You have decided to do a Rasch analysis of the Roland Morris Disability Index (RMDQ-23). The RMDQ measures functional deficits in low back pain patients with or without sciatica (pain in the leg). It has 23 items, each item has yes/no response options, and the scale range is 0-100 (high score equals high disability). The RMDQ-23 can be found in Appendix 1 at the end of the page.
full at the end of this document.
Your sample consists of 230 patients with low back pain. Approx. half have been seen by medical doctors, physiotherapists or chiropractors (primary sector patients) and the other half have consulted specialist spinal unit.
Question 1 - The gold standard
You test the Rasch model fit (1 PL model) and find the following: χ2 = 0.0000 (DF 69)
1.1 Explain what the χ2 probability means?
Keywords: invariance, hierarchical, significant test
1.2 Explain what a Guttman scale is?
Keywords: hierarchical ordering, misclassification
Question 2 – item fit
You also look at the individual item fit (Table 1) to see if any items are not fitting the Rasch model.
Table 1. Individual item fit
| Item | Location | SE | FitResid | DF | ChiSq | DF | Prob |
|---|---|---|---|---|---|---|---|
| 1 | 1,929 | 0,18 | -0,865 | 210,18 | 2,331 | 3 | 0,506543 |
| 2 | -2,334 | 0,227 | 0,624 | 218,74 | 3,892 | 3 | 0,273388 |
| 3 | -0,847 | 0,167 | -2,49 | 217,79 | 21,902 | 3 | 0,000069 |
| 4 | 0,101 | 0,157 | 0,668 | 210,18 | 1,135 | 3 | 0,768548 |
| 5 | 0,288 | 0,154 | -3,074 | 216,84 | 11,165 | 3 | 0,010865 |
| 6 | -0,173 | 0,158 | -1,852 | 213,99 | 7,254 | 3 | 0,064239 |
| 7 | -0,93 | 0,169 | -2,112 | 215,89 | 5,436 | 3 | 0,142496 |
| 8 | 1,163 | 0,16 | 0,593 | 214,94 | 2,138 | 3 | 0,544282 |
| 9 | -0,364 | 0,16 | -0,458 | 213,04 | 1,51 | 3 | 0,68 |
| 10 | -0,44 | 0,161 | -1,76 | 214,94 | 3,889 | 3 | 0,273741 |
| 11 | -0,956 | 0,169 | -0,084 | 215,89 | 1,007 | 3 | 0,799527 |
| 12 | -0,487 | 0,16 | -1,659 | 218,74 | 7,184 | 3 | 0,066248 |
| 13 | -0,17 | 0,159 | -0,865 | 210,18 | 3,637 | 3 | 0,303395 |
| 14 | 0,399 | 0,156 | -0,572 | 213,04 | 3,922 | 3 | 0,270056 |
| 15 | -0,071 | 0,158 | -0,273 | 212,09 | 1,645 | 3 | 0,649332 |
| 16 | -1,975 | 0,209 | -1,229 | 213,04 | 6,361 | 3 | 0,095318 |
| 17 | 0,231 | 0,157 | 3,162 | 209,23 | 21,339 | 3 | 0,000091 |
| 18 | -0,625 | 0,164 | -3,921 | 212,09 | 26,458 | 3 | 0,000008 |
| 19 | 3,813 | 0,31 | 0,472 | 209,23 | 2,689 | 3 | 0,442093 |
| 20 | 0,779 | 0,162 | -0,849 | 201,62 | 2,569 | 3 | 0,462998 |
| 21 | 0,231 | 0,156 | 4,282 | 211,14 | 24,54 | 3 | 0,00002 |
| 22 | -0,872 | 0,169 | -2,041 | 212,09 | 6,545 | 3 | 0,087919 |
| 23 | 1,312 | 0,163 | 3,951 | 212,09 | 51,127 | 3 | 0 |
2.1 What can you learn about the items in the RMDQ-23?
Look at the χ2 probability test results and the fit residuals (<-2.5). What do you see?
Question 3 – item difficulty
Next you turn to item difficulty. To do that you have produced a threshold map which is shown in Figure 1 (the specific item location can be found in the table on the right).
Figure 1. Threshold map
| Item | Location |
|---|---|
| 1 | 1,928736 |
| 2 | -2,33421 |
| 3 | -0,84736 |
| 4 | 0,101178 |
| 5 | 0,287807 |
| 6 | -0,17272 |
| 7 | -0,93037 |
| 8 | 1,16251 |
| 9 | -0,36365 |
| 10 | -0,44025 |
| 11 | -0,95604 |
| 12 | -0,48699 |
| 13 | -0,16972 |
| 14 | 0,399037 |
| 15 | -0,07076 |
| 16 | -1,97513 |
| 17 | 0,230672 |
| 18 | -0,62511 |
| 19 | 3,812741 |
| 20 | 0,778695 |
| 21 | 0,230737 |
| 22 | -0,87177 |
| 23 | 1,312 |
3.2 Considering the population we are looking at, does this make sense?
Question 4 – local dependence
As part of analyzing the RMDQ-23, you turn to local dependence. You have produced a person – item residual correlation matrix in Table 2 and need to consider the results.
Table 2. Person – item residual correlations
Pink = Mean residual correlation + 0.2; Yellow = Mean residual correlation + 0.3
4.1 Please explain what local dependence is?
4.2 Please describe the 3 most important item pairs showing local dependence. What do you want to do about it?
Find the three item pairs with highest mean residual correlation above + 0.3
Question 5 – Differential Item Functioning
When looking at DIF, you want to know if DIF is present in the RMDQ-23 in terms of where the patients are seen. You find the following for items 12 and 13:
Figure 2. ICC of item 12 (turning over in bed) stratified according to sector
Figure 3. ICC of item 13 (trouble putting on socks) stratified according to sector
5.1 Please explain what you see in Figure 2 and 3?
What types of DIF do you see?
Question 6 – targeting
Lastly, you decide to look at the person-item distribution. This is what you find:
Figure 4. Person-item threshold distribution
6.1 Please put the following labels on the x-axis: Easy items, difficult items, more able persons, less able persons.
Where are the ‘more and less able persons’ and the ‘easy and difficult items’?
6.2 Please explain what you see in Figure 4?
Keywords: Targeting of item thresholds and persons
