Flexible distributed lags for modelling earthquake data

type="main" xml:id="rssc12077-abs-0001"> Heavy long-lasting rainfall can trigger earthquake swarms. We are interested in the specific shape of lagged rain influence on the occurrence of earthquakes at different depths at Mount Hochstaufen, Bavaria. We present a novel penalty structure for interpretable and flexible estimates of lag coefficients based on spline representations. We provide an easy-to-use implementation of our flexible distributed lag approach that can be used directly in the established R package mgcv for estimation of generalized additive models. This allows our approach to be immediately included in complex additive models for generalized responses even in hierarchical or longitudinal data settings, making use of established stable and well-tested inference algorithms. The benefit of flexible distributed lag modelling is shown in a detailed simulation study.

[1]  S L Zeger,et al.  Bayesian Distributed Lag Models: Estimating Effects of Particulate Matter Air Pollution on Daily Mortality , 2009, Biometrics.

[2]  Shirley Almon The Distributed Lag Between Capital Appropriations and Expenditures , 1965 .

[3]  Paul H. C. Eilers,et al.  Direct generalized additive modeling with penalized likelihood , 1998 .

[4]  G. Wahba A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem , 1985 .

[5]  S. Wood Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models , 2011 .

[6]  N. Deichmann,et al.  Seismotectonics of the eastern Swiss Alps and evidence for precipitation-induced variations of seismic activity , 1992 .

[7]  M P Wand,et al.  Generalized additive distributed lag models: quantifying mortality displacement. , 2000, Biostatistics.

[8]  Paul H. C. Eilers,et al.  Flexible smoothing with B-splines and penalties , 1996 .

[9]  External forcing of earthquake swarms at Alpine regions: example from a seismic meteorological network at Mt. Hochstaufen SE-Bavaria , 2011 .

[10]  A Gasparrini,et al.  Distributed lag non-linear models , 2010, Statistics in medicine.

[11]  R. Todd Ogden,et al.  Smoothing parameter selection for a class of semiparametric linear models , 2009 .

[12]  S. Wood mgcv:Mixed GAM Computation Vehicle with GCV/AIC/REML smoothness estimation , 2012 .

[13]  S. Wood,et al.  Coverage Properties of Confidence Intervals for Generalized Additive Model Components , 2012 .

[14]  V. Muggeo,et al.  Modeling temperature effects on mortality: multiple segmented relationships with common break points. , 2008, Biostatistics.

[15]  Paul H. C. Eilers,et al.  Smoothing and forecasting mortality rates , 2004 .

[16]  Annibale Biggeri,et al.  Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health , 2007, Comput. Stat. Data Anal..