Semi-parametric mixed effects models for longitudinal data with applications in business and economics

  • Authors

    • Sunil Sapra Department of Economics and Statistics California State University 5151 State University Dr Los Angeles, CA 90032, USA
    2014-09-25
    https://doi.org/10.14419/ijasp.v2i2.3624

  • Longitudinal data is becoming increasingly common in business, social sciences, and biological sciences due to the advantages it offers over cross-section data in modeling and incorporating heterogeneity among subjects and in being able to make causal inferences from observational data. Parametric models and methods are widely used for analyzing longitudinal data for continuous, discrete, and count data occurring in these disciplines. Some popular models are Gaussian, Logit, and Poisson fixed and random effects models. These models are unreliable in situations in which the link function is nonlinear and the form of nonlinearity is not known with certainty. This paper employs a semi-parametric extension of fixed and random effects models called generalized additive mixed models (GAMMs) to analyze several longitudinal data sets. These semi-parametric models are flexible and robust extensions of generalized linear models. Following Wood [19], the GAMMs are represented using penalized regression splines and estimated by penalized regression methods treating the penalized component of each smooth as a random effect term and the unpenalized component as a fixed effect term. The degree of smoothness for the unknown functions in the linear predictor part of the GAMM is estimated as the variance parameter of the term. Applications of GAMMs studied include analysis of anti-social behavior, decision to use a professional tax preparer, and analysis of patent data on manufacturing firms. For each application, several GAMMs are compared with their parametric counterparts.

    Keywords: Generalized Additive Mixed Models (GAMMS), Generalized Linear Mixed Models (GLMMS), Logit Models, Poisson Regression Models, Penalized Regression Splines.

  • References

    1. Allison, P. Fixed Effects Regression Models, Sage, (2009).
    2. Baltas, G., Determinants of store brand choice: a behavioral analysis. Journal of Product & Brand Management, Vol. 6, No.5, (1997), pp. 315 – 324. http://dx.doi.org/10.1108/10610429710179480.
    3. Breslow, N. and Clayton, D. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, Vol. 88, No.1, (1993), pp. 9-25.
    4. Cameron, A. C. and P. Trivedi, Microeconometrics. Cambridge University Press, New York, (1998).
    5. Frees, E. Longitudinal and Panel Data. Cambridge University Press, New York, (2004). http://dx.doi.org/10.1017/CBO9780511790928.
    6. Greene, W. H., Econometric Analysis. Pearson/Prentice Hall, New York, (2008).
    7. 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. http://dx.doi.org/10.1287/mksc.2.3.203.
    8. Hastie, T. & Tibshirani, R, Generalized Additive Models, Statistical Science Vol.1, No.3, (1986), pp. 297-318. http://dx.doi.org/10.1214/ss/1177013604.
    9. Hastie, T. & Tibshirani, R., Generalized Additive Models. Chapman and Hall, London, (1990).
    10. Lin, X.and Zhang D. Inference in Generalized Additive Mixed Model by Using Smoothing Splines. Journal of the Royal Statistical Society, Vol. 61, No. 2, (1999), 381-400. http://dx.doi.org/10.1111/1467-9868.00183.
    11. McCullagh, P. and J. Nelder, Generalized Linear Models, Chapman and Hall, London (1989). http://dx.doi.org/10.1007/978-1-4899-3242-6.
    12. Manski, C. and D. McFadden, Structural Analysis of Discrete Data and Econometric Applications, MIT Press, Cambridge, (1981).
    13. Ruppert, D., M. Wand, and R. Carrol, Semiparametric Regression, Cambridge University Press, Cambridge, (2003). http://dx.doi.org/10.1017/CBO9780511755453.
    14. Sapra, S., Generalized Additive Models in Business and Economics, International Journal of Advanced Statistics and Probability, Vol.1, No. 3, (2013), pp. 64-81.
    15. Silverman, B. W. Spline smoothing: The equivalent variable kernel method. Annals of Statistics, Vol 12, No. 4, (1984), pp. 898-916. http://dx.doi.org/10.1214/aos/1176346710.
    16. Wabha, G. Bayesian confidence intervals for the :cross validated" smoothing spline, Journal of the Royal Statistical Society Series B, Vol. 45, No. 1, (1983), pp. 133-150.
    17. Wang, Y. Mixed affects smoothing analysis of variance, Journal of the Royal Statistical Society Series B, Vol. 60, No. 1, (1998), pp. 159-174. http://dx.doi.org/10.1111/1467-9868.00115.
    18. Wood, S. N., R-package gamm4, (2012).
    19. Wood, S.N., Generalized Additive Models: an introduction with R, CRC, Boca Raton, (2006).

  • Downloads