The article discusses different ways to measure how well models fit categorical data, especially when the data is sparse. The researchers found a simple solution to calculate Pearson's goodness-of-fit statistic even when some response patterns have zero observed frequencies. They also developed a new fit statistic that works well with small expected frequencies. Simulation studies showed that the new statistic performs consistently and can be a good choice for model testing. Additionally, they highlighted the importance of using two-sided model testing in certain situations for better results.