Abstract
We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Two-dimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases.
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References
Akaike, H.: Seasonal adjustment by a Bayesian modeling. J. Time Ser. Anal. 1, 1–14 (1980)
Cai, Z.: Trend time-varying coefficient time series models with serially correlated errors. J. Econom. 136, 163–188 (2007)
Currie, I.D., Durbán, M., Eilers, P.H.C.: Generalized linear array models with applications to multidimensional smoothing. J. R. Stat. Soc., Ser. B 68, 259–280 (2006)
Eilers, P.H.C., Currie, I.D., Durbán, M.: Fast and compact smoothing on large multidimensional grids. Comput. Stat. Data Anal. 50, 61–76 (2006)
Eilers, P.H.C., Gampe, J., Marx, B.D., Rau, R.: Modulation models for seasonal time series and incidence tables. Stat. Med. 27(17), 3430–3441 (2008)
Eilers, P.H.C., Marx, B.D.: Generalized linear additive smooth structures. J. Comput. Graph. Stat. 11(4), 758–783 (2002)
Fahrmeir, L., Tutz, G.: Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd edn. Springer, New York (2001)
Harvey, A.C.: Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge (1989)
Lambert, P., Eilers, P.H.C.: Bayesian proportional hazards model with time varying regression coefficients: A penalized Poisson regression approach. Stat. Med. 24, 3977–3989 (2005)
Lee, Y., Nelder, J.A., Pawitan, Y.: Generalized Linear Models with Random Effects. Chapman and Hall/CRC Press, London (2006)
Ngo, L., Wand, M.P.: Smoothing with mixed model software. J. Stat. Softw. 9(1), 1–54 (2004)
Rau, R., Doblhammer, G.: Seasonal mortality in Denmark. The role of sex and age. Demogr. Res. 9, 197–222 (2003)
Tutz, G., Binder, H.: Flexible modelling of discrete failure time including time-varying smooth effects. Stat. Med. 23(15), 2445–2461 (2004)
Tutz, G., Binder, H.: Boosting ridge regression. Comput. Stat. Data Anal. 51(12), 6044–6059 (2007)
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Marx, B.D., Eilers, P.H.C., Gampe, J. et al. Bilinear modulation models for seasonal tables of counts. Stat Comput 20, 191–202 (2010). https://doi.org/10.1007/s11222-009-9144-9
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DOI: https://doi.org/10.1007/s11222-009-9144-9