Abstract

The goodness of fit (GOF) of a statistical model, such as an item response theory (IRT) model, describes how well the model matches a set of observations. It is useful to distinguish between goodness of fit indices and goodness of fit statistics. Goodness of fit indices summarize the discrepancy between the values observed in the data and the values expected under a statistical model. Goodness of fit statistics are GOF indices used in statistical hypothesis testing. In other words, GOF statistics are GOF indices with known sampling distributions usually obtained using asymptotic methods. Because p-values obtained using asymptotic methods may behave poorly in small samples, a great deal of research has been devoted to investigate using simulation studies under which conditions the asymptotic p-values of GOF statistics are accurate (e.g., Maydeu-Olivares & Montaño, 2013).