Goodness-of-fit measures for individual-level models of infectious disease in a Bayesian framework

In simple models there are a variety of tried and tested ways to assess goodness-of-fit. However, in complex non-linear models, such as spatio-temporal individual-level models, less research has been done on how best to ascertain goodness-of-fit. Often such models are fitted within a Bayesian statistical framework, since such a framework is ideally placed to account for the many areas of data uncertainty. Within a Bayesian context, a major tool for assessing goodness-of-fit is the posterior predictive distribution. That is, a distribution for a test statistic is found through simulation from the posterior distribution and then compared with the observed test statistic for the data. Here, we examine different test statistics and ascertain how well they can detect model misspecification via a simulation study.