Modeling Seasonal Effects on the Lexis Surface

Roland Rau, Duke University
Jutta Gampe, Max Planck Institute for Demographic Research
Paul H. Eilers, Leids Universitair Medisch Centrum (LUMC)
Brian D. Marx, Louisiana State University

We are modeling how seasonality in deaths changes over age and time using two-dimensional varying coefficient Poisson regression. This analysis represents a novel approach, which allows us to look at the dynamics of seasonal patterns in both dimensions on the Lexis surface simultaneously. Due to the strong and varying annual cyclical behavior over time, sine and cosine regressors model periodicity, but their coefficients are allowed flexibility by assuming smoothness over the age and time plane. The two-dimensional varying coefficient surfaces are estimated using a gridded 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 AIC. The seasonal effects are summarized with two-dimensional amplitude and phase image plots. An illustrative example is provided using the female respiratory death monthly count data for ages 44-96 during 1959-1999.