • Traditional time-series forecasting model • Pure Diffusion models – Logistic and Gompertz • NN model

10. Build initially an adoption model over a large number of nations with factors such as economic, infrastructural and educational in two time intervals Identify the statistically relevant factors Design new diffusion models over a period of time, by incorporating the factors obtained earlier. Obtain a neural version of the improved new model Test the forecasting ability of each model on a new data set Method (contd.) • Framework of modeling Internet Diffusion

11. Data Variable Name Definition INTxxxx Internet access per thousand in each candidate nation in year xxxx GDPxxxx Base GDP per capita in year xxxx in each candidate nation TELxxxx The # of telephones per 1000 in year xxxx in each nation PCxxxx The # of PC per 1000 in each candidate nation in year xxxx EDUxxxx Average secondary level enrollment ratio in year xxxx Source: World Bank Data Base: http://www.worldbank.org

12. Data Contd. • Years 1991 – 2000 on 20 OECD Nations • Calibration sample: 1991-1999 • Held-out test sample: 2000

13. Model Performances (MAPE) on calibration Data

14. Model Performances (MAPE) on test Data

15. Rich Prediction Surface of NN

16. Conclusion • NN models are superior to traditional models in forecasting the Internet Growth • NN models can be applied to forecast any diffusion of innovation processes • NN models are flexible in creating rich prediction surfaces • NN models can handle sudden external influence on diffusion better than traditional models

17. Future Research • Extend the research to specific countries in a region • Extend the research to other innovation processes • Generating hybrid forecasting models by combining traditional methods with NN • Try different NN models to further improve the forecasting performance