  This paper underscores the vital role of the chi-square test within political
science research utilizing structural equation modeling (SEM). The ongoing
debate regarding the inclusion of chi-square test statistics alongside fit
indices in result presentations has sparked controversy. Despite the recognized
limitations of relying solely on the chi-square test, its judicious application
can enhance its effectiveness in evaluating model fit and specification. To
exemplify this, we present three common scenarios pertinent to political
science research where fit indices may inadequately address goodness-of-fit
concerns, while the chi-square statistic can be effectively harnessed. Through
Monte Carlo simulations, we examine strategies for enhancing chi-square tests
within these scenarios, showcasing the potential of appropriately employed
chi-square tests to provide a comprehensive model fit assessment. Our
recommendation is to report both the chi-square test and fit indices, with a
priority on precise model specification to ensure the trustworthiness of model
fit indicators.
