Hello, I am new to IRT models. I am trying to run an irt 1pl or 2pl for a test administered to students. My data consists of 20 questions and the data is coded as 0/1 for all students.

Specifically: in my case, questions were asked in increasing order of complexity and learning level scores were assigned to each student based on their performance. For example, in Maths, first four questions (Level 1) were based on numbers, next four (Level 2) on addition, next four (Level 3) on subtraction, next four (Level 4) on multiplication and last four (Level 5) on division. Each level consisted of 4 questions and thus we have 20 Qs in total. To pass one level, a student has to answer all 4 questions. If the student answers 3 questions correctly, they remain at the same level. If 2 questions are answered correctly, then they will be below that level. All students are asked questions starting from level 1 (the easiest level) followed by questions from the next level and so on.

Since the questions are in increasing order of difficulty, for a student to score correctly in question 'x', she has to necessarily have correct answers in all previous questions. I am wondering if IRT can be applied in a case like this where the questions are not mutually exclusive and ordered. Most students have answered the question correctly for Q1, and almost all students have answered Q20 incorrectly.

However, whenever I try to run the models, both the 1pl or 2pl give the message not concave and do not converge. I believe it is an identification issue but I am unable to find a solution to this.