27. Which of the following problems were identified with the Burnham et al. survey of Iraq mortality? (Indicate all that apply.)
(a) The survey used cluster sampling, which is inappropriate for estimating individual out- comes such as death.
(b) In their report, Burnham et al. did not identify their primary sampling units.
(c) The second-stage sampling was not a probability sample.
(d) Survey materials supplied by the authors are incomplete and inconsistent with published descriptions of the survey.
Solution to question 26
26. You have just graded an an exam with 28 questions and 15 students. You fit a logistic item- response model estimating ability, difficulty, and discrimination parameters. Which of the following statements are basically true? (Indicate all that apply.)
(a) If a question is answered correctly by students with very low and very high ability, but is missed by students in the middle, it will have a high value for its discrimination parameter.
(b) It is not possible to fit an item-response model when you have more questions than students. In order to fit the model, you either need to reduce the number of questions (for example, by discarding some questions or by putting together some questions into a combined score) or increase the number of students in the dataset.
(c) To keep the model identified, you can set one of the difficulty parameters or one of the ability parameters to zero and set one of the discrimination parameters to 1.
(d) If two students answer the same number of questions correctly, they will have the same estimated ability parameter.
(e) Under the model, if a student’s ability parameter has the same value as a particular question’s difficulty parameter, there is a 50% chance the student will get the question right.
Solution: (c) and (e).