Large-scale assessments of student achievement in physics are often approached with an intention to discriminate students based on the attained level of their physics competencies. Therefore, for purposes of test design, it is important that items display an acceptable discriminatory behavior. To that end, it is recommended to avoid extraordinary difficult and very easy items. Knowing the factors that influence physics item difficulty makes it possible to model item difficulty even before a pilot study is conducted. Thus, by identifying predictors of physics item difficulty, we can improve the test-design process. Furthermore, we get additional qualitative feedback regarding the basic aspects of student cognitive achievement in physics that are directly responsible for their  quantitative test results. In this study, we conducted a secondary analysis of data from two large-scale assessments of student physics achievement at the end of compulsory education in Bosnia and Herzegovina. Foremost, we explored the concept of "physics competence" and performed a content analysis of 123 physics items included within the assessments. Items were described by variables which reflect basic cognitive aspects of physics competence. For each assessment, Rasch item difficulties were calculated in separate analyses. In order to make the item difficulties from different assessments comparable, a virtual test equating procedure was implemented. Finally, a regression model of physics item difficulty was created. 61.2% of item difficulty variance was explained by factors which reflect the automaticity, complexity, and modality of the knowledge structure that is relevant for generating the most probable correct solution, as well as by the divergence of required thinking and interference effects between intuitive and formal physics knowledge structures. Identified predictors point out the fundamental cognitive dimensions of student physics achievement in the study's subjects.