A recent trend in education has been toward formative assessments to enable teachers, parents, and administrators assist students succeed. Cognitive diagnostic modeling (CDM) has the potential to provide valuable information for stakeholders to assist students identify their skill deficiency in specific academic subjects. Cognitive diagnosis models are mainly viewed as a family of latent class confirmatory probabilistic models. These models allow the mapping of students' skill profiles/academic ability. Using a complex simulation studies, the methodological issues in one of the existing cognitive models, referred to as compensatory reparameterized unified model (CRUM) under the log-linear model family of CDM, was investigated. In order for practitioners to implement these models, their item parameter recovery and examinees' classifications need to be studied in detail. A series of complex simulated data were generated for investigation with the following designs: three attributes with seven items, three attributes with thirty five items, four attributes with fifteen items, and five attributes with thirty one items. Each dataset was generated with observations of: 50, 100, 500, 1,000, 5,000, and 10,000 examinees. The first manuscript is the report of the investigation of how accurately CRUM could recover item parameters and classify examinees under true QMattrix specification and various research designs. The results suggested that the test length with regards to number of attributes and sample size affects the item parameter recovery and examinees classification accuracy. The second manuscript is the report of the investigation of the sensitivity of relative fit indices in detecting misfit for over- and opposite-Q-Matrix misspecifications. The relative fit indices under investigation were Akaike information criterion (AIC), Bayesian information criterion (BIC), and sample size adjusted Bayesian information criterion (ssaBIC). The results suggested that the CRUM can be a robust model given the consideration to the observation number and item/attribute combinations. The findings of this dissertation fill some of the existing gaps in the methodological issues regarding cognitive models' applicability and generalizability. It helps practitioners design tests in CDM framework in order to attain reliable and valid results. / Ph. D.