Generalized Additive Models in Business and Economics
Abstract
The paper presents applications of a class of semi-parametric models called generalized additive models (GAMs) to several business and economic datasets. Applications include analysis of wage-education relationship, brand choice, and number of trips to a doctor’s office. The dependent variable may be continuous, categorical or count. These semi-parametric models are flexible and robust extensions of Logit, Poisson, Negative Binomial and other generalized linear models. The GAMs are represented using penalized regression splines and are estimated by penalized regression methods. The degree of smoothness for the unknown functions in the linear predictor part of the GAM is estimated using cross validation. The GAMs allow us to build a regression surface as a sum of lower-dimensional nonparametric terms circumventing the curse of dimensionality: the slow convergence of an estimator to the true value in high dimensions. For each application studied in the paper, several GAMs are compared and the best model is selected using AIC, UBRE score, deviances, and R-sq (adjusted). The econometric techniques utilized in the paper are widely applicable to the analysis of count, binary response and duration types of data encountered in business and economics.
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References
Baltas, G., Determinants of store brand choice: a behavioral analysis. Journal of Product & Brand Management, Vol. 6, No.5, (1997), pp. 315 – 324.
Cameron, A. C. and P. Trivedi, Microeconometrics. Cambridge University Press, New York, (1998).
Greene, W. H., Econometric Analysis. Pearson/Prentice Hall, New York, (2008).
Guadagni, P. M. and J. D. Little, A Logit Model of Brand Choice Calibrated on Scanner Data, Marketing Science, Vol. 2, No. 3, (1983), pp. 203-238.
Gurmu, S., Semiparametric estimation of hurdle regression models with an application to medicaid utilization. Journal of Applied Econometrics, Vol. 12, No. 3, (1997), pp. 225-242.
View more references (10)
Hastie, T. & Tibshirani, R., Generalized Additive Models, Statistical Science, Vol. 1, No. 3, (1986), pp. 297-318.
Hastie, T. & Tibshirani, R., Generalized Additive Models: Some Applications, Journal of the American Statistical Association, Vol. 82, No. 398, (1987), pp. 371-386.
Hastie, T. & Tibshirani, R., Generalized Additive Models. Chapman and Hall, London, (1990).
Hill, R. C., W. E. Griffiths, and G. C. Lim, Principles of Econometrics, Wiley, New Jersey, (2012).
Jain, D. C., N. J. Vilcassim and P. K. Chintagunta, A random–coefficients logit brand–choice model applied to panel data”, Journal of Business and Economics Statistics, Vol. 12, No. 3. (1994), pp. 317-328.
McCullagh, P. and J. Nelder, Generalized Linear Models, Chapman and Hall, London (1989).
Manski, C. and D. McFadden, Structural Analysis of Discrete Data and Econometric Applications, MIT Press, Cambridge, (1981).
Paap, R. and P. H Frances, A dynamic multinomial probit model for brand choices with different short–run effects of marketing mix variables”, Journal of Applied Econometrics, Vol. 15, No. 6, (2000), pp. 717–744.
Wood, S. N., R-package mgcv, (2012).
Wood, S.N., Generalized Additive Models: an introduction with R, CRC, Boca Raton, (2006).