Dealing with the badness of goodness-of-fit

Speaker: Rishika Chopara, University of Auckland, New Zealand

Abstract:

Goodness-of-fit (GOF) testing is vital to statistical analysis, as it allows us to validate the reliability of any statistical inference we make.

In many statistical models, the deviance is used to assess GOF by comparing it against a Chi-squared distribution. However, in some situations (e.g. when dealing with sparse counts) the deviance does not have a Chi-squared distribution, even approximately, yielding such tests unusable. In principle, the true distribution for the deviance is computable, however in practice it is often intractable. We show that generally, we can accurately approximate the true underlying distribution of the deviance using a Gamma distribution. Using this approximation, we enhance the usability and power of GOF tests while retaining the familiarity and convenience of the deviance statistic.

Using a range of capture-recapture models for illustration, we show how our method can be used to accurately approximate the distribution of the deviance when dealing with various levels of data sparsity. With this approach, we aim to provide an accessible and effective GOF testing framework for complex modelling scenarios such as spatial capture-recapture.