Flexible distributed lag models for count data using mgcv

In this tutorial we present the use of R package mgcv to implement Distributed Lag Non-Linear Models (DLNMs) in a flexible way. Interpretation of smoothing splines as random quantities enables approximate Bayesian inference, which in turn allows uncertainty quantification and comprehensive model checking. We illustrate various modeling situations using open-access epidemiological data in conjunction with simulation experiments. We demonstrate the inclusion of temporal structures and the use of mixture distributions to allow for extreme outliers. Moreover, we demonstrate interactions of the temporal lagged structures with other covariates with different lagged periods for different covariates. Spatial structures are also demonstrated, including smooth spatial variability and Markov random fields, in addition to hierarchical formulations to allow for non-structured dependency. Posterior predictive simulation is used to ensure models verify well against the data.