This chapter focuses on the log-linear cognitive diagnosis modeling (LCDM), a general diagnostic classification model (DCM) family that allows researchers to model a large group of diagnostic classification models (DCMs) flexibly. Although the LCDM has important advantages over other core DCMs, it remains relatively under-researched in language assessment. This chapter first provides language testers with an introduction to the theoretical and statistical underpinnings of the LCDM. Next, it demonstrates how the LCDM could be applied to a high-stakes listening comprehension test. Finally, it presents guidelines on how to estimate and interpret the model, item, and examinee parameters with readily available software.