Friday, December 10, 2010
Winsteps Person & Item Bubble Chart
Ministep prints out a bubble chart relating how well the estimated measures for persons (blue) and items (red) fit the Rasch model.
A comparison of the two methods for expressing item discrimination (Rasch fitness and PUP item discrimination) reveals an interesting similarity: The two distributions are related. Four of the more difficult items (4, 10, 19, and 21) on the bubble chart show an almost perfect match, on the scatter chart, between fitness and item discrimination.
The Rasch overfit item 4 falls in the PUP distribution at high discrimination (upper left). The Rasch underfit item 21 falls in the PUP distribution at low discrimination (lower right). Fitness and item discrimination are negatively related. The standard fit statistic, outfit, from Tables 17.1, Person in Measure Order (blue), and 13.1, Item in Measure Order (red) are used in these two charts.
The Rasch model requires uniform discrimination (which is why the model can ignore discrimination after discarding overfit and underfit persons and items, that is, performances that show too high and too low discrimination). Values below -2 are excessive overfit and above +2 are excessive underfit. The person and item performances on this test fit the Rasch model requirements with the exception of item 21. More high scoring students marked it wrong than low scoring students.
The Rasch bubble chart presents results in terms of estimated measures of student ability and item difficulty. The two students (blue) with scores of 100% (high ability) fall at the top of the chart. The three items (red) marked correctly by all students fall at the bottom of the chart (low difficulty).
The three low scoring students (blue 16, 18, and 21) are expected to have less ability (lower on the bubble chart) than needed to answer the two items (red 10 and 19), with an estimated difficulty measure higher (higher on the bubble chart) than their estimated student ability measures.
The bubble chart clearly shows these relationships between students and items. Item fitness on the bubble chart and item discrimination on PUP Table 3a perform similar functions.