What influences COVID-19 infection rates: A statistical approach to identify promising factors applied to infection data from Germany

Moritz Mercker; Uwe Betzin; Dennis Wilken

First, we fitted the generalised additive mixed model (GAMM) [7, 21] to the entire time series of each AD, where the federal state has been used as a random intercept, and the date as a smooth predictor term. Additive regression models allow to estimate nonlinear dependencies between predictor variables (here e.g. the date) and an outcome variable (here e.g. the number of reported infections) [7, 21] . Consideration of such nonlinearities is fundamental here, since the initial increase and possible later decrease in infection numbers is often strongly nonlinear. In particular (if not stated otherwise) the optimal smoothness has been determined using generalised cross-validation methods [18] . Random intercepts (i.e., the use of mixed modelling [2, 21] ) have been applied if data are not independent, but instead nested within certain units (such as states). Since infection numbers are additionally temporally autocorrelated (infection numbers depend to some degree on the number of the day before), an auto-regression (AR) structure of order 1 has been added to the model. Finally, a negative-binomial probability distribution has been used, to account for the fact that infection numbers do not follow a normal distribution but are (possibly overdispersed) count data [9, 20, 21] . In addition to the date, also the weekday has been introduced as a smooth, in particular as a cyclic smooth [18] in order to partial out the distinct effect of the weekday on reported infection numbers.