A questionnaire was recently developed for the use with the Spanish-speaking, and evidence have been provided about the construct internal validity by means of structural equation modelling. In this paper, two research questions were considered: (i) What new evidence does application of the Rasch model provide regarding the validity of this construct?; (ii) What cutoffs should be applied to the constructed scales in order to differentiate between acceptable and insufficient levels of the construct being measured? Participants were 1,272 Spanish at both high-school and college level. The instrument is a pencil and paper questionnaire written in Spanish, comprising 20 items (5-point Likert-type scale) distributed evenly across four scales: beyond exact replicas, purpose of models, multiple models, and changing models. Students' responses were coded on an ordinal scale from zero to four. We then conducted a Rasch analysis using both a multidimensional approach and a consecutive unidimensional approach for each dimension. Data provided new evidence regarding the internal validity of the four scales of the questionnaire. The Rasch analysis also allowed us to establish cutoffs for the constructed scales. The evidence provided by this, and the previous study suggest that the questionnaire may be useful as a diagnostic tool when applied to groups or populations of students. In addition, the identified cutoffs could, hypothetically, serve to differentiate between students with an adequate versus an insufficient understanding of the nature of models. [Note: The page range (344-359) shown on the PDF is incorrect. The correct page range for this article is 344-361.]