Bilinear modulation models for seasonal tables of counts |
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Authors: | Brian D Marx Paul H C Eilers Jutta Gampe Roland Rau |
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Institution: | (2) Informatics and Telematics Institute, Thessaloniki, Greece; |
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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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Keywords: | |
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