Chen Wei raised some interesting questions. And I have some too:
(1) Is there sufficient information to estimate the parameters given that both of theta and misconceptions are measured? I suppose for the high ability examinees who have few incorrect answers and the low ability examinees who have few correct answers, the estimation is unlikely to be accurate.
(2) What's the rationale to believe that the theta is continuous and the misceptions are dichotomoused latent trait? How about fitting the real data with a MIRT that treating both of theta and misceptions as continuous latent trait?
(3) I don't real understand the statement about the correlation between theta and misconception patterns: "Theoretically, we expected that students vary in ability even when they possess the same misconception pattern, meaning a significant correlation between ability and misconception pattern was not expected or modeled." Did the author mean that it is not theoretically correct to assume there is correlation between ability and misconception?