In applying the Rasch model to language assessment data, it is important to note that unidimensionality and local independence are two crucial measurement requirements that should be addressed. This chapter focuses on these two requirements for unidimensional Rasch measurement and illustrates how they should be investigated in language assessment research. The chapter first explains the concepts and reviews recent studies in language assessment that include the examination of these two principles. It then uses a language test dataset to illustrate how these two measurement properties are investigated. While the empirical evidence for unidimensionality is manifold, that for local independence is more indirect. The chapter concludes by discussing how violations of these two principles should be addressed in language assessment development and research.