Abstract
For some measuring instruments, item responses may reflect a degree of correctness (or a degree of appropriateness in the case of survey questionnaires) in the answer to a question, rather than being simply classified as correct/incorrect.
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This probability is not 0.5, but less than 0.5, because the probability of being in categories other than k − 1 and k is not zero.
References
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Further Reading
Ostini R, Nering ML (2006) Polytomous item response theory models. Sage Publications
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Appendices
Discussion Points
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1.
For a partial credit item, there is a requirement that score categories are “ordered”. Discuss the meaning of “ordered” in this requirement. (You can consider the meaning of “ordered” in relation to ability, difficulty, expected score, probability of success, etc.)
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2.
A serious misconception about the treatment of dis-ordered thresholds is that when two categories have reversed \( \delta \), one must reverse-score the categories (e.g., code category 2 as 1, and category 1 as 2). Discuss why this should NOT be done. Under what situations should the scoring be reversed?
Exercises
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Q1.
Plot the ICC of a 3-category PCM item in a spreadsheet with \( \delta_{1} \) and \( \delta_{2} \) as parameters. For example,
Change the values of \( \delta_{1} \) and \( \delta_{2} \) and see how the ICCs change. In particular, try ordered \( \delta_{1} \) and \( \delta_{2} \), and dis-ordered \( \delta_{1} \) and \( \delta_{2} \).
An extension of this exercise is to add simulated item responses for each student, and plot the observed item characteristic curves as well.
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Q2.
Indicate whether you agree or disagree with each of the following statements
A response category has very few students. So the response category should be collapsed with an adjacent category | Agree/disagree |
Collapsing score categories of an item should have no impact on the fit of the item | Agree/disagree |
Item A has a maximum score of 4. Item B has a maximum score of 2. Item A must be more difficult than Item B | Agree/disagree |
When dis-ordered thresholds are observed, this indicates that the item does not fit the PCM | Agree/disagree |
When dis-ordered thresholds are observed, this indicates that high ability students have a lower expected score than low ability students | Agree/disagree |
When dis-ordered thresholds are observed, we should reverse score the response categories | Agree/disagree |
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Wu, M., Tam, H.P., Jen, TH. (2016). Partial Credit Model. In: Educational Measurement for Applied Researchers. Springer, Singapore. https://doi.org/10.1007/978-981-10-3302-5_9
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