The Q-matrix played a key role in implementations of diagnostic classification models (DCMs) or cognitive diagnostic models (CDMs) -- a family of psychometric models that are gaining attention in providing diagnostic information on students' mastery of cognitive attributes or skills. Using two Monte Carlo simulation studies, this dissertation investigates the impact of Q-matrix designs on the performance of the Transitional DCM or TDCM. Various attribute hierarchical structures to construct Q-matrices, including linear, convergent, divergent, and unstructured configurations are explored, in combination with different item-loading strategies (independent, adjacent, and reachability). By combining these attribute structures and item-loading approaches, eight unique Q-matrix designs are constructed: Linear-Independent, Linear-Adjacent, Linear-Reachability, Divergent-Adjacent, Divergent-Reachability, Convergent-Adjacent, Convergent-Reachability, and Unstructured Adjacent. The Q-matrix designs examined in the dissertation align with the notion of learning progression, as conceptualized through Vygotsky's Zone of Proximal Development framework, which encompasses the zone of actual development, zone of proximal development, accumulation of knowledge, and cognitive dissonance. This theoretical lens guides the modeling of transformative learning trajectories across developmental stages. Employing the TDCM, Study 1 examines how these diverse Q-matrix design approaches influence the accuracy of item parameter and attribute profile estimations under varying design factors, including sample size, growth rate, and Q-matrix design. Building upon Study 1, Study 2 extends the investigation by incorporating Q-matrix misspecification into the design, assessing the TDCM's performance and the robustness of the methods in the presence of misspecified Q-matrices. Study 1 results showed that the Q-matrix design significantly impacted item parameter and attribute profile estimation accuracy. For item parameters, the Linear-Independent design outperformed others; larger samples (N [greater than or equal to] 1000) yielded smaller bias, and the Linear-Adjacent, Convergent-Adjacent, Divergent-Adjacent, and Unstructured-Adjacent Q-matrix designs performed similarly except for inconsistencies with LA and CA at N = 500. Increasing sample size reduced estimation errors as measured by root mean squared errors (RMSEs) for LI but yielded larger RMSEs across conditions with (N [greater than or equal to] 1000). Regarding attribute profiles, the LI design demonstrated the highest classification accuracy, though accuracy declined over time across all designs. Results of study 2 revealed similar patterns of the TDCM performance in the presence of Q-matrix misspecifications, except that bias values increased with larger sample sizes and higher misspecification rates consistently but were more pronounced when the misspecification rate reached 20%. RMSEs revealed larger errors for most item parameter recovery, with fluctuations influenced by varying sample sizes and misspecification rates within different Q-matrix designs. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]