Rigorous quantitative methods are essential for drawing reliable causal inferences in the social sciences. My methodological research addresses key challenges in statistical modelling that arise across empirical political science. This includes work on how interaction and quadratic effects can be biased by omitted nonlinearities, how standard approaches to binary dependent variable models can produce misleading results in the presence of separation and rare events, and how the common practice of transforming binary event data to study onsets can distort substantive conclusions. This work recommends practical solutions, including regularised estimators and weakly-informative Bayesian priors, that researchers can apply to improve the reliability of their findings.