The aim of this research is to study the merits and complementarity of Construct Mapping and Categorical Principal Components Analysis as two approaches that explore the dimensionality of multiple-choice items in achievement tests. Data from the two forms of the Romanian National Assessment Tests on Science were used to explore the dimensionality of items and to identify potentially problematic items that affect the equivalence of the two parallel forms. The findings confirm that the two tests have at best partial equivalence, but while the two methods both agree on test unidimensionality, they flag in part different items as potentially problematic. The results enable researchers and practitioners to make coherent data-driven decision regarding the use of unidimensional vs multidimensional IRT models.