Title: Goodness of fit test and model assessment for sparse multinomials
Authors: Ioulia Papageorgiou - Athens University of Economics and Business (Greece) [presenting]
Abstract: The focus is on goodness-of-t tests under a very general framework where testing the fit of a model is equivalent with testing a hypothesis about the parameters from a multinomial distribution. A very realistic problem in such applications is that the sample size is small and at the same time the dimension of the problem is high, resulting to a sparse contingency table where asymptotic tests does not hold. Methods in the literature, such as resampling methods, posterior predictive p-values etc., require refitting of the model a number of times, and are time-consuming and computational effort demanding. Moreover, the distribution of the p-value is not uniform and therefore results are not interpretable. The proposed method is a variant of the posterior predictive p-value. The main advantage of the method is that no refitting of the model is required and the distribution of the resulting p-value is uniform. Consequently, the method outperforms all other competitive approaches with respect to computational efficiency and interpretability of the results. The proposed method is quite general and it can be implemented to a wide range of scientific areas. We present an application in capture-recapture models. More specifically, various models aiming to estimate animal population abundance based on a capture-recapture sample are assessed with respect to the model fitting, via the proposed methodology, and compared with previous relative results in the literature.