In cognitive diagnosis assessment (CDA), the impact of misspecified item-attribute relations (or “Q-matrix”) designed by subject-matter experts has been a great challenge to real-world applications. This study examined parameter estimation of the CDA with the expert-designed Q-matrix and two refined Q-matrices for international large-scale data. Specifically, the G-DINA model was used to analyze TIMSS data for Grade 8 for five selected countries separately; and the need of a refined Q-matrix specific to the country was investigated. The results suggested that the two refined Q-matrices fitted the data better than the expert-designed Q-matrix, and the stepwise validation method performed better than the nonparametric classification method, resulting in a substantively different classification of students in attribute mastery patterns and different item parameter estimates. The results confirmed that the use of country-specific Q-matrices based on the G-DINA model led to a better fit compared to a universal expert-designed Q-matrix.