I'm currently working on analysis of excess mortality during the pandemic as part of my Master's thesis. I am using UK data, from Public Health England, who use a Quasi Poisson model for expected deaths had the pandemic not occured. The methodology for the model and the data are publicly available, though the model parameters etc are not.
The methodology document mainly motivates use of a Quasi Poisson model due to overdispersion, however the fitted model has a dispersion parameter of approximately 0.3, suggesting underdispersion.
Firstly I was wondering what the explanation of this under dispersion might be? I'm fairly new to quasi poisson models and excess mortality studies.
Secondly, I'm looking to obtain some prediction intervals for the ratio of registered (actual) to expected deaths, and am doing so by simulating from the quasi poisson model as described in the previously linked methodology document. I have found this code, lines 461 to 488 to do so. I am struggling to understand the justification of why Line 480 is used in the under dispersed case. I know that a dispersion parameter less than 1 will mean the
rqpois function starting on Line 461 is ill defined, but I don't understand why the dispersion parameter is then just set to 1 in the simulations to deal with this.