Bayesian goodness-of-fit measures for individual-level models of infectious disease
In simple models (e.g. linear models) there are a variety of tried and tested ways to assess goodness-of-fit (GOF). However, in complex non-linear models, such as spatiotemporal individual-level models (ILMs), 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 (e.g. dates-of-infection). Within a Bayesian context, a major tool in 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. The statistics containing both temporal and spatial information are among the least impressive in assessing model fit, whereas a statistic that contains temporal information only provides preferable results.