This chapter presents methods for evaluating measurement quality within the framework of Rasch measurement theory with a focus on dichotomous Rasch models. Unlike traditional model selection approaches in statistics and other IRT models, Rasch analysis begins with a theoretically grounded model and tests whether empirical data conform to its principles based on invariant measurement. Measurement quality is examined through three inter-related aspects of model-data fit including a construct focus, item focus, and person focus. The construct focus evaluates the theoretical coherence of the latent variable using tools such as Wright Maps, unidimensionality analysis, local independence (Q3 statistics), and principal components analysis of residuals. The item focus examines the reasonableness of the item hierarchies, fit statistics (Infit/Outfit MSE), item response functions, and reliability of item separation. The person focus similarly assesses individual response patterns of persons, distribution of persons on the latent variability, and reliability of person separation. Illustrations using the Learning Stimulation Scale demonstrate the application of these methods using the TAM and EIRM packages in R for parameter estimation and fit analysis. The chapter emphasizes that residual-based diagnostics are central to Rasch evaluation, and that multiple sources of evidence should be integrated to support claims of measurement invariance. These foundational methods prepare the ground for explanatory Rasch models discussed in later chapters.